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Valuing pollination services to agriculture

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Apis mellifera biodiversity-ecosystem function ecosystem services native bee pollinator valuation ecosystem service valuation wild bee Crop pollination by animal pollinators is an important ecosystem service for which there is no generally ac-cepted valuation method. Here, we show that two existing valuation methods, previously thought to be unre-lated, are each a special case of a more general equation. We then present a new method, termed attributable net income, for valuing insect pollination of crops. The attributable net income method improves upon pre-vious methods in three ways: (1) it subtracts the cost of inputs to crop production from the value of pollina-tion, thereby not attributing the value of these inputs to pollinators; (2) it values only the pollination that would be utilized by the crop plant for fruit production, thereby not valuing pollen deposited in excess of the plants' requirements; and (3) it can attribute value separately to different pollinator taxa, for example to native vs. managed pollinators. We demonstrate all three methods using a data set on watermelon polli-nation by native bees and honey bees in New Jersey and Pennsylvania, USA. We discuss the reasons why dif-ferent methods produce disparate values, and why the attributable net income method most accurately reflects the actual ecosystem service that is being valued, marketable fruit production.
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Analysis
Valuing pollination services to agriculture
Rachael Winfree
a,
,1
, Brian J. Gross
b,1
, Claire Kremen
c
a
Department of Entomology, 93 Lipman Dr., Rutgers University, New Brunswick, NJ 08901, USA
b
Food and Resource Economics, University of British Columbia, Vancouver, Canada, BC V6T1Z4
c
Department of Environmental Science, Policy and Management, University of California, Berkeley, Berkeley, CA 94720, USA
abstractarticle info
Article history:
Received 7 December 2007
Received in revised form 30 July 2011
Accepted 7 August 2011
Available online 21 September 2011
Keywords:
Apis mellifera
biodiversity-ecosystem function
ecosystem services
native bee
pollinator
valuation
ecosystem service valuation
wild bee
Crop pollination by animal pollinators is an important ecosystem service for which there is no generally ac-
cepted valuation method. Here, we show that two existing valuation methods, previously thought to be unre-
lated, are each a special case of a more general equation. We then present a new method, termed attributable
net income, for valuing insect pollination of crops. The attributable net income method improves upon pre-
vious methods in three ways: (1) it subtracts the cost of inputs to crop production from the value of pollina-
tion, thereby not attributing the value of these inputs to pollinators; (2) it values only the pollination that
would be utilized by the crop plant for fruit production, thereby not valuing pollen deposited in excess of
the plantsrequirements; and (3) it can attribute value separately to different pollinator taxa, for example
to native vs. managed pollinators. We demonstrate all three methods using a data set on watermelon polli-
nation by native bees and honey bees in New Jersey and Pennsylvania, USA. We discuss the reasons why dif-
ferent methods produce disparate values, and why the attributable net income method most accurately
reects the actual ecosystem service that is being valued, marketable fruit production.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Pollination by animals is an important ecosystem service because
crop plants accounting for 35% of global crop-based food production
benet from animal-mediated pollination (Klein et al., 2007). Bees
(Hymenoptera: Apiformes) the primary pollinators for most of the
crops requiring animal pollination (Delaplane and Mayer, 2000;
Free, 1993; Klein et al., 2007). In much of the world, the cornerstone
of agricultural pollination is the managed honey bee (Apis mellifera).
Honey bees, which are native to Europe and Africa but not North
America, are maintained in hives which are moved into agricultural
areas during crop bloom. Despite the honey bee's effectiveness as a
pollinator for many crops, there are risks associated with reliance
on a single, managed pollinator species. Managed honey bee stocks
in the USA have decreased steadily since the 1940s, and are now at
less than half their original numbers (Ellis et al., 2010). Declines
since the 1990s are largely due to infestation by a parasitic mite, Var-
roa destructor (NRC, 2007). Since 2006, honey bees in the USA have
experienced further die-offs due to Colony Collapse Disorder (Cox-
Foster and VanEngelsdorp, 2009), raising further concern about the
availability of agricultural pollination.
In contrast to the sole species of honey bee, there are at least
17,000 species of native, wild bees worldwide (Michener, 2007).
Many of these species visit crops (Delaplane and Mayer, 2000; Klein
et al., 2007), and they contribute substantially to the pollination of
such crops as coffee Coffea spp. (e.g. (Klein et al., 2003), watermelon
Citrullus lanatus (Kremen et al., 2002; Winfree et al., 2007), tomato
Solanum lycopersicum (Greenleaf and Kremen, 2006a), blueberry
Vaccinium spp. (Cane, 1997; Isaacs and Kirk, 2010), sunower
Helianthus annuus (Greenleaf and Kremen, 2006b) and canola Brassica
spp. (Morandin and Winston, 2005). These native bees provide polli-
nation thus directly beneting crop production. In addition, they
complement in a number of ways the service provided by honey
bees: biologically, by enhancing the efcacy of honey bee pollination
in some cases (Greenleaf and Kremen, 2006b), and economically, by
insuring against pollination shortages. Having accurate estimates of
this value could improve land use planning by quantifying the costs
and benets of conserving habitat for pollinators in agricultural
systems.
A few studies have attempted to value wild pollinators, while a
much larger literature has attempted to value honey bee pollination.
For the most part, these valuations have focused on the benets to
producers, calculated as either 1) the cost of alternative pollination
sources (Allsopp et al, 2008), or 2) the value of production resulting
from bee pollination (Losey and Vaughan, 2006).
The rst approach estimating the cost of using an alternative
technology or organism to achieve the same function is commonly
known as the replacement value method. The idea is the same as
Ecological Economics 71 (2011) 8088
Corresponding author. Tel.: + 1 848 732 8315.
E-mail addresses: rwinfree@rutgers.edu (R. Winfree), brian.j.gross@gmail.com
(B.J. Gross), ckremen@berkeley.edu (C. Kremen).
1
Joint rst authors.
0921-8009/$ see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolecon.2011.08.001
Contents lists available at SciVerse ScienceDirect
Ecological Economics
journal homepage: www.elsevier.com/locate/ecolecon
Author's personal copy
valuation via input or factor substitution (Point, 1994). In the case of
native pollinators, this typically involves measuring the amount of
managed pollinators (usually honey bees) needed to replace the service
(de Grootetal.,2002). In the case of honey bees, this involves measur-
ing the cost of achieving pollination through either another managed
pollinator, hand pollination, or pollen dusting (Allsopp et al., 2008).
A second and more widely used approach focuses on the value of
crop production attributable to pollination. Production, or yield, is as-
sumed to fall when pollinators decline. The yield reduction is approx-
imated using studies of the dependency of fruit set on the presence of
insect pollinators (Klein et al, 2007). The expected fractional yield
loss in the absence of pollinators is then multiplied by the market
value of production (Morse and Calderone, 2000; Robinson et al,
1989). Studies interested in breaking down the service between
honey bees and native bees have estimated the proportion of pollen
deposited by respective taxa in crop elds and then used this to appro-
priate the value between the different pollinators (Allsopp et al., 2008;
Losey and Vaughan, 2006). With one notable exception, Olschewski et
al. (2006), these studies do not take account of production costs and
will be collectively referred to as production valueapproaches.
The replacement value and production value approaches produce
widely divergent results, and furthermore garner criticism on theo-
retical grounds. Allsopp et al. (2008) estimate the value of managed
honey bees and all unmanaged pollinators using both approaches;
the resulting values calculated for wild pollinators differ by nearly a
factor of a 100.
2
This alone is evidence that methodology deserves
further attention. But there are conceptual criticisms that additionally
call into question the validity of production value approaches. Muth
and Thurman (1995) raise two concerns in regards to the production
value approach: (1) it ignores the possibility for adjustments on the
part of the farmer that could abate the production losses and (2) that
it fails to distinguish between the average contribution [of pollinators]
and the marginal contribution(Muth and Thurman, 1995). These two
concerns, coupled with the empirical inconsistency, argue for an im-
provement to one or both of the methods.
In this paper, we rst unify the replacement value and production
value approaches conceptually by demonstrating that each is a spe-
cial case derived from the same general equation. Next, we address
the problematic issues raised above through a modication of the
production value approach. The choice to focus attention on the pro-
duction value method is supported by three considerations: it is the
most common method employed, the calculations are simple, and it
is relatively easy to acquire the necessary data. We illustrate this im-
proved approach, which we term the attributable net income meth-
od, using a data set on watermelon Citrullus lanatus pollination by
native bees and honey bees, and compare the resulting values to
those obtained by using the two traditional methods. By native
bees, we mean the native, unmanaged bees. Our denition of honey
bees includes both managed and feral Apis mellifera as it is not possi-
ble to separate the two in most data sets.
2. Field Study of Watermelon - Materials and Methods
The materials and methods for the eld study of watermelon are
briey summarized here and are reported at length elsewhere (Winfree
et al., 2007, 2008).
2.1. Study System
The eld study was conducted in 2005 at 23 watermelon farms lo-
cated in central New Jersey and east-central Pennsylvania, USA. The
study plant, watermelon, requires insect pollen vectors to produce
fruit because it has separate male and female owers on the same
plant (Delaplane and Mayer, 2000). An individual ower is active for
only one day, opening at daybreak and closing by early afternoon. In
order to be fully pollinated and set a marketable fruit, a female ower
needs to receive at least1400 pollen grains, and fruit production asymp-
totes when 50% of owers are fully pollinated (Stanghellini et al., 1997;
Stanghellini et al., 1998; Stanghellini et al., 2002; Winfree et al., 2007).
Knowledge of these values and in particular the rate of fruit abortion
gives greater condence in our economic estimates which could other-
wise be confounded by the relationship between pollination and fruit
production (Bos et al., 2007).
Sixty-ve percent of the farmers in the study either own or rent
hived honey bees for crop pollination purposes. Most honey bees
recorded in the study were probably managed bees, because feral
honey bees have been rare in the study region since in the 1990s
due to mites and other problems (Stanghellini and Raybold, 2004), al-
though they may be rebounding in recent years (Seeley, 2006). Be-
cause it is not possible to separate managed and feral bees in the
eld our estimates of honey bee pollination combine the two. Thus
our results will over-estimate the value of pollination from managed
honey bees alone.
2.2. Measuring Flower Visitation Rates and Pollen Deposition
Wevisitedeachfarmontwodifferentdaysandmeasuredbeevisita-
tion rate to watermelon owers in units of bee visits ower
-1
time
-1
.
Visits were recorded separately for honey bees and various types of na-
tive bees. Per-visit pollen deposition was measured by bagging unopened
female owers with pollinator-exclusion mesh, and then offering virgin
owers to individual bees foraging on watermelon. After a bee visited a
ower, the pollinated stigma was prepared as a microscope slide so
that the number of watermelon pollen grains could be counted with a
compound microscope (Kremen et al., 2002). Control owers were left
bagged until the end of the eld day, and contained few pollen grains
(mean= 3 grains, N = 40 stigmas). In the eld study of watermelon, we
observed a total of 6187 bee visits (2359 by honey bees and 3828 by na-
tive bees) and collected 271 counts of per-visit pollen deposition.
2.3. Simulation Methods
In order to estimate the contributions of honey bees and native
bees separately, we developed a Monte Carlo simulation (Matlab
R2006a, The MathWorks, Inc., 2006) of the pollination process. The
simulation estimates total pollen deposition by each bee taxon by
multiplying the daily number of visits to a watermelon ower by
the number of grains deposited per visit, using distributions based
on the eld data for both variables (Winfree et al., 2007). The esti-
mate is made separately for each of the 23 farms, and means and
standard errors (SE) are calculated across farms. Program output is
the frequency distribution across owers for the number of pollen
grains deposited on a ower over its lifetime by (a) all native bees
combined, and (b) honey bees. Further details of the simulation
methods are reported at length elsewhere (Winfree et al., 2007).
Simulation results indicated that across the study system as a
whole, native bees provide 62% ( 5% SE) of the pollen deposited on
female watermelon owers, and honey bees provide 38% ( 5% SE)
(Winfree et al., 2007). These values are used for the parameters ρ
nb
and ρ
hb
in our economic calculations, below. We also calculated the
fraction of owers at each farm that were fully pollinated by either
native bees alone or honey bees alone by comparing the amount of
pollen deposited on owers at a given farm to the pollination re-
quirements of the plant. The mean of these values taken across
farms is used below for the parameters F
nb
for native bees, and F
hb
for honey bees. Lastly, we calculated the fraction of farms where
the crop is fully pollinated by native bees (91% ± 6% SE) and honey
2
The authors calculate the value of wild pollinators using the production value
(proportional dependence) as $215.9 million. Although not specifying the value as
such, they also calculate the cost of replacing wild pollination with honey bees as
$2.6 million (Allsopp et al, 2008).
81R. Winfree et al. / Ecological Economics 71 (2011) 8088
Author's personal copy
bees (78% ±9% SE). These last values are used in the replacement
valuation method below.
3. Economic Valuation of Pollination: Theory and Methods
The goal of valuation studies of pollination services is to under-
stand the value that would be lost following the loss of certain polli-
nators (for example, native wild pollinators, or all pollinators) to a
specied area (for example, regionally, nationally, or globally). For
want of a logistically- and ethically- appropriate controlled experi-
ment, the loss of pollinators is posed as a hypothetical experiment.
A loss of pollinators could affect production of a pollinator-
dependent crop by reducing yield and/or by increasing the growers
costs. When pollinators are lost, fruit set might decline and as a con-
sequence overall yield falls. This is the most intuitive economic conse-
quence. But growers can also adjust inputs to compensate for the loss,
thus mitigating or eliminating yield losses, while increasing costs
instead.
These two effects both impact producer prots negatively, and ad-
equately describe the value lost from a loss in pollinators on a rela-
tively small scale. However if the pollination loss results in yield
reductions on a large enough scale, then the market price of the
crop may increase. This third, indirect effect positively impacts
growers both within and outside of the affected region. It also nega-
tively impacts consumers at a large scale.
To understand the value of pollination, we thus want to know the
aggregate economic effect of a change in the pollination service on
these three stakeholders: producers of the crop in the affected region,
producers of the crop outside this region, and consumers of the crop.
When the market price is unaffected by the hypothetical change in
pollination, then the value computation would involve only the rst
group: assessing the impact on production. But, computing the
value of pollination on a large scale, such as for an entire industry
or globally, involves assessing not only the impact on production
but also the economic consequences of market adjustments resulting
from this impact. For this reason, large scale analysis is analytically
distinct and considerably more complex than analysis on a small
scale. In this study, the (hypothetically) affected region, New Jersey
and Pennsylvania, produces less than 2% of the domestic market sup-
ply of watermelon, so we can reasonably rule out price effects in our
analysis. We therefore focus on yield and cost effects only. We invite
interested readers to see Appendix A for a discussion of valuation at
large scales, which includes price effects.
3.1. A Conceptual Framework for Pollination Value
Consider the production of a pollinator-dependent crop in a re-
gion that currently has a certain level of pollination service input,
denoted by q. Following McConnell and Bockstael (2005), we consid-
er agricultural prot, π, as the net value to production, or revenue
minus cost:
π=P·Y qðÞCYqðÞ;qðÞ ð1Þ
where Pis crop price, Yis the aggregate yield of the affected region,
which is a function of the amount of pollination service, q, to the re-
gion, and C(Y(q), q) is the total cost of production, which is a function
of both aggregate yield and pollination service to the region. We as-
sume here that price (P)isxed in accordance with the assumption
that the region's yield is small relative to the market supply.
The value of a certain amount of insect pollination (Δq) can then
be depicted by using the chain rule to consider the rst order changes
to net income were this amount of service to be eliminated:
Δπ =ΔY
Δq

CY·ΔY
Δq

Cq

Δqð2Þ
where ΔY
Δq

is the change in yield, if any, resulting from the change
in pollination, C
Y
is the marginal cost of production the extra cost for
producing one more (or less) unit of yield, and C
q
is a marginal cost
adjustment, such as the cost of renting more bees to compensate for
lost pollination, if any, for the change in pollination, Δq.
From Eq. (2) it can be seenthat the value of pollination to production
is composed of three components: revenue effects from yield changes,
cost adjustments to yield, and cost adjustments to pollination service.
For a loss in pollination (Δqb0), the value lost to producers is equal to
the revenue lost from reduced yield, less the cost savings from reduced
yield, plus the additional costs to substitute the lost pollinators.
There are circumstances in which one or more of the three compo-
nents will be negligible. In particular there are two important cases to
consider, which interestingly correspond with the two most promi-
nent valuation methodologies. The rst case occurs when pollinator
loss is perfectly substituted and thus no yield is lost. In this case, the
rst two components of Eq. (2) drop out and what's left is C
q
Δq, the
cost of the substitution. This is precisely what replacement cost stud-
ies estimate. When yield does not remain constant, then replacement
cost measures are not fully capturing the adjustments to production
(McConnell and Bockstael, 2005). In addition, yield may fall despite
substitution, or substitution may not occur if replacing the service is
too costly. For instance, measures of replacement cost that exceed
the total production value, as Allsopp et al. (2008) nd, would
never be pursued as farmers would rather lose the entire crop. Substi-
tution is a key component; however it typically cannot be decoupled
from yield effects.
The second case would be one in which the farmer does not com-
pensate in any way for the loss in pollinators. If the farmer is able to
neither employ substitutive pollination, nor reduce input costs in
the face of yield losses for example in the case of a sudden, unantic-
ipated loss of pollinators after all costs have already been outlaid
then the latter two terms of Eq. (2) would be dropped, leaving simply
PΔY
Δq

Δq, the lost revenue. This is exactly the calculation that pro-
duction value approaches use. However, if there is any capacity to ad-
just to the expected loss in pollination by reducing input costs, then
the production value approach will over-estimate the value of polli-
nation because it ignores cost adjustments.
3.2. Improving the Production Value Method
The production value method estimates the value of pollination
under this latter assumption of no substitutive pollination and com-
plete revenue loss. To estimate the change in yield the production
value approach uses the crop's dependency on insect pollination,
D, which represents the fractional reduction in fruit set that occurs
when insect pollinators are absent (Klein et al, 2007). Dis measured
as 1(f
pe
/f
p
), where f
pe
= fruit set under conditions of pollinator
exclusion and f
p
= fruit set with insect pollinators present. Then
ΔY
Δq

Δq, the expected reduction of yield for a ρ%reductioninin-
sect pollinators, is approximated as YDρ. Substituting this ex-
pression in for the lost revenue results in the common equation
used in production value approaches (Allsopp et al., 2008; Gallai
et al., 2009; Kremen et al., 2007; Losey and Vaughan, 2006; Morse
and Calderone, 2000; Robinson et al., 1989):
VΔpollination =P·Y·D·ρð3Þ
The value of all pollination is calculated by replacing ρwith 1. The
value of pollination contributed by particular taxa, for example, the
value of all pollination from native bees, or from honey bees, is calcu-
lated by replacing ρwith ρ
nb
or ρ
hb
, which represents the fraction of
all pollen grains that are deposited by native bees or honey bees,
82 R. Winfree et al. / Ecological Economics 71 (2011) 8088
Author's personal copy
respectively. When pollination data are not available, ρ
nb
or ρ
hb
can
be estimated as the fraction of all ower visits provided by each
group, which should provide a reasonable proxy in most cases
(Vazquez et al, 2005).
A problem we have noticed in the published literature is that the
calculation of Eq. (3), is commonly applied in contexts other than the
special case for which it is appropriate. First, the calculation is often
employed for nation-wide or global analysis (e.g. Gallai et al., 2009;
Losey and Vaughan, 2006; Morse and Calderone, 2000; Robinson et
al., 1989), in which case the assumption that prices are unaffected
is not valid. Secondly, most studies are interested in valuing the pol-
lination service in annual terms. Under these circumstances, the as-
sumption that producers could not adjust their input mix to
accommodate the reduced pollination every year is awed, and
leads to inated values for pollination services (Muth and Thurman,
1995). We discuss these issues at greater length in the Discussion
and Appendix A.
The production value approach can be amended easily by consid-
ering changes to costs. Cost adjustments to yield can be estimated
using estimates of yield change and the marginal cost of production.
When measures for marginal costs can't be found, they can be ap-
proximated using average variable costs. Variable costs, which are de-
ned as the expenses that vary according to output, will fall by
approximately the same proportion that quantity declines, D. Using
VC to denote total current variable costs, the assumption can be
expressed as ΔC(Y,q)VCΔY/Y ≈−VC D. This approximation will
generally over-estimate the cost adjustment to yield (McConnell
and Bockstael, 2005), since some variable costs may not be reduced
in proportion to Dfor example, if the farmer is not aware of polli-
nation failure until after some costs have been incurred.
We can now use a simple calculation to represent the value
depicted in Eq. (2):
VΔpollinationP·YVCðÞ·D·ρð4Þ
where VC again denotes the total variable cost, and other terms are de-
ned in Eqs. 1 and 3. We term this approach the net income method fol-
lowing Point (1994).WenotethatOlschewski et al. (2006) used a
similar approach by reporting changes in net revenue.The only dis-
tinction between their method and ours is that we include only variable
costs in VC, on the assumption that only variable costs willbe recouped
should pollination fail, whereas Olschewski et al. used total costs.
The second issue that our new valuation method addresses is the
calculation of expected yield reductions, and the importance of accu-
rately relating pollen deposition to the expected yield. Most plants
have a threshold number of pollen grains that are required to set
the maximum-sized fruit; this is referred to as the plant's pollination
threshold. Additional pollen deposited beyond this threshold will not
increase yield. Pollination thresholds can be exceeded in agricultural,
as well as natural, settings. For example, in our eld study, pollen de-
position exceeded the threshold for watermelon fruit set at all farms
(see Fig. B.1).
In the context of over-pollination, the question arises as to which
pollinators are residual that is, superuous. The answer to this ques-
tion need not be the same in all contexts. In many cases farmers rent
honey bees for their crops, a choice that can be revoked, whereas na-
tive pollinators are provided by the ambient ecosystem. This implies
that honey bee pollination is more easily removed and thus deemed
superuous. Counterexamples exist, such as when honey bees are
feral (supplied by the ambient ecosystem) or come from hives be-
longing to someone else, the farmer has no control over them. And
in some situations, farmers can affect native bee populations by mod-
ifying habitat on the farm. In this case, the habitat management deci-
sion could be revoked, and native bee pollination considered
superuous. We present the results in both ways to cover all cases.
3.3. Attributable Net Income Method
We derived the parameter values for our study area as follows. We
estimated the annual dollar value of watermelon production in New
Jersey and Pennsylvania combined (PY) using the total ha in water-
melon production
3
, watermelon production in kg per ha
4
, and price
per kg
4
. For watermelon D = 1 because f
pe
=0(Stanghellini et al.,
1998); that is, watermelon doesn't produce any fruit under condi-
tions of pollinator exclusion and thus its dependency on pollinators
is 100%. We used the output of the simulation to calculate the fraction
of all pollen deposition attributable to native bees (ρ
nb
), along with its
SE. The value for honey bee pollination (ρ
hb
) was estimated similarly.
In a second step, we subtract the costs of variable inputs to pro-
duction from the total production value. In place of PY, the total pro-
duction value, we now use (PYVC), where VC is the summed cost
of all known variable inputs to production. Crop production budgets
provided by extension programs are a good source for average costs
per unit yield and this is what we used for our calculations
5
. As an in-
termediate step, we compare these results, which we term net in-
come, to the other methods.
We then modify the equation to relate the pollination delivered to
the pollination needs of the crop, and to partition the resulting value
among various taxa of pollinators. First, rather than attributing value
to native bees according to the fraction of total pollen that they de-
posit (ρ
nb
), the attributable net income method values only the pollen
that is needed for fruit production. In other words, it does not value
pollen delivered in excess of the pollination requirements of the
plant. In this way it directly ties the ecosystem service (pollen depo-
sition by native bees) to the production of value to people (market-
able watermelon fruits). Second, the attributable net income
method accounts for the presence of other pollinator taxa by option-
ally considering a given taxon as either the primary pollinator in the
system (i.e., all of the pollination it provides up to the plant's pollina-
tion threshold is valued) or residual (i.e., the pollination it provides is
only valued if the pollination already provided by other pollinator
taxa is insufcient).
We demonstrate the attributable net income method by consider-
ing native bee pollination rst, and valuing honey bee pollination
only in addition to native bee pollination. However, the alternate
order (honey bee pollination valued rst, native bee pollination sec-
ond) can also be done and those numbers are also presented in the
Results.
Eq. (5) values native bee pollination based on the extent to which
native bees alone fully pollinate the crop. There are two components
to full pollination: at the ower scale, a ower must receive a certain
amount of pollen deposited in order to set a marketable fruit; and at
the eld scale, fruit set will asymptote as the percentage of owers
that are fully pollinated approaches a saturation point. In the case of
watermelon, a ower must receive 1400 conspecic pollen grains
in order to set a marketable watermelon fruit, and fruit set asymp-
totes at the eld scale when around 50% of owers are fully pollinated
(see Methods 2.1). These two components can be incorporated into
the value function:
Vnb =P·YVCðÞ·D·min 1
αFnb;1
 ð5Þ
3
Based on data recorded by agricultural extension agents in eachstate: for New Jersey,
by M. Henningerof Rutgers University, andfor Pennsylvania,by M. Orzolekof Pennsylvania
State University (Henninger and Orzolek, pers. com.).
4
USDA-NASS2010. Values from 2009 for the neighboring state of Delaware wereused
because USDA-NASS does not record watermelon production statistics for New Jersey or
Pennsylvania.
5
Source for watermelon production cost budget: University of Delaware Cooperative
Extension Vegetable Crop Budgets 200920011, available online at http://ag.udel.edu/
extension/vegprogram/publications.htm.
83R. Winfree et al. / Ecological Economics 71 (2011) 8088
Author's personal copy
Where VC= the summed costs of the producersvariable inputs to
watermelon production, α= the asymptotic fruit set proportion at
the eld scale, i.e. the maximal proportion of owers that can produce
fruit, F
nb
= the fraction of owers that are fully pollinated by native
bees, i.e., that receive 1400 pollen grains from native bees,
6
and
the other parameters are as in Eq. (3).
Honey bee pollination is valued based on the additional pollina-
tion honey bees contribute, above the amount contributed by native
bees but only up to the pollination threshold:
Vhb =P·YVCðÞ·D·min 1
αFhb;1min 1
αFnb;1

ð6Þ
Where F
hb
= the fraction of owers that are fully pollinated by
honey bees and the other parameters are as in Eqs. (3) and (5).As
in Eq. (5), the factor of 1
αassociated with the F
hb
and F
nb
terms ac-
counts for the fact that fruit production asymptotes when 50% of
owers are fully pollinated.
All valuations reported in this paper were done using 2009 US dol-
lars. In all ofour estimates we were only able to propagate error through
the parameters obtained from our own work (ρ
nb
,ρ
hb
,F
nb
,F
hb
;from
Winfree et al, 2007). The parameters obtained from other sources did
not include the information necessary to propagate error. Therefore,
the standard errors (SE) reported in the Results are under-estimates
of the true SE.
3.4. Replacement Value Method
A replacement value for native bee pollination is what it would cost
farmers to rent enough honey bees to replace the pollination currently
provided by native bees. We calculated this value by multiplying the
area in watermelon production (746 ha)
2
by the industry-wide recom-
mended honey bee stocking rate ( 4.5 hives ha
-1
;Delaplane and
Mayer, 2000) by the annual rental cost of a honey bee hive in the
study area ($60-$75 hive
-1
)
7
by the fraction of farms at which native
bees alone are fully pollinating the crop (91%). We used the same
method to estimate the replacement value of honey bee pollination,
substituting the fraction of farms fully pollinated by honey bees
(78%) for the fraction fully pollinated by native bees (91%). This re-
placement value represents what it would cost to replace the pollina-
tion services currently provided by honey bees with equivalent
services provided by new honey bees.
Our calculation of the replacement value differs from what has
been used by other workers, who have not included information
about how much pollination bees are currently providing (our coef-
cients of 0.91 and 0.78 above). For this reason, these previous esti-
mates are too high. Previous estimates value what it would cost to
provide complete pollination by honey bees, not what it would cost
to replace the pollination provided by native bees.
4. Results
The value of native bee pollination based on the replacement
value of renting enough honey bee hives to replace native bees is
$0.21 million year
-1
(range, $0.20 - $0.21 million year
-1
) and the re-
placement value of honey bee pollination is $0.18 million year
-1
(range, $0.17 - $0.18 million year
-1
); (Fig. B.2). The results are pre-
sented as ranges because one of the input variables, the cost of hive
rental, is only available as a range.
The production value method provides a higher estimate. The esti-
mated annual production value of watermelon in New Jersey and
Pennsylvania combined (PY), before subtracting the costs of inputs
to production, is $7.64 million year
-1
. Multiplying this production
value by the 62 5% (SE) of all pollen deposition done by native
bees provides an annual value of $4.74± 0.38 (SE) million for the pol-
lination service provided by native bees. For honey bees, the corre-
sponding value is $2.90± 0.38 (SE) million year
-1
(Fig. B.2). After
subtracting the costs of variable inputs to production, the estimated
annual net income value (Eq. (4)) of watermelon in New Jersey and
Pennsylvania combined is $3.63 million year
-1
, leading to estimates
of $2.25 0.18 (SE) million for the pollination services provided by na-
tive bees and $1.38 0.18 (SE) million year
-1
for honey bees (Fig. B.2).
The annual attributable net income value of native bee pollination,
when native bees are considered primary pollinators (Eq. (5)), is
$3.40± 0.16 (SE) million year
-1
. The value of honey bee pollination,
when honey bee pollination is valued residually (Eq. (6)), is $0.24 ±
0.16 (SE) million year
-1
(Fig. B.2). When honey bee pollination is val-
ued as primary (Eq. (5)), its value is $3.07 ± 0.25 (SE) million year
-1
.
When native bee pollination is valued residually (Eq. (6)), its value is
$0.56± 0.25 (SE) million year
-1
(Fig.B. 2).
5. Discussion and Conclusions
There is a great need for a better understanding of ecosystem ser-
vices in terms of both their ecology (Kremen and Ostfeld, 2005) and
their economic value (Daily et al., 2000; Turner et al., 2003). There
are many methods for valuing ecosystem services and each has its
limitations (Heal, 2000; Turner et al., 2003). Our goal here is to
make these valuation methods more consistent and their assump-
tions more explicit, using pollination as a model ecosystem service.
We rst demonstrate that the two main valuation methods currently
in use, the replacement value and the production value methods, are
special cases of the same general equation (Eq. (2)). We then use a
single data set to compare the estimates of producer-side pollination
service value obtained with these two widely-used methods, as well
as with a third valuation method that we develop here and call the at-
tributable net income method. The attributable net income method
modies the production value to subtract the costs of inputs to pro-
duction, thereby reducing the extent to which this method over-
estimates pollination value. It also accounts for the pollination re-
quirements of the plant, and the pollination already provided by
other pollinator taxa, thereby better relating the measured service
(pollination) to the marketable good (fruit production). The attribut-
able net income method produces valuations that are intermediate
between those obtained with the replacement value and the produc-
tion value approaches. We further discuss the strengths and limita-
tions of these methods, and the relationships among them, below.
The replacement value method assumes that production does not
change when pollinators are lost, and values the cost of obtaining re-
placement pollination services. For native bee pollination this re-
placement is based on the cost of renting honey bees, since for most
crops the given level of pollination from native bees could be
obtained equivalently from honey bees. We measured this value
using current honey bee rental costs and obtain a relatively small
value (Fig. B.2). However, this method assumes that honey bees are
indenitely available as a replacement for native pollinators, whereas
an important component of the value of native bees is their ability to
compensate, in part, for the potential loss of the honey bee. Current
challenges to honey bee health such as Colony Collapse Disorder
(VanEngelsdorp et al., 2009) make the assumption of indenite
honey bee availability questionable. Furthermore, the replacement
value method excludes potential future price increases in honey bee
rental costs, which seem likely given continued honey bee health
problems. For example, the cost of renting a single honey bee colony
for almond pollination increased from $35 in the early 1990s to $150
6
As for ρ
nb
, values of F
nb
come from the data and simulation presented in Winfree et
al., 2007.
7
Range of rental costs for pollinating cucurbit crops in our study region; Tim Schuler,
State Apiarist for New Jersey, pers. com. Prices vary by beekeeper and according to the
number of hives rented,but no further information that would allow a variance to be cal-
culated is available.
84 R. Winfree et al. / Ecological Economics 71 (2011) 8088
Author's personal copy
in 2007 (Johnson, 2007). The same conceptual problems apply when
this method is used to calculate the replacement cost for honey bees,
i.e., the cost of replacing the existing honey bees with new honey bees.
An alternative way to use the replacement value method, which
does not assume the availability of honey bees, would be to calculate
the cost of a replacement for both native bees and honey bees, such as
hand-pollination by people (Allsopp et al., 2008). This approach pro-
duces much higher valuations (Allsopp et al., 2008) but is only possi-
ble for the small number of crops that have been pollinated by other
means other than bees. No cost estimates for non-bee pollination of
watermelon are available.
The production value method makes the opposite assumption
from the replacement value method: it assumes that no replacement
for the lost pollinators is possible, and values pollination services as
the loss in production that would occur subsequent to pollinator loss.
This widely-used method (Allsopp et al., 2008; Gallai et al., 2009;
Losey and Vaughan, 2006; Morse and Calderone, 2000; Robinson et
al., 1989), essentially calculates the proportion of the total value of
the crop that depends on pollinators. There are several problems
with the production value method which may lead it to its over-
estimating the producer welfare value of pollination. The attributable
net income method corrects most of these problems.
First, the production value method ignores the possible reduction of
other inputs to production that would ensue from a signicant loss in
production capability (McConnell and Bockstael, 2005). For example,
if pollination failed then farmers would not invest further in inputs
that vary with yield, such as harvest costs. The production valuemethod
disregards these cost savings, thereby over-estimating the value of pol-
lination. This problem can be ameliorated by subtracting the costs of
variable inputs production from the value of production, as we do in
our net income method. In our case this reduces the value of pollination
services by 52% (Fig. B.2), and suggests that many of the previous esti-
mates of pollination value have been too high. Absent the distinction
of xed and variable costs, the subtraction of total costs as done by
Olschewski et al. (2006) would still be preferable, thereby attributing
the net, not the gross, value of crop production to pollination.
A second problem with the production value method is that the
method assumes all the pollen deposited is necessary for fruit set,
whereas in reality plants may be getting more pollination than they
need (Muth and Thurman, 1995). The attributable net income meth-
od solves this problem by valuing only the pollination that is likely to
be utilized in fruit production, i.e., the pollen delivered up to the
threshold pollination requirements of the plant. The attributable net in-
come method also allows for valuing a given pollinator taxon either in-
dependent of, or in addition to, another taxon. In systems such as ours
where most farms are over-pollinated, the decision about whether to
consider a pollinator taxon as primary or residual can lead to a 613
fold difference in its ecosystem service value (Fig. B.2). This highlights
the importance of specifying the goal of the valuation - a decision that
must be made by stakeholders or users.
A third problem with the production value method is that it does not
account foropportunity costs in this case changes growers could make
if pollination became more costly, such as switching to less pollination-
dependentcrops (Muth and Thurman, 1995; Southwick and Southwick,
1992). These are long-term considerations, however. Both the produc-
tion value and the attributable net income methods are best interpreted
as estimates of values over the short-term.
A fourth problem with the production value method is that it as-
sumes the market price of the output crop is xed, and would not adjust
to the resulting loss in yield. If the area in question is signicant say, at
a national scale or even for a large region the resulting (hypothetical)
loss in yield would surely affect the market price and mean the calcula-
tion is not accounting for the consequential effects. It is problematic
then that this method has been used in contexts where its assumptions
are violated. While theattributable net income method presented in the
text suffers from the same limitation, we present in Appendix A a
generalized attributable net income method and framework for calcu-
lating the value of pollination in these larger contexts.
In this paper we have shown that the two commonly used methods
for valuing pollination services to agriculture, the replacement value
method and the production value method, are special cases of the
same general equation. This equation has implicit spatio-temporal as-
sumptions which we clarify here as they have at times been violated
in the published literature. We introduce a new method, Attributable
Net Income, which overcomes some of the limitations of existing
methods. In so doing, it brings the valuation of the regulating service
of pollination into better alignment with the provisioning service that
provides the nal utility to people: crop production. We hope that this
work moves the science of ecosystem service valuation one step closer
to the level of accountability required for use in the policy arena.
Acknowledgements
We thank the farmers and research assistants who participated in
the watermelon eld study; Neal M. Williams for assistance with the
eld study of watermelon pollination and for comments on the manu-
script; and David Zilberman and Kenneth Mulder for their insights
about developing the attributable net income method of valuation.
Funding for the watermelon eld work and/or support for RW was pro-
vided by the National Fish and Wildlife Foundation and NSF collabora-
tive grant #DEB-05-54790 / #DEB-05-16205 (PIs CK and Neal M.
Williams, Co-PI RW). BJG was supported by funding from McDonnell
Foundation 21st Century Award (PI CK), the Chancellor's Partnership
Fund (PIs CK and D. Zilberman), an NRCS California Conservation Inno-
vation Grant (PIs CK and S. Hoffman-Black), and Genome British Colum-
bia (PI L. Foster).
Appendix A. Generalizing the Framework to Larger Scales
In Section 3.1, we discussed valuing a loss in pollination when the
scale of the loss was small enough to not affect the market price of the
crop. One of the shortcomings of this framework is that it is not appli-
cable for valuations on the global, national or even regional scales if
the output of the area in question represents a sizable portion of the
market. In this Appendix, we generalize the model to allow for price
effects, and thus provide a more broadly applicable framework.
Our objective here is to articulate the necessary components for this
more comprehensive analysis. The layout is as follows: we rst depict
the total welfare at stake when it comes to a loss in pollination, we
then relate the approaches of existing studies within this framework,
and end by simplifying the calculation of each component to maximal-
ly take advantage of existing data. The approach of this framework is,
as in the main text, a rst order approximation: a linearized prediction
of outcomes based on small changes from the current situation.
A loss of bees is assumed to occur for a specied area, and directly
impact the production of a pollinator-dependent crop in this area,
which we now denote by a. If both the effect on yield and the area's
total production relative to the market are signicant, then the mar-
ket price of the crop may adjust and consequently affect two addi-
tional stakeholders apart from the producers in the area: consumers
of the output crop, as well as producers of the crop in other areas,
the latter of which will be denoted by a.
The total social welfare then is the sum of net benets accruing to
the producers of the crop in the area, to producers of the crop outside
the area, and to consumers of the crop:
SW =πa+πa+CS ðA:1Þ
where π
a
is net income (or prot) of producers in the affected area,
π
a
represents the net income to producers in the rest of the market,
and CS represents the consumer surplus the value to consumers
for the output crop.
85R. Winfree et al. / Ecological Economics 71 (2011) 8088
Author's personal copy
We now dene each of the three terms in Eq. (A.1). The producer
prot of the affected area is very similar to that laid out in Section 3.1,
with one important exception:
πa=PY
a+Ya

·YaCY
a;qa
ðÞ ðA:2Þ
Here, unlike in Eq. (1), the price, P, is now recognized to be a func-
tion of the total market production, which is the sum of that produced
within the area (Y
a
) with that from the rest of the market (Y
a
). But
apart from the substitution of P, the equation is otherwise the same as
before (now with subscripts a). In a similar fashion, the producer
prot of the entire market, less the affected area, is dened as
πa=PY
a+Ya

·YaCY
a;qa
 ðA:3Þ
For simplicity, we assume the same cost structure, C(Y,q), for both
the affected area and out-of-area producers.
The value of the crop to consumers is dened as the consumer sur-
plus and is represented by the area above the price and under the de-
mand curve for the crop:
CS PðÞ=P
PQpðÞdp ðA:4Þ
where Q(p) is market demand at price p, and Pis the threshold price
above which there is no demand.
The loss of insect pollination to the area (Δq
a
) can then be valued
by considering rst order changes, employing prodigious use of the
chain rule, to total social welfare (Eq.(A.1)) were this amount of ser-
vice to be eliminated:
VΔpollination =Δπa
Δqa
+Δπa
Δqa
+ΔCS
Δqa

Δqa
=ΔP
ΔYa

·ΔYa
Δqa

·Ya+ΔYa
Δqa

CY·ΔYa
Δqa

Cq

Δqa
+ΔP
ΔYa

·ΔYa
Δqa

·Ya

Δqa
+Ya+Ya

·ΔP
ΔYa

·ΔYa
Δqa

Δqa
ðA:5Þ
where ΔYa
Δqa

is the change in the area's yield, if any, resulting from
the change in pollination, ΔP
ΔYa

is the change in crop price, if any,
resulting from the change in yield, and as before C
Y
is the marginal
cost of production the extra cost for producing one more (or less)
unit of yield, and C
q
is cost adjustment, if any, for the change in polli-
nation, Δq
a
. Eq. (A.5) is cumbersome, but not overly complex once it
is broken down and simplied. The rst line is very similar to
Eq. (2), with an additional term for the change in price, ΔP
ΔYa

. This
line represents the value to the area's producers. The second line repre-
sents the spillover effects of the area's productivity to producers outside
the area. And the last line represents the change in Consumer Surplus.
Eq. (A.5) can be verbally interpreted as follows. A loss in pollina-
tion potentially affects the welfare of three groups: affected area's
producers (the rst line of Eq. A.5), out-of-area producers (the second
line), and consumers of the crop (the last line). If the crop price rises,
consumer welfare unambiguously declines, out-of-area producers
unambiguously gain with higher prices, while affected producers
could lose or gain depending on the magnitude of the price effect.
The economic effect on producers in the area is equal to the revenue
gain from increased price, less the revenue lost from reduced yield,
plus the cost savings from reduced yield, less the additional costs to
substitute the lost pollinators. While in most cases we would expect
producers to lose when a environmental service is stripped away,
the potential for price increases to negate this loss is important and
must not be disregarded. As will be discussed below, existing studies
have estimated measures of impacts on one of these three groups, but
what Eq. (A.5) demonstrates is that the appropriate valuation should
unite producer and consumer welfare in a single value calculation.
As discussed in Section 3.1, there are certain circumstances in
which one or more of the terms will be negligible. In that section
we presented two important cases which correspond with the two
most common methodologies employed. In the rst case, yield losses
are averted through input substitution leaving just C
q
Δq
a
(the re-
placement cost), which is still the case under this framework. The sec-
ond case was sudden, short run loss precluding any possible cost
adjustments. From Eq. (2), this resulted in PΔYa
Δqa

Δqa(the produc-
tion value approach). The more complete framework presented here
reveals the limitations of that approach. First, we see that ignoring the
change in price means that production value calculations overesti-
mate the value to the area's producers (who can benet from price in-
creases), while ignoring entirely the possible spillover benets to
other producers (who benet from those same increases while not
sustaining yield losses). Second, the production value approach calcu-
lation ignores the loss to consumers, which is an important compo-
nent of the value of pollinators, and provides no guidance as to how
that loss compares with the value calculated for producers.
Focusing on that consumer welfare component, a third case is
worth considering. This case corresponds with another common
methodology, consumer surplus approaches. As it has been framed
in existing studies, this analysis focuses on the so-called long run
(Southwick and Southwick, 1992). The long run assumption is that
crop choice is not xed and entry is free so supply is highly elastic.
Even slight changes in price drive large changes in supply: an increase
in price drives supply up as more land is enrolled into production, and
the converse is true for price decreases. The net result is that price
changes very little as increased or decreased production moves the
price back towards the long-run equilibrium. Thus, long-run supply
is more-or-less at (i.e. long-run price is xed), implying zero prot.
It should be noted at this point that this long-run assumption of per-
fect elasticity (an implication of zero prot) is less a reection of real-
ity as it is a simplifying assumption to focus solely on consumer
surplus: with zero prots, the rst two terms of Eq. (A.1) vanish
and we are left with only the consumer surplus. The marginal impact
is then just: Ya+Ya
ðÞ·ΔP
ΔYa

·ΔYa
Δqa

. This is the measure used
by Southwick and Southwick (1992) to value pollination services.
Another study has considered consumer surplus losses and is worth
an extended discussion. Gallai et al (2009) estimate the global value of
pollination using a production value approach in addition to a quantita-
tive consideration of consumer surplus effects. The scale of analysis in
that study (a global assessment) certainly implies price effects and so
a production value approach alone would not be sufcient. Thus the
consideration of consumer surplus is warranted. However, there are
three problems with the approach of Gallai et al (2009).Therst prob-
lem is that costs are not included; thus if producers are able to adjust
and/or substitute for the loss in bees, the value calculation will be an
over-estimate. The second issue is that the total value of pollination is
comprised of the sum of the welfare changes to producers and to that
of consumers (see Eq. (A.5))thus, while Gallaietal(2009)calculate
both, the two should be united in a single calculation. The third issue
is a conceptual one. As stated above, the consumer surplus approach
of Southwick and Southwick (1992) assumes prot to be negligent,
which is an assumption that runs into direct conict with the produc-
tion value approach, which measures the effect of pollination loss on
prot. Instead, the calculation of consumer surplus need not follow
the framework of Southwick and Southwick (1992), which ignores
the effects on producers, and can instead simply estimate consumer
surplus effects as but one component of the overall calculation, as in
86 R. Winfree et al. / Ecological Economics 71 (2011) 8088
Author's personal copy
Eq. (A.5). Despite these issues, Gallai et al (2009) make an important
step in the right direction by at least considering measures of losses to
both producers and consumers.
As the main point of this Appendix is to elucidate efcient and suf-
cient ways of calculating the value of pollination, we now attempt to
simplify Eq. (A.5). The main text focuses on the terms ΔYa
Δqa

,C
q
, and
Δq
a
, so here we focus on the key additional term in Eq. (A.5) the
change in price, ΔP
ΔYa

and how to estimate it. The question is:
what is the relationship between the area's yield and the market
price? This relationship is contained within a parameter commonly
estimated in industry analyses: the price elasticity of supply. The
price elasticity is denoted
a
,dened as a=ΔYa
ΔP

P
Ya, and repre-
sents the sensitivity of supply to changes in price (specically, it is
the percent change in supply for a 1% change in price). Rearranging
this denition, we have the simple representation of the change in
price as a result of a change in area yield:
ΔP
ΔYa

=1
a

·P
Ya
:ðA:6Þ
In other words, the price change can be estimated with the current
price, the area's yield and an estimate of the price elasticity of supply.
We can then use this equation for the change in price to substitute
for ΔP
ΔYa

in Eq. (A.5), exchanging variables for quantities that are
more easily measured, and simplifying the value calculation. Using
Eq. (A.6), and in some cases grouping terms, the total value of the pol-
lination (Eq. (A.5)) can be simplied to:
VΔpollination =1+
1
a

·P· ΔYa
Δqa

CY·ΔYa
Δqa

Cq

Δqa
+1
a

·ΔYa
Δqa

·Ya
Ya

Δqa
+1
a

·ΔYa
Δqa

·Ya+Ya
Ya

Δqa:
ðA:7Þ
Eq. (A.7) has the same elements as Eq. (A.5), but now it is
expressed entirely in variables that can be estimated using current
data and information. And to reiterate, this value calculation unites
producer and consumer welfare in a singular calculation, and does
so without requiring the assumptions that are made in the existing
production value and consumer surplus approaches.
The framework presented in this Appendix represents an approx-
imation to the value of pollination at scales large enough to impact
supply and the market price. The strength of this framework is that
it unites the values for different components (that is, the different
stakeholders affected by pollination) within a single calculation, and
allows for comparisons between different existing methodologies.
The main drawback of this framework, which is common to all cur-
rent approaches, is that it extrapolates welfare effects based on a lim-
ited set of information. The framework utilizes current measures of
yield, price, and price elasticity of supply, along with ower-level es-
timations of crop-pollination dependency, to predict the effect a loss
of pollination on aggregate supply and producer and consumer wel-
fare. It does this by considering rst-order changes to supply (or in
other words, assuming linear supply and demand curves around the
equilibrium), which works well for small changes in supply and
price. It can be improved by considering second-order effects (that
is, non-linear supply and demand curves), or using actual estimates
of supply and demand curves and impacts. We invite further work
that would make this approach more applicable to large scale
analyses.
Appendix B. Figures
Fig. B.1. Pollen Deposition by Bees.
A graphical representation showing how different valuation methods
attribute value to multiple pollinator taxa. In this example using data
from one of our study farms, native bees deposit a median of 5427 grains
per ower and honey bees deposit a median of 2558 grains per ower,
whereas asymptotic fruit set is obtained when the median ower re-
ceives only 1400 grains (the pollination threshold, indicated by the red
line). The production value method attributes 68% (= 5427/7985 grains)
of the crop pollination to native bees, and 32% (=2558/7985 grains) to
honey bees. In contrast, because each taxon fully pollinates the crop,
the attributable net income attributes 100% of the pollination to which-
ever taxon is valued rst, and 0% to the taxon valued second.
Fig. B.2. Calculating the Value of Pollination.
The annual value of watermelon pollination by honey and native bees
in New Jersey and Pennsylvania, as estimated using different valuation
methods. PV: Production Value, NI: Net Income, ANI_hb1: Attributable
net income, honey bees primary pollinators, ANI_nb1: Attributable net in-
come, native bees primary pollinators, RV: Replacement Value. Depend-
ing on which pollinator is deemed primary and which residual, the
attributable net income results differ signicantly for each taxa, although
in sum remain the same as net income.
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