The Value of Nature to Our Health and Economic Well-Being: A Framework with Application to Elephants and Whales

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The Value of Nature to Our Health
and Economic Well-Being: A Framework
with Application to Elephants
and Whales
Ralph Chami, Thomas Cosimano, Connel Fullenkamp, Fabio Berzaghi,
Sonia Español-Jiménez, Milton Marcondes, and Jose Palazzo
1 Introduction
As the intense but relatively brief economic disruptions caused by the SARS-
CoV-2 pandemic subside, Europe must resume its focus on longer-term economic
challenges. Foremost among these is the need to avert climate disaster by limiting
global temperature rise to less than 2 ◦C. In order to reach this goal, the European
Union (EU) has committed itself to net-zero greenhouse gas emissions by the
year 2050. Yet the long-term carbon strategy communicated by the EU (European
Commission, 2018) projected that only 60% of this goal could be reached based on
full implementation of EU climate-related legislation. Additional methods to further
R. Chami ()
International Monetary Fund, Washington, DC, USA
T. Co simano
Blue Green Future, Falls Church, VA, USA
C. Fullenkamp
Duke University, Durham, NC, USA
e-mail: cfullenk@duke.edu
F. Berzaghi
Laboratory for Sciences of Climate and Environment (LSCE) - UMR, CEA/CNRS/UVSQ,
Gif-sur-Yvette, France
e-mail: fabe@unitus.it
S. Español-Jiménez
Fundación Centro MERI, Castro, Chile
e-mail: sespanol@fundacionmeri.cl
M. Marcondes · J. Palazzo
Baleia Jubarte, Caravelas, Brazil
e-mail: milton.marcondes@baleiajubarte.org.br;jose.truda@baleiajubarte.org.br
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022
L. Paganetto (ed.), Economic Challenges for Europe After the Pandemic,
Springer Proceedings in Business and Economics,
https://doi.org/10.1007/978-3-031-10302-5_7
117

118 R. Chami et al.
limit greenhouse gas emissions or increase carbon capture have been proposed, but
nearly all of these rely on technology—either scaling up existing technologies or
developing new technologies.
A promising means of supplementing these efforts can be found in so-called
Nature-based Solutions (NbS). Scientific research increasingly reveals that ecosys-
tems and individual species contribute significantly to carbon capture. And to the
extent that these same ecosystems and species have been greatly reduced in extent
and number, an opportunity exists to augment carbon capture through concerted
efforts to conserve and restore them. Although most people are aware of the role
that trees can play in carbon capture, other habitats and species have the potential
to capture similar quantities, and in some cases, much more. Many of these natural
resources, moreover, such as salt marshes and kelp forests, are present in Europe.
Because NbS rely on conservation and restoration of nature, the case must be
made to commit scarce resources to this approach. The fundamental question is
whether the gains from enhanced carbon capture would be worth the significant
investments of financial and human capital required to restore the carbon-capturing
habitats and species to their former abundance. This, in turn,is essentially a question
of valuation. But it has proven extremely difficult to value ecosystems and their
services in ways that can convince policymakers and taxpayers that benefits exceed
costs. A reliable way to value natural assets must be found well before the climate
target is breached—and well before the dwindling natural resources are lost forever.
Thus, solving the valuationproblem is key to unlocking a potential source of carbon
capture that could help Europe—and many other regions as well—attain their net-
zero greenhouse gas or carbon-neutrality targets.
In most economic and financial contexts, the tools of valuation are used to make
resource allocation or capital budgeting decisions. In these situations, the prior
decision of whether to expend resources in order to reach an objective has already
been made in favor of doing so, so that the purpose of valuation is to determine
how best to deploy resources to attain the objective. For example, an individual’s
portfolio allocation problem, solved by applying models such as the Capital Asset
Pricing Model or Arbitrage Pricing Theory, presumes that a household has already
decided to smooth consumption over time or save toward goals such as starting a
business.
In environmental economics, however, the tools of valuation are used not only
to answer the allocation question, but also to motivate agents to answer the prior
question—whether to expend any resources at all in pursuit of environmental
objectives—affirmatively. As an example, The Economics of Ecosystems and
Biodiversity (TEEB) initiative describes its goals in this way on its website (http://
www.teebweb.org/about/the-initiative/):
The Economics of Ecosystems and Biodiversity (TEEB) is a global initiative focused
on “making nature’s values visible”. Its principal objective is to mainstream the values of
biodiversity and ecosystem services into decision-making at all levels. It aims to achieve this
goal by following a structured approach to valuation that helps decision-makers recognize
the wide range of benefits provided by ecosystems and biodiversity, demonstrate their

The Value of Nature to Our Health and Economic Well-Being: A Framework... 119
values in economic terms and, where appropriate, suggest how to capture those values in
decision-making.
The National Research Council (2005, p. 2) describes the role of valuation in this
way:
Despite growing recognition of the importance of ecosystem functions and services, they
are often taken for granted and overlooked in environmental decision-making. Thus, choices
between the conservation and restoration of some ecosystems and the continuation and
expansion of human activities in others have to be made with an enhanced recognition of
this potential for conflict and of the value of ecosystem services.
These examples show that environmental economists explicitly employ valuation
tools in an attempt to persuade individuals, businesses, and governments to expend
resources on environmentalprotection and restoration. These attempts are necessary
in order to overcome the significant disincentives to taking action associated with
externalities and collective-action problems.
Because of these additional demands being placed on valuation tools by the
environmental economics profession, it is sensible and necessary to reflect on
whether the valuation tools and strategies currently being employed are effective
at motivating people to commit their scarce resources to pursuing environmental
protection and restoration. Unfortunately, it would be both very difficult and highly
controversial to evaluate the impact of environmental valuation efforts on the
amounts of resources (both financial and physical) expended in the pursuit of
environmental protection and restoration. Nonetheless, it is probably fair to say
that there is room for improvement. For example, since 1997 TEEB has produced
estimates of the total value of ecosystem services provided by all of the planet’s
biomes. These estimates, which consistently produce a value larger than global
GDP, do not appear to have catalyzed a wave of new investments in environmental
protection and restoration.
It is still possible to evaluate the effectiveness of valuation methods and strategies
in motivating environmental investments, however, by considering their charac-
teristics rather than attempting to measure their impacts. One key characteristic
is the ability of the information produced by the method to motivate or inspire
people to take action. Several types of agents exist who use the information from
environmental economics to make different types of decisions: individuals, business
leaders, and policymakers. In order for a valuation method to be effective, each type
of agent must find that the information produced by the method motivates them to
take action. Although making judgments about the motivational power of a valuation
method may at appear subjective, there is an extensive literature from economics,
psychology, and marketing that we can draw from regarding attributes that make
information persuasive or effective in provoking action.
This literature suggests that the motivational power of information comes from its
ability to stimulate excitement or concern in the recipient. Information interacts with
human emotions and cognitive biases to exert powerful influence over behavior and
decision making. For example, Hesketh (2015) argues that information is persuasive
when it enables people to satisfy important psychosocial needs, like the need to

120 R. Chami et al.
be loved. Crimmins (2016) discusses how information that works with people’s
cognitive biases, such as the many heuristics that humans use to make decisions,
is more successful at motivating people to act than information that works against
these biases.
In many contexts, the motivational power of information is the sole measure
of its effectiveness. But people whose decisions are publicly scrutinized, such as
policymakers and business leaders, place additional demands on the information
they use, in order to withstand this scrutiny. These include many qualities such
as accuracy, reliability, and replicability, but we summarize them in a criterion
we call credibility. Credibility of information reflects the difficulty of doubting or
disproving its truth or accuracy: the more difficult it is to doubt or disprove a piece of
information, the more credible it is. This is important to policymakers and business
leaders because they need to defend their decisions in the face of public scrutiny. If
a decision is based on credible information—ideally, the best information available
at the time—it is difficult to attack or fault.
In addition to being credible, and able to stimulate excitement or concern,
valuation information must also be relatable. Relatability describes the extent to
which information is expressed in terms that humans find relevant and useful. For
example, from the point of view of businesses, relatable valuation information is
helpful in identifying and evaluating feasible business opportunities. People find
information on costs and benefits expressed in monetary terms to be useful for
making decisions. On the other hand, they generally find imprecise, complex or
abstract information difficult to relate to their objectives and hence a much weaker
motivation for making decisions or taking action.
As an example of environmental information that performs well with respect
to all three criteria, consider a television advertisement for the World Wildlife
Fund (WWF) that was widely broadcast in early 2020, which had the purpose
of encouraging donations to fund efforts to protect polar bears. It featured video
sequences of mother polar bears and their offspring, while the voiceover in the
advertisement discussed how climate change was causing the ice floes that polar
bears depend on to vanish. The advertisement mentioned scientific studies, which
viewers would find credible, but expressed the implications of the studies in simple,
concrete, relatable terms that people could understand: the disappearance of ice
floes and the polar bears that need them for survival. The advertisement also took
advantage of the emotional impact created by the video images, and the brain’s
tendency to jump to conclusions,to create the impression of polar bears desperately
searching for ice floes, stimulating the viewer’s concern.
Although we are not suggesting that the WWF advertisement should be a tem-
plate for environmentalvaluation, it nevertheless offers some lessons for improving
the ability of environmental valuation to motivate the recipients and users of these
valuations to take action. In particular, we argue that the criteria discussed above and
the example of the WWF advertisement suggest that the following valuation strategy
would be more successful at inspiring action than current valuation approaches:
•Use only market-based methods of valuation.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 121
•Value individual resources rather than groups of disparate resources or ecosys-
tems.
Valuations based on these two broad guidelines will perform well according to the
criteria discussed above. Market-based methods of valuation will tend to have high
levels of credibility, as long as the markets from which prices are obtained are
relatively free of distortions, because of the confidence that free-market prices are
fully reflective of all social costs and benefits and thus reveal the “truth” regarding
how society values a good or service. They will also have high levels of relatability
because they express values in monetary terms, and because they will naturally
identify the markets that are relevant to a particular natural resource.
Estimating the value of individual resources will also support the credibility
of the valuations, since the linkages from the resource to its value should be
transparent. This approach is also highly relatable, since an individual resource
and the market-valued services it provides are both concrete and specific. Valuing
individual resources also has high potential to work with human emotions and
cognitive biases in order to create concern or excitement. Although the term
“charismatic megafauna” sometimes carries negative connotations because these
species tend to draw attention away from other natural resources, it nonetheless
acknowledges that individual resources can take advantage of humans’ affinity and
availability heuristics in order to arouse excitement and concern. And the surprise
that an unexpectedly high valuation of an individual resource engenders can also
strongly stimulate excitement or concern.
There is a cost to this approach to environmental valuation, which is the fact
that it omits any non-market and non-use values and therefore does not capture the
total economic value (TEV) of a natural resource. Our approach thus necessarily
represents a conservative approach to valuation, which places lower bounds on the
values of individual natural resources. We argue that this is a contribution of our
method rather than a drawback. By including only those services to which market
prices can be readily assigned, we remove as much subjectivity as possible from
the estimated values. Valuation will always be as much art as science, in which
human judgement plays a key role in identifying the determinants of value as
well as in selecting and applying valuation models. But our approach removes
unsupported claims and cheap talk from the critical step of assigning monetary
values to the service flows or to the resource itself. Therefore, we argue that the
estimates produced by our method are reliable and convincing starting points for
public discussion regarding whether—and how much—to invest in environmental
protection.1
Because our estimated values are lower bounds, they still allow for additional
discussion about how the non-market-valued attributes of a particular natural
resource should factor into the investment decision. We believe such discussions
should always take place when making decisions about environmental protection
1See Lew (2015) for a discussion of criticisms of standard estimation methods.

122 R. Chami et al.
investments. But if agreement cannot be reached about these difficult to measure
sources of value, then the baseline monetary value provided by our estimates can
still form a basis for constructive action, effectively preventing the perfect from
becoming the enemy of the good.
In this paper, we outline a valuation procedure that follows the guidelines
introduced above. Then we implement this valuation strategy on two resources—
elephants and whales—to demonstrate its feasibility and its ability to produce
valuations that people find more persuasive or motivational than existing methods
and strategies. Part of the reason these resources were chosen is that new research
has identified additional services, of significant market value, that are provided by
these animals. Integrating these additional service flows into the values of whales
and elephants is a further contribution of this paper.
The remainder of the paper is organized as follows. Section 2develops the
valuation model and the discusses its parameter requirements. Sections 3and 4
apply the valuation procedure to African forest elephants and cetaceans (the nine
great whales), respectively. Section 5concludes.
2 A Valuation Framework for Natural Resources
Valuation of natural resources is an important area of research in the environmental
economics literature. Although some benefits that flow from individual natural
resources are traded and priced on markets, many if not most are not, and moreover,
many natural resources produce only non-market-traded benefits. Thus, one focus
of valuation research has been to use economic fundamentals such as preferences
to estimate values for natural resources that cannot be fully valued by markets. One
of the primary valuation benchmarks in this literature is willingness to pay (WTP),
which is the amount that an individual would pay to enjoy a natural resource or
contribute toward an effort to preserve it.
WTP is generally estimated using one of two methods.2Revealed preference
methods utilize data on purchases to estimate hedonic pricing models, or data on
other related expenditures, such as travel costs incurred, to estimate WTP. These
methods are suitable for estimating the amount that people would pay to enjoy a
natural resource. The opportunities to apply revealed preference models to natural
resource valuation, however, have proven to be limited. Most natural resources
are not purchased (or consumed) by their users, and other revealed preference
approaches such as travel cost models are limited in the types of service flows (such
as recreational flows) they can value.
The vast majority of studies that estimate WTP, therefore, use stated preference
methods. As the name suggests, stated preference methods employ different types
2See Freeman (2004) for an extensive discussion of the methods used to estimate WTP. Lew (2015)
also gives an extensive review of these methods and their applications to marine resources.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 123
of surveys in which respondents state their willingness to pay taxes or fees that
will be used to invest in specific natural resource preservation or enhancement
programs. Stated preference methods are used to estimate public willingness to pay
for individual conservation programs and for ranking competing programs. And for
programs that aim to increase the population of a living resource, stated preference
estimates could be interpreted as the value of an increase in the population.But they
generally do not attempt to estimate the total values of specific natural resources.
Stated preference estimates of WTP tend to have lower credibility than market-
based valuations, because the respondents to surveys are not generally required to
pay the fees or taxes they claim they would pay. And it should not be forgotten
that the valuations obtained are technically those of the programs proposed in the
experiments rather than the resources to be protected by the programs.
In some cases, market valuation of individual resources may be possible as a
consequence of quota or cap-and-trade systems designed to limit harvesting. For
example, Costello et al. (2012) propose that the International Whaling Commis-
sion’s whaling quotas be replaced by tradable harvesting rights. To the extent
that such a market would be open to any willing purchaser, the resulting price
would establish market values for whales that are more reflective of all of society’s
preferences. Such arrangements, however, presume that the case for preserving
the resources has already been argued successfully, as reflected in the decision to
implement a system of harvest limits. This method also begs the question of how
to set the initial quotas and caps, which would presumably depend on the value
assigned to the resource. And as in the case of revealed preference methods, only a
very small subset of natural resources are harvested whole and could be valued in
this way.
Most approaches to market valuation focus on the services produced by natural
resources. These borrow the idea from financial economics that the value of a
physical capital good is derived from the stream(s) of services that the good
produces. Physical capital goods are created for the purpose of producing streams
of services that have an explicit market value. Many natural resources also produce
streams of services that are valuable to society, although this is not their primary
goal or purpose. TEEB (2010) provides an overview of the types of services and the
market-based methods of valuing them. While some services are priced in markets,
such as ecotourism, other services provided by natural resources are regulatory
services (such as predator or flood control) that are not directly priced in markets.
Market values can be assigned to these services, however, by estimating what it
would cost to replace them. Natural resources may also provide services that are
inputs into the production of other goods and services to which market values can
be assigned. Market values may be assigned to these factor-of-production services
if the contribution of the natural resource to production can be estimated.
The valuation approach most similar to ours is embodied in the TEEB initiative as
well as the Natural Capital Accounting method being developed by the U.K. Office
of National Statistics (ONS) and Department for Environment, Food and Rural
Affairs (Defra) (Philips, 2017). As in our approach, Natural Capital Accounting
seeks to recognize and quantify the goods and service flows arising from natural

124 R. Chami et al.
resources, so that a monetary value may be placed on them. For example, Natural
Capital Accounting recognizes regulatory services such as greenhouse gas seques-
tration and market-valued services such as ecotourism, both which are also essential
to our valuation analysis.
The aims of Natural Capital Accounting, however, are not well suited to the
valuation of individual natural assets. This approach takes ecosystems as its unit
of analysis, focusing on the valuation of entire biomes or ecosystems rather than
their individual constituents. This method has also emphasized biodiversity, an
ecosystem characteristic which has proven difficult to integrate into the Natural
Capital Accounting framework as well as difficult to quantify and value (CIEEM,
2019). Although there appear to be no theoretical obstacles to valuing individual
natural resources using Natural Capital Accounting, no valuations of individual
resources such as whales or elephants utilizing this framework have been published
to date that we are aware of. To the extent that Natural Capital Accounting remains
focused on valuing ecosystems, this approach does not perform well with respect to
the relatability criterion. Biodiversity is too abstract, and ecosystems can be too large
or too complex, to be helpful to individuals and businesses in making decisions. In
addition, ecosystems do not appear to have a high ability to create excitement or
concern, particularly in comparison to individual components of ecosystems.
Each of the above methods of valuation produces useful information for poli-
cymakers and the general public. But as our discussion indicates, none of them is
well suited for estimating the value of individual natural resources. Therefore, we
propose the following approach to natural resource valuation, which fills the need
for this information. First, an individual natural resource is chosen. Then the services
the resource produces are identified. These include onlythose services flowing from
the natural resource that have been identified and measured in the academic and
professional literature, and to which market values may be assigned.
Next, discounting is used to estimate the total market value of the services. The
market value of an asset at any time is the discounted sum of the value of the
services it is expected (or scheduled) to produce during all subsequent periods.
Discounting the future values is necessary because these services are produced
during many different future periods, and their value must be adjusted by the
appropriate opportunity cost of waiting to receive these services. We initially assume
for simplicity that only one type of service is produced by a physical capital asset. If
we let sbe the quantity of services produced, pbe the market value (price) of these
services, and rbe the appropriate discount rate, then the value Vof the physical
capital asset is given by
Vt=
∞

i=1
pt+ist+i
(1+r)i

The Value of Nature to Our Health and Economic Well-Being: A Framework... 125
This valuation equation is easily modified to accommodate multiple, distinct service
streams because of the additivity of present values. If a physical capital good
produces n distinct service streams with market prices p1,...,p
n, then the value of
the capital good is given by
Vt=V1,t +V2,t +···+Vn,t =
∞

i=1
p1,t+is1,t +i+p2,t +is2,t+i+···+pn,t +isn,t+i
(1+r)i
To summarize, the following procedure is used in this paper and can be used to
estimate the money value of any individual natural resource:
1. Identify the services produced by the resource.
(a) Verifiable estimates of the quantities of services produced must exist in the
academic or professional literature.
(b) If the quantity produced of a service is not measured in money, market prices
must exist that can be sensibly assigned to the service.
2. Project the market values of each service (pj,t+isj,t+i) into the future.
3. Assign a discount rate appropriate to the natural resource and the service(s)
produced.
4. Using the values projected in Step 2, calculate the value of the resource using
the definition of Vt.
The best way to demonstrate the utility of this approach—and to recognize the issues
it raises—is to move directly to extended examples in which we apply the above
procedure to estimate the values of natural resources. In the following sections,
therefore, we apply our framework to value African forest elephants, and to value
great whales found off the coasts of Brazil and Chile.
3 Applying the Framework to the Valuation of Forest
Elephants in Africa
Our first application estimates the value of African forest elephants (Loxodonta
cyclotis, Matschie, 1900), a sub-species of the African elephant (Loxodonta
africana, Blumenbach, 1797). Forest elephants live in the rain forests of central
and western Africa and are genetically and morphologically differentfrom the ones
inhabiting savannas. Further differences between savanna and forest elephants are
their ecosystem engineering role. We focus on forest elephants as their ecosystem
services (described below) have recently been quantified (Berzaghi et al., 2019).

126 R. Chami et al.
3.1 Step 1: Identify the Services Produced by the Resource
Elephants produce several types of services that could be valued using market prices.
First, in some places such as south- and southeast Asia, elephants are employed
commercially as beasts of burden. Forest elephants are generally not used for this
purpose. Elephants also undoubtedly generate ecotourism revenues, since they are
one of the “big five” species that tourists wish to see when they visit African game
preserves and parks. It is difficult to separate ecotourism revenues into those due
specifically to elephants, however. Moreover, the majority of African ecotourism
takes place in the savannahs rather than in the rainforests, where tourism is still
underdeveloped. Because of these difficulties with measurement, we do not include
these services in our elephant valuations.
On the other hand, forest elephants do produce carbon-capture services that can
be valued. Elephants contribute to carbon capture and long-term storage in two
ways. First, as large animals, elephants store nontrivial amounts of carbon on their
bodies. Considering the average body mass of a mature forest elephant is 3000 kg
(Grubb et al., 2000), we estimated that each individual body is composed of 24
percent carbon, or 720 kg (see methods).
Although an individual elephant will eventually die and the carbon carried on
its body will be released back into the ecosystem or the atmosphere in the form of
CO2, a stable population of elephants will continuallystore some amount of carbon.
We can therefore value the carbon currently stored on the bodies of the existing
population of elephants as if it were sequestered, assuming that current populations
are maintained. In addition, any permanent increase in the population (that is,
increase to the equilibrium or steady-state population) implies that an additional
amount of carbon can be added to the total amount sequestered in elephant bodies.
The second way in which African forest elephants sequester carbon is through
their impact on the forest ecosystem. Large herbivores and megaherbivores are
known to have significant impacts on their ecosystems, and by extension on
the biogeochemical cycles taking place in these ecosystems. Recent research by
Berzaghi et al. (2019) has shown that the activity of forest elephants contributes
to the net accumulation of aboveground biomass (carbon) stored in trees. While
moving through the forest and foraging for food, elephants reduce the density of
trees smaller than 30 cm in diameter. This reduction in tree density changes light
and water availability in the forest leading to an increase in the proportion and
the average size of late-succession trees. Compared to other type of trees, late-
succession trees are longer lived, require less light and water to survive, and become
dominant once they reach the canopy. Late-successional trees store more carbon
than other types of trees (given the same volume), so as their average size and
abundance increase, there is a net increase in the amount of carbon stored in the
forest.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 127
3.2 Step 2: Project the Market Value of Services Provided into
the Future
An important question that arises when valuing living organisms is how to model
future populations. The services provided by future offspring can be a significant
source of the current population’s value, which implies that both over- and
undervaluation are possible. In addition, the projected future population embeds
assumptions about conservation and restoration that should be made transparent.
Therefore, a population growth model is needed for each species. How population
growth affects the production of services must also be specified.
In this paper, we project that future populations of both elephants and whales
will grow from their current levels and eventually return to their estimated sizes
before the advent of large-scale poaching and industrial whaling, respectively. We
have two reasons for doing so. First, the current populations of elephants and whales
are far below—on the order of ten percent of—their historical numbers. We argue
that assuming a return to what scientists believe are their equilibrium populations
strikes the right balance between over- and undervaluation. Second, estimates of the
services provided by elephants and whales found in the literature are often based on
the assumption of a return of the species to their previous population sizes.
We construct a model of population growth for elephants that utilizes data on
birth rates, survival rates of calves and adults, ages at first reproduction, and intervals
between births (Turkalo et al., 2017,2018). A logistic function is used to model the
birth rate, which converges to the death rate as the population reachesits steady-state
value equivalent to the estimated pre-poaching population. Free parameters of the
growth model are calibrated so that the initial numbers of births imply a constant
ratio of births to population. Details of the construction of the population growth
models are given in Appendix 1.
3.2.1 Carbon Capture and Sequestration Through Elephant Biomass
In order to value carbon capture, an estimate of the market price of this service
is needed. The most developed markets for carbon capture deal in carbon dioxide
rather than pure carbon, since these markets were created in order to limit carbon
dioxide emissions from industrial production, power generation, and transportation.
Thus, all estimates of carbon capture and sequestration must be converted to their
CO2equivalent by multiplying the amount of carbon by 11/3. Although many
carbon-trading markets exist globally, the most liquid is the European market ETS.
We argue that this market provides the best estimate of the market price of carbon.
We estimate the value of carbon sequestration on elephant bodies by first
calculating the amount of carbon sequestered by current and future elephant

128 R. Chami et al.
populations. Then the carbon is converted to its CO2equivalent and multiplied by
the price of $24.72 per tonne of CO2.3
From above, the amount of carbon on the average elephant’s body is 720 kg,
which is multiplied by the current population of 100,000 individuals to obtain
the starting amount of carbon sequestered. Additional carbon is sequestered each
period equivalent to the change in elephant population implied by the growth model,
multiplied by 720 kg. The amount of carbon on each elephant is equivalent to
720*11/3 =2640 kg or 2.64 tonnes of carbon dioxide.
3.2.2 Carbon Capture and Sequestration Through Stimulating Forest
AGB I ncre ase
Our approach is to first value the carbon capture contributed by the current elephant
population and then add the carbon sequestered by each additional elephant as
the population increases. We assume that the changes made to the forest by
elephant activity are permanent, so that the increase in carbon capture is effectively
permanent.
Berzaghi et al. (2019) estimate that if forest elephant populations were to recover
to their historic population, each forest elephant would stimulate a net increase
in carbon capture in central African rain forests of 26 tonnes of C per hectare.
Given the historic density of 0.5 elephants per km2, this implies an actual increase
in carbon capture of 13 tonnes of C per hectare. This increase in carbon capture
will take place over a long period, however, for two reasons. The change in forest
composition due to elephant activity will take decades to be completed, and the
increase in the elephant population from their current number of approximately
100,000 individuals to their historic level of 1.1 million will require centuries to
occur.
In order to make the carbon sequestration calculations simple and manageable,
we make the following assumptions. First, we assume that the existing elephant
population currently occupies only 200,000 km2of their historic range of 2.2 million
km2at a population density of 0.5 elephants per km2(but see Maisels et al., 2013
as the current population is highly fragmented across central Africa). This enables
us to estimate the current carbon sequestration services of the existing elephant
population by assuming that these individuals have already increased carbon capture
of forests by 13 tonnes per hectare in this area.
For each new cohort born, we assume that the cohort moves to an unoccupied
portion of the forest elephants’ historic range and lives there at a density of 0.5
elephants per km2. The area of the plot occupied is therefore determined by the size
of the cohort and the assumed population density of 0.5 elephants per km2. On each
3The price of CO2per tonne is the average daily value during 2019 on the EU ETS. See https://
markets.businessinsider.com/commodities/historical-prices/co2-european-emission-allowances/
eur/1.1.2006_2.5.2020

The Value of Nature to Our Health and Economic Well-Being: A Framework... 129
newly occupied plot, we assume that the initial amount of carbon captured is 3.25
tonnes, and this increases due to the elephants’ activity at a constant rate over the
next 150 years until the full 13 tonnes per hectare is reached, which is equivalent
to 9533 tonnes of carbon dioxide per km2. Once the carbon capture has increased
by 13 tonnes per hectare, the increment goes to zero so that no further services are
contributed to the valuation by the cohort. The annual increments are multiplied by
the price of carbon dioxide.
This assumed process of new cohorts settling unoccupied portions of the historic
range and increasing carbon capture within these new settlements continues until the
elephant population has grown to its pre-poaching population, at which time they
will fully occupy their historic range.According to the parameters of the population
growth model we developed, this will require about 9 centuries.
3.3 Step 3: Assign a Discount Rate Appropriate to the Natural
Resource and the Service(s) Produced
According to financial economic theory, the discount rate used to value an asset
consists of two components. The first is the risk-free interest rate, which is better
understood as the return required to overcome human impatience and induce a
person to wait for a future payment. The second component is a risk premium,
which compensates the holder of an asset for the systematic or nondiversifiable risk
that the asset incurs. The identifying feature of systematic risk is that it is common
to many assets, making their payoffs fluctuate in concert. Thus, the most common
measure of systematic risk is the covariance of an asset’s payoff with the payoffs of
other risky assets, such as the return to the market portfolio of assets.
Although the payoffs to a naturalresource can be risky,this risk is not necessarily
systematic. If the values of the streams of services provided by the resource do not
exhibit significantcovariance with other assets’ payoffs, then the risk in the resource
is idiosyncratic risk, which does not earn a risk premium. The flows of carbon-
capture services from living adult elephants will remain roughly constant on a per-
elephant basis, no matter how the payoffs from other assets fluctuate. Fluctuations
in the quantities of these service streams come mainly from two sources. The first is
expected population growth, which is likely to be uncorrelated with fluctuations in
the payoffs from other assets. Unexpected fluctuations in services would primarily
come from higher-than-average mortality among elephants. The events that cause
unexpected mortality in elephants include poaching and disease. The occurrence of
such events is likely to be uncorrelated with fluctuations in the payoffs from other
assets.
The value of carbon-capture services produced by elephants can also vary
because of fluctuations in the price of carbon. The most actively traded carbon
market in the world currentlyis the EU’s ETS market for carbon-dioxide emissions.

130 R. Chami et al.
We obtained data on monthly closing prices of carbon emissions credits from this
market and estimated a standard CAPM regression of the form
RCO2,t −Rf,t =α+βRM,t −Rf,t +εt
where RCO2 is the monthly return on carbon emissions credits, Rfis the risk-free
rate proxied by three-month U.S. Treasury bill yields, and RMis the market return
proxied by the monthly return on the S&P 500 equity index. Our estimate for
the 2014–2019 period produced a positive but statistically insignificant coefficient.
This implies that the price of carbon is not significantly correlated with other
asset returns, suggesting that the appropriate discount rate for carbon-sequestration
services is the long-term, risk-free rate.
Given that a long-term, risk-free discount rate is appropriate for valuing the
benefits of elephants, the next question is how to estimate it in the context of
environmental valuation. TEEB (2010) argues that the “impatience” component of
the risk-free rate should be exactly zero, implying a near-zero risk-free rate when
the effect of intertemporal substitution is taken into account. Philips (2017)usesthe
HM Green Book Social Discount rates, which decline from a top rate of 3.5 percent
for periods up to 30 years, to a rate of 2.5 percent for periods up to 100 years but
cautions that these rates tend to “overdiscount”the future, or are in other words too
high. Professional investors commonly use the 10-year government bond yield as
their estimate of the risk-free rate. Using the U.S. 10-year government bond rate
and adjusting for inflation estimated via the GDP deflator, we obtain an average 10-
year yield of approximately 2.65 percent over the 1954–2018 period. We choose two
percent for the risk-free rate, since this reflects market evidence and the practices in
the existing literature, but also lessens the likelihood that we are over discounting.
3.4 Step 4: Using the Values Projected in Step 2, Calculate
the Value of the Resource Using the Definition of Vt
Present values were calculated using a 1000-year horizon. Using a starting pop-
ulation of 100,000 mature elephants, the future population path generated by the
population growth model, and the other valuation parameters described above, we
calculate a present value of carbon sequestration on elephant bodies of $166 per
individual.
The present value of carbon sequestration through an increase in carbon stored in
AGB, however, is quite large.The total present value of this service is the sum of the
contribution of the current elephants and the contribution from future generations of
elephants.
PV of Increased Forest Biomass =$23.5656 Billion +$152.7173 Billion
=$176.2829 Billion.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 131
Dividing this total value by the current population of elephants implies a value of
$1,762,829 per elephantfor this service. If we add the $166 for carbon sequestration
on elephants’ bodies, we obtain a total value of $1,762,995 per elephant.
3.5 Discussion
The result of this valuation demonstrates the potential of our approach to stimulate
excitement, concern, and ultimately action. At over $1.75 million, the value of
a single forest elephant is a striking number that is likely to gather significant
attention, since people will want to know what exactly makes this creature so
valuable. These inquiries will lead to further opportunities to educate the public
about elephants’ contributions to carbon capture and convince individuals to spend
their resources on preservation of this species and its habitat. For example, a public
relations campaign could be built around comparing the value of a live forest
elephant capturing carbon—$1.75 million—to one that has been killed for its ivory,
about $20,000 per tusk. Showing that the loss of a forest elephant implies the loss
of valuable and important carbon sequestration services—which benefit humans—
converts an intangible and remote psychic harm (the brutal and unnecessary death
of a forest elephant) to a more direct and concrete harm to personal wellbeing
(worsening consequences of climate change). We argue that this will significantly
increase people’s willingness to commit resources to elephant preservation and
restoration.
This number should also generate interest among investors. Our valuation
creates a “fundamentals” based estimate of the worth of a specific, tangible asset.
This in turn creates a potential investment opportunity that is similar to the
standard investmentopportunities that financial professionals are familiar with. The
challenge for investors is to devise instruments that would enable them to realize
this potential value in terms of cash. Although this will be difficult, the size of
the prize—over $176 billion total for the existing population of forest elephants—
would undoubtedly attract many entrepreneurs and investment professionals who
could profit either from taking an ownership stake in this investment or earning
commissions from marketing this instrument to other investors.
4 Applying the Framework to the Valuation of Great Whales
Frequenting the Brazilian and Chilean Coasts
This application considers great whales found off the coasts of Brazil and Chile.
The great whales we include in our valuation are the nine large baleen whales (blue,
bowhead, fin, minke, sei, right, humpback, gray and Bryde’s), plus the sperm whale.
Most but not all of these different species spend significant parts of the year off the

132 R. Chami et al.
coast of Brazil, and some are resident year-round. In the case of Chile, we consider
only the blue whale due to data limitations. Whales make an interesting valuation
case study because they produce several distinct services to which market values
can be assigned, including services that recent research has helped to quantify.
As in the case of elephants, we project future populations by assuming that the
populations of whales will eventually grow to reach their historical (pre-industrial-
whaling) numbers. We construct a model of population growth for each whale
species that utilizes data on birth rates, survival rates of calves and adults, ages
at first reproduction, and intervals between births for each species of great whale. A
logistic function is used to model the birth rate, which convergesto the death rate as
the population reaches its steady-state value. Free parameters of the growth model
are calibrated so that the initial numbers of births imply a constant ratio of births to
population. Details of the construction of the populationgrowth models are given in
Appendix 1.
4.1 Step 1: Identify the Services Produced by the Resource
Whales produce at least three services that society values and which have been
measured by scientists and economists: ecotourism (whale watching), carbon
capture, and fisheries enhancement. The carbon capture services can be further
separated into the carbon captured in whale biomass, and the carbon captured by
phytoplankton production that can be attributed to whale activities.
4.2 Step 2: Project the Market Value of Services Provided into
the Future
4.2.1 Ecotourism (Whale Watching)
A benchmark estimate of the market value of whale-watching services can be
obtained from the direct and indirect expenditures on whale watching worldwide.
The International Fund for Animal Welfare estimated that whale watching tours
generated $2.1 billion of expenditures in 2008, including both direct ticket sales
and indirect expenditures generated by whale watching. At the time this estimate
was made, many countries with the potential for whale watching had not developed
this industry. Cisneros-Montemayor et al. (2010) estimate that the global whale-
watching industry could generate up to $2.5 billion per year if fully developed. We
assume that the current income flow from whale-watching is $2 billion.
We also argue that ecotourism revenues vary positively with whale biomass,
so that as whale populations increase, ecotourism revenues will also increase. In
particular, we assume that a return of whales to their pre-whaling populations will
result in a doubling of global ecotourism revenues, to $4 billion annually. This

The Value of Nature to Our Health and Economic Well-Being: A Framework... 133
Tab l e 1 Global whale populations
Species Current population Steady-state population Carbon on body (tonnes)
Blue 5400 303,500 12.2692
Bowhead 26,000 110,000 4.4719
Bryde’s 132,000 146,000 2.4359
Fin 110,000 763,000 6.7067
Gray 16,000 25,000 2.9262
Humpback 66,000 307,000 5.4842
Minke 704,000 928,000 0.4190
Right 14,500 124,000 6.0215
Sei 49,100 246,000 2.0493
Sperm 360,000 1,101,000 6.7125
Tot a l 1,483,000 4,053,500
projection is conservative in the sense that it allows for diminishing returns of
services from whales. As shown in Table 1, if whales return to their pre-industrial
whaling numbers, this is an average increase of over 173 percent in great whale
populations for each species. Thus, an increase in services on the order of 100
percent would allow for significant diminishing marginal returns. In the case of
ecotourism, the diminishing returns could be caused by lower novelty of watching
whales, should whales become much more abundant.
4.2.2 Carbon Capture and Sequestration Through Whale Biomass
Because whales are some of the largest animals on earth, their bodies contain
nontrivial amounts of carbon. The total amount of carbon captured by whale
biomass over time can be decomposed into the carbon stored in the current
population of whales, the carbon captured by future net additions to the whale
population, and the carbon effectively sequestered by future whale falls.
The carbon captured in whale biomass has been calculated by Pershing et al.
(2010) for various species of great whales. A stable population of whales will
effectively sequester a quantity of carbon proportional to the number of individuals.
Estimates of current whale populations are given by Smith et al. (2019), and are
presented in Table 1, along with estimates of the pre-industrial whaling populations
of each species, which are from Pershing et al. (2010), and Whitehead (2002). Table
1also shows the amount of carbon sequestered on the body of the average whale by
species. We estimate the value of the carbon currently sequestered on whale bodies
by converting the carbon per body to its CO2equivalent, and then multiplying by
the current population as well as the price of $24.72 per tonne of CO2. In addition,
as the equilibrium population of whales increases, the net increase in the population
will also create additional flux proportional to this increase. Our population growth
model implies a time-varying increase in whale populations until they reach their
long-run, steady-state equilibrium number.

134 R. Chami et al.
Because whale falls (deaths in which the whale carcass falls to the ocean floor)
effectively sequester carbon on the ocean floor, there is an additional annual flux in
carbon sequestration equal to the annual number of whale falls multiplied by the
carbon sequestered on the body of the particular species. The rate of whale falls
lowers the rate of population growth used in our model, but the amount of carbon
sequestered by these falls must be accounted separately from the carbon captured
by the increases in population.
4.2.3 Carbon Capture and Sequestration Through Enhancement
of Primary Production (Phytoplankton Fertilization)
Whales play an additional role in carbon capture and sequestration by promoting
phytoplankton growth. Through their normal feeding behavior, which involves
diving in search of food followed by resting and defecating at the ocean surface,
whales transport nutrients upward through the water column in a process dubbed
the “whale pump” (see for example Roman & McCarthy, 2010). In the Southern
Ocean, whales transport needed iron to the ocean surface, where it leads to increased
phytoplankton blooms. In addition to the whale pump, the migration behavior of
whales also transports nutrients to areas where they are in limited supply. This
process, dubbed the “whale conveyor” (Roman et al., 2014), transports nitrogen
from high-latitude feeding areas to low-latitude calving areas, where availability of
nitrogen limits phytoplankton growth.
Whales’ contributions to phytoplankton growth in turn lead to increased capture
and sequestration of carbon. Because phytoplankton currently capture the equivalent
of 37 billion tonnes of carbon dioxide annually, a small percentage increase in
the quantity of phytoplankton due to whale activity could result in large absolute
contribution to carbon capture.
Several studies estimate the impact of the whale pump and whale conveyor on
primary production. Lavery et al. (2010) estimates that the 12,000 sperm whales in
the Southern Ocean export 400,000 tonnes of carbon annually through their impact
on phytoplankton. Roman et al. (2014) estimate that the nitrogen transported by
whales may increase primary production in whale calving areas by 15 percent. This
large increase is a localized effect and is difficult to extrapolate to an impact on total
primary production, however. On the other hand, Lavery et al. (2014) estimates that
a return of the blue whale population to its pre-whaling level in the Southern Ocean
would increase primary production by 0.23% in that body of water. Ratnarajah et
al. (2016) estimate the impact of three whale species on primary production in the
Southern Ocean. Mean estimates of the contributions of these species to primary
production, assuming they return to their pre-whaling populations, sum up to nearly
one percent of current primary production.
Given the limited number of studies and the variation in their estimates of
whale impact on primary production, caution is warranted when using their results.
Nonetheless, attributing one percent of current phytoplankton production to the

The Value of Nature to Our Health and Economic Well-Being: A Framework... 135
current whale population appears, given the current state of the research, to be a
reasonable initial estimate of the impact of whales on primary production.
We further argue that the amount of carbon capture services produced increases
with whale populations. In particular, we assume that the quantities of services pro-
duced increase as whale biomass increases. We reason that whales’ contributions to
primary production should vary according to the quantity of feces produced, which
we assume is positively related to biomass. The increase in primary production
will in turn increase carbon capture by phytoplankton as well as further enrich
fisheries, as we discuss below. Specifically, we project an increase on the order of
one percent of global primary production due to whale activity, if whales were to
return to their pre-whaling numbers. Because existing phytoplankton is estimated
to capture ten billion tonnes of carbon annually (equivalent to 37 billion tonnes
CO2), this implies that whales currently stimulate the capture of 100 million tonnes
of carbon (equivalent to 370 million tonnes CO2) and will increase phytoplankton
carbon capture by a further 100 million tonnes as their populations returns to pre-
whaling levels. Again, we note that this projection allows for significant diminishing
marginal returns of whale contribution to primary production.
4.2.4 Fisheries Enhancement
In addition to carbon capture, the increase in phytoplankton due to whale activity
has also been shown to increase production throughout the marine food chain. We
therefore attribute a portion of commercial fisheries income, one percent per year,
to whale activities. This portion is equivalent to our estimate of whales’ contribution
to phytoplankton production. The UN’s Food and Agriculture Organization (FAO)
estimates that annual global fish production in 2018 was worth $401 billion (FAO,
2020), which was divided between $250 billion in aquaculture and $150 billion
in traditional commercial fishing. Although much aquaculture takes place in ocean
environments and therefore would potentially benefit from whale activity, we base
our estimate on the value of traditional commercial fishing, which implies a value of
$1.5 billion per year for the current annual service flow from fisheries enhancement.
In addition, we project that whales’ contributions to fisheries revenues increase from
$1.5 billion to $3.0 billion per year as whale populations return to pre-whaling
levels.
Using the population projections and the upper bounds on the increases in the
three services described above, we then project the annual increases in the three
services. We assume that the annual rate of increase vi,t in ecotourism, carbon
capture through primary production, and fisheries enhancement services for each
whale species iis equal to the ratio of the annual increase in the population, Ni,t –
Ni,t-1 to the difference between the steady-state and current populationsNi,T –N
i,0 :
vi,t =Ni,t −Ni,t−1
Ni,T −Ni,0.
The annual service flows of each service j=1, 2, 3 from each species i=
1, 2, ..., 10 during each future year tare therefore equal to the initial flows

136 R. Chami et al.
multiplied by one plus the cumulative sum of the increases up to that year: si,j ,t =
si,j,01+
t

u=1
vi,u.
4.3 Step 3: Assign a Discount Rate Appropriate to the Natural
Resource and the Service(s) Produced
As in the case of service flows from elephants, we argue that the flows of carbon-
capture and fisheries enhancement services from living adult whales will remain
roughly constant on a per-whale basis, no matter how the payoffs from other
assets fluctuate. Fluctuations in the quantities of these service streams come mainly
from two sources. The first is expected population growth, which is likely to
be uncorrelated with fluctuations in the payoffs from other assets. Unexpected
fluctuations in services would primarily come from higher-than-average mortality
among whales. The events that cause unexpected mortality in whales include
ship strikes, entanglement in fishing lines, disease, and ingestion of plastics. The
occurrence of such events is likely to be uncorrelatedwith fluctuations in the payoffs
from other assets.
We have already argued that carbon prices do not exhibit systematic risk, so
that the carbon sequestration services from whales should also be discounted at
the risk-free rate. Ecotourism revenues, on the other hand, are probably at least
somewhat correlated with the business cycle and hence with other asset returns.
Likewise, the values of fisheries are probably also correlated somewhat with the
business cycle. Thus, there is probably some systematic risk in the values of the
service flows that whales produce. Sufficient data does not exist to enable estimation
of the correlations of the returns on these service flows with the overall market
return, however. We argue that the systematic risk component of the overall value
of the services provided by whales is small, because the cyclicality of ecotourism
and fisheries revenues are not expected to be very high, and because (as we show
below) the majority of the value of the services provided by whales is associated
with carbon capture, which should be discounted at the risk-free rate. Therefore,
we conclude that the risk-free rate is a good first approximation of the appropriate
discount rate.
4.4 Step 4: Using the Values Projected in Step 2, Calculate
the Value of the Resource Using the Definition of Vt
The projected values constructed in Step 2 include the services produced by the
entire world population of great whales. Therefore, the next step in valuing the
whales off the coasts of Brazil and Chile is to assign the appropriate shares of global

The Value of Nature to Our Health and Economic Well-Being: A Framework... 137
Tab l e 2 Whale populations in Brazil and Chile
Species Current population Steady-state population Share of total whale biomass
Blue (Brazil) 64 3583 0.00015547
Blue (Chile) 760 57,000 0.00185364
Bowhead 0 0 0
Bryde’s 1558 1723 0.00186513
Fin 1298 9007 0.00173128
Gray 0 0 0
Humpback 25,000 28,198 0.02725305
Minke 25,000 32,955 0.00208124
Right 800 6841 0.00103650
Sei 580 2904 0.00023615
Sperm 10,000 30,583 0.01334434
values to the local populations.4In principle, valuation of the whales in a particular
area can begin by prorating the total value of each service produced by the fraction
of total whale biomass present in local species. In the case of carbon sequestration
on whale bodies, however, the value of this service can be constructed by applying
the population growth models described in Step 2 to each local species.
In order to apply the population growth model to the whales off the coast of
Brazil, we obtained or constructed estimates of both current and steady-state (pre-
whaling) populations in this location. The Brazilian research organization Baleia
Jubarte provided per-species estimates of current populations for minke, humpback,
right, and sperm whales in Brazil.5Bowhead and gray whales are not present
in Brazilian waters. Baleia Jubarte also estimated that the total number of blue,
Bryde’s, fin and sei whales present off the coast of Brazil is currently 3500 but
did not provide estimates for each species. We allocated this total among the four
species by assuming that the population of each of these four species in Brazilian
waters is proportional to their current relative abundance in the world.
Estimates of pre-industrial whaling populations for each species present off the
coast of Brazil were constructed by assuming that the steady-state levels reached
by local populations will be proportional to their relative abundance in the global
pre-industrial whaling population. The initial and steady-state population estimates
are presented in Table 2.
The current local population estimates and data on the average biomass of each
species were used to construct biomass weights wiequal to the current biomass
of each whale species found off the coast of Brazil, divided by total current great
4It is possible that the flows of services produced by whales vary by their location. But sufficient
data does not yet exist to measure local variations in services produced, let alone test the hypothesis
that migrating whales produce identical flows of services at each location they visit. Our estimates
assume this hypothesis is true.
5See Appendix 2for details on the sources of the estimates provided by Baleia Jubarte.

138 R. Chami et al.
whale biomass: wi=biNBrazil
i,0
10

i=1
biNi,0
where NBrazil denotes the local whale population
in Brazilian waters. These weights were used to estimate each species’ initial
contribution to the flows of services from ecotourism and primary production. The
weights are reported in Table 2.
The calculations for the population of blue whales off the coast of Chile were
done in a similar way. Galletti Vernazzani et al. (2017) estimates that the current
population of blue whales is between 570 and 760, and we assume that this
represents one percent of the country’s pre-industrial whaling population of blue
whales. In order to keep the valuation as conservativeas possible, we assume that the
pre-whaling population is based on the lower current population estimate, or 57,000
blue whales, while the higher estimate of 760 is used for the current population.
Doing so will lower the valuation of whales by reducing the present value of total
services (the numerator of the per-whalevalue) and increasing the number of whales
producing these services (the denominator of the per-whale value). The parameters
of the population growth model used to estimate future blue whale populations in
Chile are the same as those used for the Brazilian blue whales, with the exceptions
of the starting and ending populations. A biomass weight used to estimate the
Chilean blue whales’ initial contribution to the flows of services from ecotourism
and primary production was also constructed analogously to the biomass weights
for the Brazilian whales.
As described above, the service flows from ecotourism, phytoplankton carbon
capture, and fisheries enhancement are assumed to be proportional to each species’
share of global whale biomass, reported in Table 2. The implied initial values for
these services are reported in Table 3. The annual rates of increase in the production
of ecotourism and phytoplankton-related services were then constructed for each
species as described in Step 2. Similarly, estimates of carbon sequestered on the
bodies of whales were constructed directly from local population forecasts, as
described in Step 2. The value of the initial stock of carbon presently sequestered
on the bodies of the Brazilian and Chilean whale populations is also reported in
Table 3.
Annual service flows for each species were discounted and summed in order to
estimate the total value of each species as well as the average values of individual
whales. These are reported in Table 4.
The difference between the values of the Brazilian and Chilean blue whales
is due to the difference in the ratios of starting to ending populations in the two
countries. In the case of the Chilean blue whales, we are assuming that the starting
population is a greater fraction of the steady-state population than for the Brazilian
whales, which in turn implies an earlier acceleration of population growth in Chile,
producing larger service flows that occur sooner, leading to a higher overall value
of the services.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 139
Tab l e 3 Values of current service flows/stock of carbon
Current values of annual service flows: Value of stock:
Phytoplankton
Species Ecotourism Carbon capture Fisheries enhancement Carbon on body
Blue $310,941 $1,421,994 $233,206 $74,754
Bowhead
Bryde’s $3,730,269 $17,059,268 $2,797,702 $357,927
Fin $3,462,555 $15,834,959 $2,596,917 $816,453
Gray
Humpback $54,506,095 $249,267,274 $40,879,571 $12,496,213
Minke $4,162,488 $19,035,891 $3,121,866 $969,621
Right $2,072,994 $9,480,217 $1,554,746 $456,281
Sei $472,296 $2,159,906 $354,222 $111,226
Sperm $26,688,674 $122,052,644 $20,016,506 $6,207,708
Totals (Brazil): $95,406,313 $436,312,152 $71,554,736 $21,490,183
Blue (Chile) $3,707,269 $16,954,085 $2,780,452 $845,183
Tab l e 4 Present value of
whales in Brazil and Chile Species Total v al ue Average per whale
Blue $230,079,877 $3,609,454
Bowhead
Bryde’s $3,573,801,371 $2,293,839
Minke $4,129,486,080 $165,179
Fin $2,862,258,915 $2,205,130
Gray
Humpback $52,191,344,148 $2,087,654
Right $1,766,748,598 $2,208,436
Sei $400,868,032 $691,634
Sperm $22,282,689,815 $2,228,269
Total: $87,437,276,836
Blue (Chile) $3,107,530,267 $4,088,856
4.5 Discussion
Although this exercise produces a wide range of values for the great whales from
$165,000 for a Minke whale to $4 million for a blue whale, most of the whales have
a value of about $2 million. We argue that, like the example of forest elephants, our
estimated values of whales will generate excitementand concern among individuals
and investors, for the same reasons as discussed above.
The whale valuations, however, incorporate services beyond carbon sequestra-
tion, namely ecotourism and fisheries enhancement. This is important because the
flows from these services provide additional ways to use these valuationsto promote
action. As we show in Table 3, the values of the annual flows of services such as
ecotourism and fisheries enhancement are significant. These amounts translate into

140 R. Chami et al.
economic activity and opportunity for local residents, which are both tangible and
immediate benefits. Thus, quantifying these annual flows can be quite important in
convincing important ecosystem stakeholders who interact directly and frequently
with the resource to take actions to preserve or restore it.
5 Conclusion
In the introduction to this paper, we argue that our valuation strategy will be
more effective at prompting action because it takes better advantage of humans’
psychological tendencies. In this section, we also argue that our method will be
more effective because it opens up new possibilities for action.
First, we argue that our valuation method will stimulate further research into
the services produced by all natural resources and the value of these services to
society. By demonstrating that individual resources such as elephants and whales
can have significant value, our method will prompt efforts to identify and price the
services produced by other individual resources—much as a profitable investment
in one company leads investors to investigatethe fundamentals of related companies
in order to uncover hidden or overlooked value. Similarly, we believe that the
demonstration effect arising from valuations of individual resources will stimulate
additional interest in valuing the services flowing from entire ecosystems, using our
framework.
Our valuation approach also facilitates a transformation in how people view
natural resources, which in turn enables new approaches to conservation and
restoration policies. The assignment of credible money values to individual natural
resources, even if lower bounds, prompts society to view each natural resource as an
agent that produces services with a marketable monetary value. This can lead to the
legal recognition of the natural resource, not necessarily as a person, but nonetheless
as an agent with rights (and obligations).6Chief among these can be the rights to
legal protection against harm and to reasonable compensation for services rendered.
This change is a foundation upon which to build a new generation of conservation
and restoration policies. Because natural resources do nothave the capacity to speak
for themselves or defend themselves, guardians or advocates can be appointed to
protect them and their interests, including the standing to initiate lawsuits on behalf
of the resource.
One legal tool that our valuation method makes possible is the levying of
economically appropriate and meaningful fines on agents who damage or destroy
protected natural resources. These fines should be based on the values assigned to
the resource. For example, a ship that strikes and kills a blue whale off the coast of
Brazil should be fined the full value of the whale, or $3.6 million. The value could
also be used to incentivize private monitoring of the (mis-)use of natural resources.
6New Zealand, for example, has recently recognized all animals as sentient beings.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 141
Rewards linked to the values of whales could be paid to those who provide evidence
leading to the successful prosecution of agents who harm or kill whales.
Similarly, our valuation of forest elephants can be used to establish penalties for
poaching and incentives for monitoring that more nearly represent the true social
costs and benefits of doing so. Turkalo et al. (2017)) estimated that poaching of
elephants increases the mortality rate of elephants by 1.71 percentage points. The
current population growth rate of 1.9% is conditional on the existence of poaching,
so that removing poaching would increase the growth rate of elephants in African
tropical forests to 3.62%. Under this higher growth rate of elephants, we repeated the
same analysis of the three cases of elephants’ contribution to tropical forest carbon
stocks. When the higher population growth rate is used, the value of increased
carbon capture in tropical forests increases to $375.2405 billion, or $3,752,405 per
elephant. This means that poaching reduces the present value of the current 100,000
elephants by $198.9576 Billion or $1,989,576 per elephant.
The establishment of meaningful fines can stimulate private investment directed
at protecting individuals and businesses from these penalties, but which simulta-
neously promotes the protection of natural resources. In other words, government-
imposed penalties on the destruction of natural resources that are linked to the values
of these resources can create markets for protecting them. For example, maritime
insurers can develop whale-strike products that will compensate shippers for large
fines incurred by ships that inadvertently harm whales. And insurers will doubtlessly
wish to limit moral hazard-related losses by requiring the purchasers of insurance
to take actions to avoid whale strikes, such as using goods or services that alert ship
captains of whale proximity. This in turn provides incentives for private companies
to improve existing methods of monitoring whales, or to invent better ones.
Credible valuations also justify the levying of user fees and license fees on
those who enjoy or profit from natural resources. Such fees accomplish two
complementary purposes. First, they give agents an incentive to stop overusing a
resource, because doing so is no longer costless. In addition, the revenues from such
fees can be earmarked for the financing of protection and restoration programs. As
in the case of fines, the amounts of the user and license fees can be calibrated to
the value of the services, so that they are effective in both curbing overuse and
generating revenues.For example, significant user fees could be built into the prices
of whale watching or elephant watching tours, or licensing fees on the companies
that offer them (or both).
Moreover, imposing fees on the use of natural resources can also serve as a
catalyst for private investment in conservation and restoration projects. A portion
of fee revenues can provide impact investors, who seek both social and financial
returns on their investments, the money component of return that up to now has
largely been missing or nearly impossible to secure, due to lack of property rights.
Such impact investing initiatives would be structured as public-private partnerships
(PPPs) in which private-sector entities contribute management skills and technology
to restoration projects, as well as the ability to recruit other private investors. PPPs
could raise the initial capital required to start conservation and restoration projects
from the private sector, based on the dual promises of improved protection for

142 R. Chami et al.
natural resources and future income flows from fee revenues. This would help
establish natural resources as a new asset class for private investment, and also
relieve governments of the burden of funding conservation projects from general
tax revenues. This approach has great potential for protecting all resources, but
particularly for resources like elephants that are illegally misused or destroyed, since
PPPs would have a direct and strong incentive to protect their investments.
The potential gains discussed above also create incentives for international
cooperation on conservation and restoration. Many natural resources are shared by
countries, either because an immobile resource spans multiple countries’ territories,
or because a migratory resource visits multiple countries. The total value of a shared
resource often depends on how well it is managed or protected by each of the
countries sharing it. The value of a river in one country, for example, depends
on how upstream countries managed their section of the river. The value that a
resource provides to a particular country can be impaired or destroyed if the resource
is misused in one of the other countries sharing it. Thus, if a particular country
would like to assign value to a shared resource in order to stimulate private sector
investmentin its conservation and restoration, it will need other countries to commit
to at least doing no harm to the resource.
On the other hand, the benefits of acting jointly to conserve and protect resources
could be a strong incentive for more active cooperation. Countries could agree
to coordinate the fines they levy on agents who misuse shared resources, and to
share the proceeds from these fines. Governments could harmonize rules to create
larger, single markets for protection of resources that would attract more private
investment. Similarly, they could create international PPPs that would attract greater
numbers of investors, who would be attracted by the more reliable promises of
income flows due to larger user bases and uniform user and license fees across
countries.
The policies described above will not necessarily result from the adoption of
credible monetary valuations of individual natural resources, but it is difficult to
imagine how such policies could develop without this foundation. Expert valuation
of natural resources can—and indeed, we argue must—play the role that price
discovery performs in markets for private goods and services.
Acknowledgement Berzaghi was supported by the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie grant number 845265.
Appendices
Appendix 1: Population Model
The populations of elephants and whales are based on a logistic model of births
and an exponential model of the survival of living individuals. We assume each
population follows the differential equation dN(t)
N(t) =ν(t)dt subject to an initial
population N(0), where v(t) is the population growth rate. Following Karlin and

The Value of Nature to Our Health and Economic Well-Being: A Framework... 143
Taylor (1981 p. 420), the population under exponential growth rate νleads to
N(t) =N(0)exp t
0
ν(τ)dτ(1)
where N(0), the initial population of each species, is taken to be the number
of elephants after poaching, and the number of whales after industrial whaling,
respectively. N(T) is the steady-state population, for which we use the number of
elephants before poaching and whales before industrial whaling.
Because we do not expect the populations of elephants or whales to grow
indefinitely, we assume that ν(t)→0ast→∞. We also want to account for
birth and deaths. As a result, we define ˆν(t) =v(t) +c,sothatˆν(t) is the birth rate
of whales or elephants, cis their constant instantaneous death rate, and ν(t)isthe
(net) growth rate of the population. Thus, ˆν(t) →cas t→∞.
These properties are captured by a logistic model for the birth rate such that
ˆν(t) =β1−N(t)
αfor N(t) ≤α(β−c)
β
cforN(t)>
α(β−c)
β
(2)
where α(β−c)
βis the level of population when the birth rate is equal to rate of death
and the population growth rate is zero. As a result, α(β−c)
βis the steady state value
of the population. For simplicity we set β=v(0) +c.
We know the survival rate Safor mature elephants and whales over one year, so
that the mortality rate cis given by the solution of
1
0
e−ca da =1
c1−e−c=Sa.(3)
Substituting v(t) =ˆv(t) −cand (2) into the differential equation dN(t)
N(t) =ν(t)dt
for the growth rate of the population gives
dN(t)
dt =N(t) (β−c)−βN(t)2
αfor N(t) ≤α(β−c)
βand 0 otherwise.
The solution to this ordinary differential equation is
N(t) =α(β−c) N(0)
βN(0)[1−e−(β −c)t ]+α(β−c)e−(β−c)t for N(t)≤α(β−c)
βand 0 otherwise.
(4)

144 R. Chami et al.
As stated above, we use the post poaching or whaling population for N(0). The
population converges to N∗=α(β−c)
β, which we associate with the population
before poaching or whaling. This means
α=N(T ) β
(β−c).
Now we add a model of births that will be consistent with the above population
model. We do so in order to be able to construct alternative scenarios in which we
can show the impact of different birth and survival rates on future populations. We
assume that births are always the same proportion bof population (which implies
that births also follow the logistic model of population). This means ν(0) is the same
for both population and births. If B(t) is the number of births, then
B(t) =bN(t) ⇒B(0)
B(T ) =N(0)
N(T ) ⇒B(T ) =N(T)
N(0)B(0). (5)
This implies from Eq. (1)that
bN(t) =bN(0)exp  t
0ν(τ)dτ⇒B(t) =
B(0)exp  t
0ν(τ)dτ.
(6)
To complete the differential equation model we need to set B(0). We know the
average number of births in the first year is m=1
IBI for an average female, where
IBI is the interval between births. Let AFR be age of first reproduction. Therefore,
there are AFR years before a female born at time 0 can give birth at time AFR,
so that the females born at time 0 mature in AFR years with survival chance of
S0AFR =(So)AFR.
Let Obe the oldest age of reproducing females. We assume the distribution of
the ages of individuals is uniform across ages 0 to O. The number of female births
(half the population) at time 0 is given by
B(AFR) =O−AF R
O
mN( AF R)
2
=O−AF R
O
mN(0)AFR −1
i=00xSAFR−i
oB(i)+O
i=AFR 1
OSi
a
2
=O−AF R
2O2mN(0)
O

i=AF R
Si
a
=O−AF R
2O2mN(0)SAF R
a
O−AF R

i=AF R
Si
a
=O−AF R
2O2mN(0)SAF R
a
1−SO−AFR
a
1−Sa
where Sa is the survival rate of adults. The female calves from ages 0 to AFR do
not give birth, so that the first summation in the second equality is equal to zero and
drops out.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 145
We let B(AFR) be the number of births by mature females at the end of the initial
period, so that
B(AFR) =B(0)exp  1
0ν(τ)dτ
=O−AF R
2O2mN(0)SAF R
a
1−SO−AFR
a
1−Sa.
As a result, the initial number births by mature females is given by
B(0)=1
exp 1
0ν(τ)dτ
O−AF R
2O2mN(0)SAF R
a
1−SO−AFR
a
1−Sa=
1
1
ν[eν−1]
O−AF R
2O2mN(0)SAF R
a
1−SO−AFR
a
1−Sa.
(7)
Now that we have the initial births, we can solve the differential equation for births
at any time. Because births are a constant fraction of population, the differential
equation for births can be written as (see Eq. (6))
dB(t)
dt =ν(t)B(t).
Also, since births are a constant share of population, we can rewrite (2)intermsof
births:
ˆν(t) =β1−B(t )
αBfor B(t)≤αB(β −c)
β
cforB(t)>
αB(β−c)
β
(8)
where αB=bα.
Substituting ˆν(t) −cfor v(t), as well as the logistic model for ˆν(t) in terms of
births (8) into the differential equation for births above gives
dB(t)
dt =⎧
⎨
⎩
B(t) (β−c)−β
αBB(t)2for B(t)≤αB(β −c)
β
0for B(t)> αB(β −c)
β
.(9)
This differential equation has the solution
B(t) =αB(β−c)B (0)
βB(0)[1−e−(β−c)t ]+αB(β−c)e−(β −c)t
for B(t)≤αB(β −c)
β,and c otherwise.(10)

146 R. Chami et al.
Births net of deaths converge to 0 when B(T ) =αB(β −c)
β.
αB(β−c)
β=B(T ) ⇒αB=β
β−cB(T ).
We also know that the population and births grow at the same rate with initial ratio
of bN(t)=B(t), so that
N(t) =1
b
αB(β−c)B(0)
βB(0)[1−e−(β−c)t ]+αB(β−c)e−(β −c)t
for N(t) ≤αB(β −c)
bβ .
(11)
Appendix 2: Valuation of Elephants in Central Africa Forest
This Appendix values forest elephants in Central Africa based on two services: (1)
carbon capture on elephant bodies, and (2) increased carbon capture in trees. The
quantities of each service produced per period depend on the elephant population.
We use the same logistic model discussed in Appendix 1to estimate the evolution
of the elephant population. The parameter values for elephants are given in Table
5. We take these parameters from Turkalo et al. (2017,2018). The population is
currently 100,000, and we assume that the elephant population will stabilize at
the pre poaching level of 1,100,000. The Central Africa forest covers an area of
2,200,000 km2, which is about 44% of the size of the Amazon forest. Most of the
Central African forests do not have elephants, so that the elephants can be spread
over the current forest without changing the density of elephants per hectare.
AFR is age of first reproduction, O is oldest age of reproducing females, IBI is
the interbirth interval, Sa is the survival rate of adult elephants, So is the survival
rate of elephant calves, and ν(0) is the population growth rate.
We know the survival rate over 1 year Sa=0.9691 for mature elephants, so that
(3) yields a continuously compounded death rate of
c=0.0631.
This means β=ν(0) +c=0.019 +0.0631=0.0821.
Tab l e 5 Parameters for population model for elephants
AFR OIBI Sa So ν(0) Pop pre poaching Current elephants
10 65 5.6 0.9691 0.97 0.019 1,100,000 100,000

The Value of Nature to Our Health and Economic Well-Being: A Framework... 147
Given these parameter values, the population of elephants following (4) with
α=4, 753, 552 is given in the next graph.
The birth of elephants following Eq. (8)startsat
B(10)=O−AF R
2O2mN(0)S11
a
1−SO−10
a
1−Sa
=2,259.
Consequently, the initial value of births, following Eq. (9), is given by
B(0)=2,238.
Since the population of elephants grows to 11 times its initial size, the terminal
births also increase by 11 times. Consequently, B(t) =0.0348 N(t) for each time
period, following Eq. (5). We use the solution to the logistic model for births (10)
with parameter
αB=106.3739.

148 R. Chami et al.
This leads to the graph of elephant births over time in the next Figure.
The population of elephants follows (11)
Carbon Capture in Elephant Bodies
Assuming an average body mass of 3000 kg (Grubb et al., 2000), of which 24%
is carbon, we can calculate the CO2equivalent of the carbon captured in elephant
bodies:
C=0.24x3,000 =720 kg;CO2=11x720
3
=2,640 kg or 2.64 metric tons.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 149
The cash flow per year from increased carbon capture on bodies, CF(i) is equal to
the increase in population multiplied by the CO2captured per body, multiplied by
the price of carbon, PC=$24.72, so that for each species we have the market value
for this service during period t+i
p1,t+is1,t +i=PCCO2[N(i) −N(i−1)]for i >0.
This corresponds to the increase in the value of carbon dioxide sequestration
because of the increase in elephants.
Assuming a discount rate of r =0.02, the present value of carbon content of
100,000 elephants is
V1,t =PV (Body Carbon)=PCCO2N(0)+
∞
i=1PCCO2[N(i)−N(i−1)]
(1+r)i=$6,526,080 +$10,059,942 =$16,586,022.
This corresponds to a present value of carbon on an elephant’s body of $166.
Carbon Capture Enhancement Through Interaction with Tropical Forest
The historical elephant population was 1.1 million individuals spread over
2,200,000 km² of the central Africa tropicalrain forest, implying an average density
of 0.5 elephants/km² (Turkalo et al., 2017). At a density of 0.5 elephants per km2,the
carbon boosting effect of 0.5 elephants has been estimated at 13 metric tons (tonnes)
per hectare. Since 1 km2=100 hectares, the increase in carbon capture at a density
of 1 elephant per km2is 13 * 2 * 100 =2600 tonnes of carbon per km2.TheCO2
equivalent is given by 2600 * 11/3=9533.33 tonnes. This calculation allows us to
compute the increase in carbon capture based on the number of elephants.
We assume that as the elephant population increases, it will distribute itself
among the African tropical forest in a way that maintains a density of 0.5
elephants/km2. Therefore, as the population grows, elephants will expand their
range maintaining an average density of 0.5 elephants/km2. Thus, our calculations
are based on maintaining the averageeffect of elephants per hectare while extending
the elephant-occupied range.
The effect of elephants on CO2depends on how long the elephants are in a
particular area of the forest. We begin with an initial plot of forest containing the
currently existing 100,000 elephants (200,000 km2) and assume that these elephants
have been around long enough to increase carbon capture in this plot to its higher
steady state. Consequently, CO2(0) =9533 tonnes per elephant on the initial plot.
The initial population of elephants N(0) =100,000 occupies a plot of forest of
200,000 km2with a biomass of 953 million metric tons of CO2. Thus, the initial
100,000 elephants produces carbon capture services worth $23.5656 billion at the
price of $24.72 per metric ton of CO2.

150 R. Chami et al.
Now we consider how elephants affect carbon capture when they move to a
currently unoccupied plot of land that is nonetheless within their historical range.
Given that elephants had occupied these areas before, it is possible that the previous
occupants had already enhanced the carbon capture in them and that some of this
enhancement continues despite the lack of elephant activity.
Let C(0) be the initial CO2in a forest plot. We assume that it takes 200 years to
reach the steady state of 9533 tonnes per elephant when C(0) starts at zero. In this
case, the change is 9533/200 =47.67 tonnes per year. We also assume that carbon
is captured at this constant rate irrespective of the initial CO2, i.e. C(0). Therefore,
given an initial C(0), we can solve for the number of years to reach a CO2of 9533
metric tons per elephant using
Change =9533 −C(0)
years =47.67.
Given the uncertainty about the initial carbon level on each re-occupied plot, we
consider three cases:
1. Initial Carbon per hectare is one quarter of its maximum (3.25 tonnes) or C(0) =
9533/4 =2383 tonnes per elephant. Elephant activity increases capture by 47.67
tonnes per year for 150 years.
2. Initial Carbon per hectare is one half of its maximum (6.5 tonnes) or C(0) =
9533/2 =4767 tonnes per elephant. Elephant activity increases capture by 47.67
tonnes per year for 100 years.
3. Initial Carbon per hectare is 0 or C(0) =0. Elephant activity increases capture
by 47.67 tonnes per year for 200 years.
At time 1 there is an increase in population of N(1) - N(0), following the logistic
population growth model for elephants. This new generation enters a plot of forest
with biomass of C(0) tonnes per elephant and increases it to 9533 metric tons of
CO2over 150, 100, and 200 years for cases 1, 2, and 3 respectively. The size of
the plot is adjusted so that the density of elephants in the forest is maintained at 0.5
elephants/km2.
At time 2, a new generation of elephants is born with size N(2) – N(1), which
occupies a new plot and contributes to the growth of the biomass of the tropical
forest as described above. We repeat this process for 1000 generations to ensure
convergence of the elephant population to its steady state, at which point the total
increase in carbon capture converges to zero.
Given the growth rate of carbon sequestration in the tropical forest for each
generation, we can determine the value of the contribution of each generation of
elephants. Assuming a price of carbon Pc=$24.72 and an interest rate of 2%, the
present value of each generation k’s contribution to carbon capture in aboveground
biomass, Vk,2,t,isgivenby24.72∗47.67∗[N(k)−N(k−1)]
.02 1−1
1.02 Y1
1.02 k,where
Y is the number of years corresponding to each case. Then the present value of
each generation’s contribution is summed to obtain the total present value of carbon

The Value of Nature to Our Health and Economic Well-Being: A Framework... 151
capture by all future generations. The total present value of the biomass added to
the tropical forest, V2,t, is the sum of the contribution of the current elephants and
the present value of the contributions from the future generations of elephants.
Results of these calculations are as follows:
Case 1 :C(0)=9533/4=2383 per elephant,Y=150 years.
These calculations imply a present value of biomass added to the tropical forest by
future generations of elephants of $152.7173 billion. The total V2, tof forest biomass
added by elephant activity =$23.5656 billion +$152.7173 billion =$176.2829
billion.
This corresponds to a contribution to the biomass of the tropical forest worth
$1,762,829 per elephant. If we add the $166 for the carbon on the body of the
elephant, we obtain a total value of $1,762,995 per elephant.
Case 2 :C(0)=9533/2=4767,Y=100 years.
Total V2, tof forest biomass added by elephant activity =$23.5656 billion +
$113.1792 billion =$136.7448 billion.
The contribution to the biomass of the tropical forest is worth $1,367,448 per
elephant.
Case 3 :C(0)=0.Y=200 years.
Total V2, tof forest biomass added by elephant activity =$23.5656 billion +
$173.4365 billion =$197.0021 billion.
The contribution to the biomass of the tropical forest is worth $1,970,021 per
elephant.
Our preferred case is case 1, since we believe that the impact of elephant activity
has persisted, though elephants have been removed from much of their habitat for
several decades, dramatically reducing their impact on these areas. Table 6presents
a sensitivity analysis showing how the total present value of carbon enhancement
in each case depends on the number of years considered in the calculations. The
present value of the elephants starts at $43.8705 Billion in 50 years and increases to
$176.2222 Billion in 300 years. The last value is within $0.0607 Billion or $607 per
elephant relative to the present value over 1000 years.
Tab l e 6 Impact of years on
present value of elephants
(billion $)
Years/cases Case 1 Case 2 Case 3
50 $43.8705 $43.8705 $43.8684
100 $98.7666 $98.7666 $98.7587
150 $149.5936 $129.4208 $149.5804
200 $171.3928 $135.7389 $182.0976
300 $176.2222 $136.7378 $196.6588

152 R. Chami et al.
In Table 6the first 100 years is the same since the same amount of carbondioxide
is being added each year. Starting at 150 years the amount is smaller, since the first
generation is no longer adding to carbon dioxide under case 2.
The first 150 years are similar for Case 1 and Case 3, but the present values
deviate over the next 50 years because the contribution of 47.67 tonnes per year of
carbon dioxide lasts for 200 years for Case 3.
The Cost of Poaching
By Turkalo et al. (2017), poaching of elephants increases the mortality rate of
elephants by 1.71 percent per year. The current growth rate of 1.9 percent is with
poaching, so that removing poaching would increase the growth rate of elephants in
African tropical forest to 3.62 percent. Using the higher growth rate of elephants, we
carry out the same analysis of the elephants’ contributions to carbon capture under
each Case. Under Case 1, the Vtof elephant activity increases to $375.2405 billion
or $3,752,405 per elephant. This implies that poaching reduces the present value of
the current 100,000 elephants by $198.9516 billion, or $1,989,516 per elephant.
Appendix 3: Estimation of Whale Populations Off Brazil’s Coast
Humpback whales: The Humpback Whale Institute (2015, unpublished data),
estimated 17,000 humpbacks off the coast of Brazil in 2015. Wedekin et al. (2017)
recorded a population increase of 12 percent per year between 2002 and 2011.
Therefore, the most recent estimate, from Zerbini et al. (2019) of 25,000 humpbacks
is consistent with previous findings.
Right whales: Groch et al. (2005) and Renault-Braga et al. (2018) present partial
estimates of right whales off the coast of Brazil, but the numbers in these papers
relate only to the South/Southeast of Brazil, although the species distribution is
confirmed all the way to 12 degrees S. The estimate used in this paper is from a
personal communication from Groch, K.R., head scientist of the Brazilian Right
Whale Project. A report (Torres-Florez, 2020) presented to the IWC Scientific
Committee includes the following comment:
Population analyses and trends in abundance of Southern Brazil right whales are being car-
ried out under a PhD thesis to be concluded in the end of May, 2020. The information will
be available upon final approval of the thesis. IWC estimated 3,300 Southern Right whales
in Western South Atlantic in 2009. In Brazil the population probably will be something
between 500-900 animals.
Minke whales: Unfortunately for the two species of minkes (B. acutorostrata and
B. bonaerensis), recent population estimates for Brazil do not exist. The IWC’s
most recent estimate was 515,000 minkes for the southern hemisphere in 2003/2004.
Based on whaling data in Williamson (1975), da Rocha (1983),anddeLaMare

The Value of Nature to Our Health and Economic Well-Being: A Framework... 153
(2014), and given that these species were always considered the most abundant, the
same number estimated for humpbacks was used for Minke whales, assuming they
would at least be as abundant as humpbacks.
Fin, Sei, Bryde’s and Blue whales: Aerial surveys conducted in the Santos
Basin (off Santa Catarina, Paraná, São Paulo and part of Rio de Janeiro States)
recorded an estimated 2990 masticates (interval: 2038–4385); this area included the
main range of these species for which records have been kept. Given that the aerial
survey covered only a small part of the historic range, however, author (Palazzo)
estimated a total population of 3500 individuals spread over the four species.
Sperm whales: Author’s (Palazzo) calculations, based on frequent records
(mostly unpublished) of sightings at the continental shelf edge.
Appendix 4: Valuation of Whales
We value whales based on four services: (1) carbon capture in whale bodies, (2)
carbon capture through phytoplankton enhancement, (3) fisheries enhancement, and
(4) ecotourism. As in the case of elephants, the quantities of each service produced
per period by whales depend on whale populations. We use the same logistic model
developed in Appendix 1to estimate the evolution of whale populations. The growth
model parameters are given in Table 7.7The populations before and after whaling
are provided in Table 2of the paper. In the discussion below, we use Brazilian Blue
whales as our example.
First, we use the basic logistic model (1)and(2). From Table 7we have
Sa=0.9750 for the Blue whale, which implies a continuous time mortality rate
of c =0.0509. As a result, β=ν(0) +c=0.05 +0.0509 =0.1009. The population
of Brazilian Blue whales is given in the following Figure.
7The same parameters are used for Brazilian and Chilean blue whales except for the beginning
and ending populations. See Table 2.

154 R. Chami et al.
Tab l e 7 Population
parameters for each species
of whales
Species AFR OIBI Sa So ν(0)
Blue (Brazil) 11 65 2.5 0.9750 0.8190 0.05
Blue (Chile) 11 65 2.5 0.9750 0.8190 0.05
Bowhead 20 118 3.1 0.9800 0.8230 0.03
Bryde’s 10 69 40.9900 0.8800 0.05
Fin 10 62 2.24 0.9600 0.8060 0.04
Gray 10 55 20.9500 0.7000 0.03
Humpback 655 2.36 0.9600 0.7600 0.05
Minke 851 10.9600 0.8060 0.09
Right 10 69 40.9900 0.8800 0.05
Sei 20 53 2.5 0.9600 0.8060 0.04
Sperm 12 59 50.9860 0.8280 0.03
AFR is age of first reproduction, Ois oldest age of reproducing females, IBI is
the interbirth interval, Sa is the survival rate of adult Blue whales, So is the survival
rate of Blue whale calves, and ν(0) is the population growth rate for Blue whales.
The parameters come from Taylor, Chivers, Larese and Perrin (TCLP, 2007).
Next we examine the population of Brazilian Blue whales using the model of
births and deaths, Eqs. (4)–(12). Suppose the survival rate is s(a)=e−ca where c is
the continuously compounded mortality rate. Following TCLP (Table 1, first row),
reproduced in Table 7for the 11 species of whales, the interval between births for
Blue whales IBI =2.50. The average births over one year (see page 3, last paragraph
TCLP) are m=1
IBI =1
2.50 =0.4. We know the number of births in the first year
is m =0.4 for an average female Blue whale. However, there are 11 years before
a whale born at time 0 can give birth at time 11, so that the births at time 0 mature

The Value of Nature to Our Health and Economic Well-Being: A Framework... 155
in 11 years with survival chance given by S011 =(So)11 =0.1112. We assume the
distribution of the age of whales is uniform across ages 0 to O. The number of
female births (half the population) at time 0 is given by (8), so that
B(11)=O−AF R
2O2mN(0)S11
a
1−SO−10
a
1−Sa
=3.6910.
We let B(11) be the number of female Blue whales at the end of the initial period,
so that
B(11)=B(0)exp 1
0
ν(τ)dτ=3.6910.
This implies that ν=0.05, which we assume is constant for the first year. As a
result, we have from Eq. (9) that the initial number of mature females satisfies
B(0)=2,259
1
ν[eν−1]=3.5995.
By Eq. (10), the births converge to αB(β−c1)
βand B(T ) =3,583
64 3.5995 =201.5
with N(T) =3,583.
αB(β−c)
β=201.5⇒αB=201.50.1009
0.05 =406.5.
The number of annual births over 300 years for Brazilian Blue whales are given in
the following figure.

156 R. Chami et al.
We also know that the population and births grow at the same rate with initial
ratio, b=0.0562, so that the total population implied by Eq. (12) is graphed in the
next figure over 300 years for the Brazilian Blue whales.
The Chilean population of Blue whales starts between 570 and 760,which is only
1% of the pre-whaling number of whales. As a result, we set the upper limit of Blue
whales in Chile at N(T) =57,000 based on the initial number of 570 whales. The
next graph depicts the population of Blue whales in Chile using the same logistic
model. The parameters for the Blue whales in Chile are the same as for the Brazilian
whales in Table 7.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 157
Tab l e 8 Parameters for
Weight of Each Species of
Whales
Species a b L(m)
Blue (Brazil) 0.000061 3.25 27
Blue (Chile) 0.000061 3.25 27
Bowhead 0.00255 2.916 16
Bryde’s 0.0005 2.74 7
Fin 0.00025 2.9 23
Gray 0.0054 3.28 15
Humpback 0.00049 2.95 16
Minke 0.003188 2.31 7
Right 0.000348 3.08 16
Sei 0.001436 2.43 16
Sperm 0.000152 3.18 18.5
The values of a and b from Pershing et al.
(2010)
Carbon Capture in Whale Bodies
The quantity of the carbon captured in the body of a mature whale is dependent on
the biomass of the whale. The weight of Blue whales is given by
W=aLb=0.000061x[3.281 x27]3.25 =130.0809 metric tons,
where a and b are parameters from Table 8. The weight is the same for the Chilean
Blue whales, so that the carbon content (and carbon dioxide equivalent) is the same
for Brazilian and Chilean Blue whales.
The first two parameters in Table 8are for each species of whales. The length
comes from Smith et al. (2019), Table 3, for each species.
The carbon dioxide content, in metric tons of CO2per Blue whale, is
CO2=0.1048 xWx0.9x11
3=0.1048 x130.0809 x0.9x11
3
=44.9872 metric tons.
The cash flow per year from increased carbon capture on bodies, CF(i), is equal
to the increase in population multiplied by the CO2equivalent captured per body,
multiplied by the price of carbon dioxide, PC=$24.72, so that for each species we
have
p1,t+is1,t +i=PCCO2[N(i) −N(i−1)]+PCFall N(i) for i >0.
The last term reflects the carbon content of whales that die and fall to the ocean
floor, where Fall =1−Saper year and per whale.

158 R. Chami et al.
Assuming a discount rate of r =0.02, the present value of carbon captured by
the bodies of the 64 Blue whales in Brazil is
V1,t =PV (Body Carbon)=PCCO2N(0)+300
i=1p1,t+is1,t +i
(1+r)i
=$74,754 (845,183)+$2,260,168 (13,907,802)
=$2,334,922 (14,752,985).
The present values for Chilean Blue whales are in parenthesis. These values are
larger because of the larger population of Blue whales in Chile.
Phytoplankton Capture Enhancement
We now value the benefit of whale activity on phytoplankton, assuming that
current whale populations are responsible for one percent of existing phytoplankton
biomass, which captures the equivalent of 370 million metric tons of CO2.We
assume that as whales return to their pre-whaling populations, they stimulate an
additional one percent increase in phytoplankton and therefore an additional one
percent increase in carbon capture. We apportion this benefit according to the
percentage of the total whale biomass accounted by each species, where these shares
are reported in Table 2. For the 64 Brazilian Blue whales the biomass weight is
0.0001555 of the total population of whales in the world. This means that the Blue
whales in Brazil currently account for the equivalent of 0.0001555 * 370 million =
57,524 metric tons of CO2. The 760 Chilean Blue whales account for 0.001853 of
the biomass of all whales in the world, which accounts for 685,845 metric tons of
CO2.
In each period the population of each species grows, so that the increase in
capture each period by Blue whales in Brazil is given by
p2,t+is2,t +i=value of P hyto CaptureBlue per period(t)
=1+ t
0dN(a)
T
0dN(a) xPc57,524
=1+N(t)−N(0)
N(T)−N(0)xP
cx57,524.
Since we know the beginning and ending population as well as the population at
each time, this can be easily calculated.8This value at time 0 is Pcx57, 524 and
converges to Pcx2x57, 524 at the steady state.
8In the second step we use the fundamental theorem from Calculus.

The Value of Nature to Our Health and Economic Well-Being: A Framework... 159
For Chilean Blue whales, we replace the 57,524 with 685,845 because of the
larger population. Using an interest rate of r =2% and a price of carbon dioxide of
$24.72, the present value of a one percent increase in phytoplankton from additional
Blue whales in Brazilian waters is
V2,t =PV Phyto Capture
Blue
= T
01+NBlue(t)−NBlue(0)
NBlue(T )−NBlue(0)xPCx57,524 xe
−rtdt
=$164,714,579 (1,916,963,736).
The present value of carbon capture from increased phytoplanktonis $164, 714.579
for Brazilian blue whales under continuous compounding.9Thepresentvalueofthe
570 Chilean Blue whales is $1, 916, 963, 736.
Fisheries Enhancement
The total contribution to fisheries in the world is $1.5 billion per year for all whales,
which we assume increases by another one percent or an additional $1.5 billion
per year as whales return to their pre-whaling populations. Again, we apportion
each species’ contribution to increased fisheries according to its share of total
whale biomass. This weight is 0.0001555 for Blue Brazilian whales, which implies
a current flow of 0.0001555 * $1.5 billion or $233,206 per year. Each species’
contribution to fisheries enhancement increases with its population so that
V3,t =PV (Fish
Blue)
= T
01+NBlue(t)−NBlue(0)
NBlue(T )−NBlue(0)x$233,206 xe
−rtdt
=$27,013,018.
The present value of Brazilian Blue whales’ contribution to fisheries is valued at
$27, 013, 018 using a 5% growth rate for Brazilian Blue whales. For 760 Chilean
Blue whales, the present value of fisheries enhancement is $314,380,041.
Ecotourism Revenues
Tourism from all whales is currently $2.0 Billion per year, which we assume
increases to $4 billion per year as whales return to their pre-whaling populations.
Once again the contributions are apportioned according to biomass weights, so that
for Brazilian Blue whales we estimate the current contribution to ecotourism by
0.0001555 * $2.0 billion, which is $310,941. The contribution increases with its
9We approximate the integral by using summation over the T years and using discrete compound-
ing.

160 R. Chami et al.
population so that
V4,t =PV (Tourism
Blue)
= T
01+NBlue(t)−NBlue(0)
NBlue(T )−NBlue(0)x$310,941 xe
−rtdt
=$36,017,358.
The 760 Blue whales in Chile has a present value for tourism of $418,818,311.
In the Table below we summarize these results for the Brazilian Blue whale
in column 2. The total value is $230,079,877 for 64 whales or $3,609,454 per
Blue whale in Brazil. In Chile the total present value of the 760 Blue whales is
$3,107,530,267 or $4,088,855.61 per Blue whale.
Present value Brazilian blue whales 760 Chilean blue whales
Carbon Capture $2, 334, 922 $14, 752, 985
Phyto Expansion $164, 714, 579 $1,916,963,735
Fisheries $27, 013, 018 $314,380,041
Tourism $36, 017, 357 $418,818,311
Tot a l $230,079,877 $3,107,530,267
The values of the other great whales off the coast of Brazil are estimated in a
similar way, using the corresponding parameters from Tables 2,7,and8.
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