An ecological economic assessment of risk-reducing effects of
species diversity in managed grasslands
Finger, Robert; Buchmann, Nina
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Ecological Economics 110, http://doi.org/10.1016/j.ecolecon.2014.12.019
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Finger, R., Buchmann, N. (2015). An ecological economic assessment of risk-reducing effects of species
diversity in managed grasslands. Ecological Economics 110: 89–97.
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An ecological economic assessment of risk-reducing effects of species diversity in managed
Authors: Robert Finger, Nina Buchmann
Abstract: Over the last decade, it has been shown in the ecology literature that species diversity
increases yield stability in managed grasslands. Here, we develop and apply ecological economic and
econometric frameworks to evaluate potential risk-reducing effects of species diversity in terms of yields
and their temporal stability from a farmer’s perspective. Our empirical analysis is based on a rich panel
data set obtained from a diversity experiment covering in total 60 species and a period of 6 years. We
find empirical evidence for the risk-reducing effect of species diversity and the economic assessment
reveals significant insurance values associated with diversity for a risk-averse decision maker. Thus, the
economic value of diversity would be underestimated if not accounting for this property, and species
diversity may serve as valuable ex-ante risk management strategy.
Keywords: species diversity, risk, insurance value, grassland, yield, stability
There is ample evidence for a positive effect of species diversity on net primary productivity of
ecosystems (see e.g. Cardinale et al. 2012, Hector et al., 1999, Hooper et al., 2012, Isbell et al., 2011,
Tilman et al., 2005). Furthermore, a wide body of research has indicated an increase in the resilience
and resistance of ecosystems with higher species diversity (e.g. Roscher et al., 2008, Baumgärtner, 2007,
Haddad et al., 2011, Lehmann and Tilman, 2000, Walker et al., 1999, Naeem and Li, 1997). A particular
focus of this literature was laid on grassland systems, due to their high relevance for feed and food
production and for the provision of ecosystem services. From a farmer’s perspective, increased on-field
diversity may thus imply higher mean profitability (e.g. Hodgson et al., 2005). Moreover, diverse
grassland systems have been found to be more stable in terms of production (Hector et al., 2010, Proulx
et al., 2010, Marquard et al., 2009). For instance, higher diversity has been found to reduce the
vulnerability of grassland to climatic extreme events such as droughts as well as to pests and diseases
(e.g. Kahmen et al., 2005, Lin 2011, Sanderson et al., 2004, Vogel et al., 2012). The higher temporal
stability of production resulting from higher species diversity might be additionally valued by farmers
because a less volatile biomass production increases the utility of a risk-averse decision maker. Along
these lines, Lugnot and Martin (2013) show that French farmers and farm advisors perceive the risk
reduction property of plant diversity as important factor, and diversity is perceived to serve as an
insurance-like mechanism. Thus, the economic value of on-field species diversity for farmers might be
substantially underestimated if only mean returns from grassland yields are considered. If farmers
account for these effects in their grassland management decisions, this also underlines that farmers’ risk
preferences might shape agroecosystem diversity (e.g. Di Falco, 2012, Mouysset et al., 2013).
The potentially risk decreasing property of species diversity and its relevance for optimal management
of ecosystems has been the subject of several recent studies (e.g. Baumgärtner, 2007, Baumgärtner and
Quaas, 2009, 2010, Derissen et al., 2011, Di Falco and Chavas, 2006, 2009, Dörschner and Musshoff,
2013, Koellner and Schmitz, 2006, Schläpfer et al., 2002). However, the empirical literature
investigating the relationship between species diversity in grasslands, production risks and its valuation
from the farmers’ perspective is still scarce (see e.g. Baumgärtner and Quaas, 2010, Di Falco, 2012,
Dörschner and Musshoff, 2013, Koellner and Schmitz 2006, for recent overviews). Furthermore, these
empirical studies have relied either on a small number of years (e.g. Schläpfer et al., 2002), on
combinations of different, independent sets of short-term experimental data (e.g. Koellner and Schmitz
2006) or highly aggregated data (e.g. Dörschner and Musshoff, 2013). Thus, these approaches have not
fully accounted for the field-level effects of species diversity on (the distribution of) grassland yields
over time (e.g. arising from variable weather conditions) and space (e.g. due to different biophysical
conditions). Furthermore, earlier research has often relied on comparisons of a limited number of
grassland systems with respect to its species diversity (e.g. Dörschner and Musshoff, 2013, Schläpfer et
al., 2002). Overall, these studies do not allow to sufficiently specify and test the relationship between
species diversity and production risks.
Thus, based on a comprehensive panel dataset from the Jena Experiment, one of the longest running
biodiversity experiments in Europe (see e.g. Roscher et al., 2004, and Weigelt et al., 2010 for details).
we investigate the value of species diversity in managed grassland from the farmer’s perspective with a
specific focus on its effects on production risks. We develop an ecological economic and econometric
framework capturing the relationship between species diversity and production risk. Our empirical
analysis estimates stochastic specifications of production functions, which are then combined with the
developed economic model, integrating both components in the assessment of risk reducing effects of
species diversity in managed grasslands. Finally, this setup is used to derive certainty equivalents, risk
premiums as well as insurance values of diversity under various scenarios for output prices, risk aversion
and species diversity.
The remainder of this article is structured as follows. First, we present an ecological background
describing the mechanisms underlying the relationship between species diversity and grassland
production in section 2. This background is used to develop an ecological economic and econometric
framework that will be presented in section 3. In sections 4 and 5, data and results are presented, while
concluding remarks are content of section 6.
2 Species diversity and grassland system stability
The concept of increased ecosystem stability with increasing biodiversity is one of the core theories in
plant ecology, particularly in biodiversity-ecosystem functioning studies (e.g., Hooper et al., 2005,
Lehman and Tilman, 2000, McCann, 2000, Tilman et al., 2006, Yachi and Loreau, 1999). Most
experimental studies have focused on plant community biomass, e.g., grassland yield, to test this theory
in experimental grassland systems, just like in the Jena Experiment (Roscher et al., 2004). Often, yield
stability over time has been one of the main interests, particularly in the long-term grassland biodiversity
experiments (such as the Cedar Creek Experiment of Tilman and coworkers or the Jena Experiment).
Temporal yield stability refers to the fact that grasslands withstand environmental impacts and keep up
their biomass production, therefore providing forage yields with a low temporal variation. Recently,
Proulx et al. (2010) could show that temporal stability for many ecosystem functions was higher in
species-rich than in species-poor grasslands, indicated by temporal variations of these processes being
lower in species-rich relative to species-poor grasslands, also known as the “insurance effect” (e.g.
Ehrlich and Ehrlich, 1981, Yachi and Loreau, 1999). The “insurance effect” is based on the likelihood
of more diverse responses to disturbances such as drought or pests expressed (response diversity) and
of more diverse resource niches occupied (niche complementarity) in a diverse compared to a less
diverse plant community or monoculture. This was true not only for biomass production, but for many
other above- and belowground processes, across trophic levels and at different scales of organization
(community to ecosystem levels). Linking this result from the ecology literature to a valuation of this
insurance effect from an economic perspective is, however, scarce.
Niche complementarity, i.e., a mechanism where plant species growing together in species-rich
communities specialize in taking up resources, is intensively studied as the basis for the positive
biodiversity-ecosystem productivity relationships (e.g., Loreau et al., 2002). In terms of nutrient or water
use, niche complementarity refers to the fact that plants take up resources in different places within the
soil profile, during different times or in different forms, and thus jointly exploit the available resource
more efficiently than in monoculture, resulting in higher ecosystem functions, for example biomass
production. Over the last decade, the search to find the underlying mechanisms of complementarity has
often focussed on nutrients (mainly nitrogen) (e.g., Balvanera et al., 2006, Di Falco, 2012, Fargione et
al., 2007) as well as – although to a lesser extent – on light (Hautier et al., 2009, Spehn et al., 2000) and
water use (Caldeira et al., 2001, De Boeck et al., 2006). Also in the Jena Experiment, nitrogen and light
use (Bessler et al., 2012, Gubsch et al., 2011, Roscher et al., 2011a,b,c) have been reported to contribute
to the overall complementarity effect (Marquard et al., 2009). The high N uptake in diverse mixtures
thus not only led to higher aboveground productivity, but also to higher nitrogen pools with diversity
(Oelmann et al. 2011). In addition, facilitation among species also plays an important role in
biodiversity-ecosystem functioning relationships (e.g. Hooper et al., 2005). A key example of
facilitation is the presence of legumes in a plant community: (1) due to their ability to fix atmospheric
N2 via their root symbionts, legumes use less mineral nitrogen from the soil, which in turn is then
available for non-legume plants (e.g. Temperton et al., 2007); and (2) due to their high tissue nitrogen
concentration, neighboring plants benefit from the additional high nitrogen input into the soil when soil
microbes mineralize dead legume tissues. In the Jena Experiment, clear indications for a facilitative role
for legumes were found in the main experiment (Temperton et al., 2007). Data further suggested that
the main driving force behind such facilitative interactions in plots containing legumes was reduced
competition for soil nitrate. Consequently, the presence of legumes (as well as tall herbs) had a strong
positive effect on annual yield production (Marquard et al., 2009). However, despite clear evidence of
facilitation by legumes in many studies, the wide-spread relationship between species diversity and
productivity is not dominantly driven by legumes, as convincingly shown by van Ruijven and Berendse
(2003) in a biodiversity study without any legume species. A third mechanism, the selection effect, has
also been discussed extensively in this context (Huston, 1997, Loreau et al., 2002). With increasing
biodiversity, the chance to include a high-productive species also increases, resulting in high yields in
diverse communities. For the Jena Experiment, it has been shown that the selection effect decreased
over time (Marquard et al., 2009), indicating that differences among plant species in resource niches
become more and more important (i.e., niche complementarity), while the importance of individual
species diminished over time. All three mechanisms contribute to the positive biodiversity-productivity
relationships. While their exact shapes can differ among different studies, these relationships typically
first increase very steeply, before saturating at a certain extent of diversity.
3 Conceptual and methodological framework
In this section, we first develop an ecological economic framework for the valuation of species diversity
in grasslands from the perspective of a risk-averse farmer. Based on this framework and the background
of the ecological background summarized above, an econometric approach is derived to assess the
empirical relationship between species diversity and the distribution of returns from grassland
production. Finally, we present the parameterisation used in our analysis to investigate farmers’
valuation of species diversity under different scenarios.
3.1 An ecological economic perspective on species diversity
In order to analyze the potential on-farm economic benefits arising from the risk reducing property of
species diversity in grasslands, we consider the perspective of a farm household. Without loss of
generality, we assume that the grassland yield is a random variable that is a function of (controllable)
species diversity D and (non-controllable) environmental conditions reflected by the factor e. These
factors determine the stochasticity of production levels, so that following Just and Pope (1978, 1979)
the relationship between yield and species diversity in a changing environment can be described as
, where is the deterministic production function describing expected
production levels in response to species diversity, and the term captures the stochasticity of
grassland production. We assume and , where is the expectation operator.
Thus, the expected production level depends on the deterministic part of the production function, i.e.
, and the yield variance is influenced by general production risks, e.g. influenced by
environmental conditions, and the yield variance function : . Of particular
interest for our analysis is the assumption that is dependent of D, i.e. we assume that the variance of
grassland yields is affected by species diversity.
An expected yield level of
is produced at costs and is sold at price p, generating a non-
deterministic income of . We use a von Neumann Morgenstern utility function
to represent (risk) preferences of the farm household (Chavas, 2004). The risk stemming from
fluctuating grassland yields causes implicit costs of risk bearing for the household that are approximated
by the risk premium R. For a risk-averse decision maker, these risks are a burden, and the risk premium
R>0, reflecting a concave utility function with and . The risk premium can
be interpreted as an amount of money a decision maker would be willing to pay to substitute the random
profit by a non-random payoff, equal to the expected value of profits , so that
where , i.e. is the certainty equivalent (CE) of profits. Thus, CE represents a
non-random payoff that in terms of utility is rated equivalent to the random profit . Following Pratt
(1964), the risk premium can be approximated as
is the variance of profits that is a function of , i.e.
, and r denotes the Arrow-
Pratt risk aversion coefficient that is defined as . Focusing on production risks in grassland
management, the output price p is assumed to be deterministic, so that the variance of profits is
. Recalling that the relationship between the variance of grassland yields and species diversity is
captured by the yield variance function so that
. The marginal effect of species
diversity on the risk premium is thus defined as:
The negative value of this first derivative represents the insurance value of species diversity ,
quantifying the property to reduce the risk premium (Baumgärtner, 2007). Thus, this insurance value
V(D) reflects farmers’ utility gains arising from the yield stabilizing effect of species diversity. The
insurance value contains both a farmer-specific component (the coefficient of risk aversion r) and an
objectively measurable component (the marginal yield variability reducing effect of species diversity
). If species diversity is decreasing the risk so that , an increase in D decreases the
risk premium , i.e. an increase in D decreases the implicit costs of risk for the farmer. This
R=0 and R<0 for risk neutral and risk loving decision makers.
property is increasing with r, i.e. , indicating that an increase in
risk aversion increases the insurance value of species diversity. In agreement with the literature (e.g.
Baumgärtner, 2007) (and our empirical analysis), there is a saturating effect of species diversity on yield
stability, , so that the insurance value of species diversity is decreasing with D:
Combining information of species diversity effects on both expected profits and the risk premium the
certainty equivalent maximizing condition for the optimal level of species diversity is as follows
The right hand side of equation 4 represents the marginal costs (MC), which has to be equal to the
marginal benefits (MB) to satisfy certainty maximizing diversity levels. The latter term consists of a
marginal gain in expected revenues due to increasing species diversity and its insurance value. It shows
that the marginal benefit of species diversity is i) increasing with the price p for grass yield,
; ii) increasing with the risk aversion of the farmer, ; and iii) decreasing with the level of
. Increasing species diversity induces at least short-term costs for the
farmer (Dörschner and Musshoff, 2013) that may comprise direct costs such as establishment costs for
seeds, management, etc., but also opportunity costs associated with higher species diversity. The latter
arise if higher species diversity is achieved by an increase of grassland acreage at the expense of
alternative on-farm activities, or associated with giving up alternative, more profitable, production
methods. Thus, marginal costs are positive and increasing with D: and
. In our analysis, however, we focus on the total and marginal benefits of species
diversity in grassland systems, and particularly aim to quantify its insurance value
. Thus, we specify
the relationship between species diversity and the mean as well as the variance of grassland yields using
the econometric framework presented in the subsequent section.
3.2 Econometric framework
Next, we derive an econometric framework to empirically assess the relationship between species
diversity and the distribution of grassland yields. We identify diversity effects on mean and variance of
grassland yields, using a stochastic specification of a production function following Just and Pope (1978,
Reflecting the property of our empirical application (i.e. an experimental setup with constant management and
variation in species diversity only), we do not consider other inputs in our analysis. Thus, we analyse effects of
species diversity conditional to the management setup used. But, other management decisions, such as fertilizer
use, may interact directly (by affecting species composition) and indirectly (by affecting production risks) with
optimal management in respect to species diversity, see e.g. Di Falco and Chavas (2006) for examples.
(e.g. Hooper et al., 2005).
This assumption on positive and increasing marginal costs of diversity provision is even more pronounced in
our analysis because we use diversity indexes (e.g. the Shannon index) as measure for diversity. in the increases
of such index due to farmers management actions (e.g. introducing an additional species) have saturating effects
on such an index.
In addition, certainty equivalents of these revenues will be presented.
1979). Based on the conceptual framework introduced above, the expected mean yield level can be
estimated in the econometric implementation as follows:
In line with the grassland ecology literature (e.g. Hooper et al., 2005),
is expected to be a concave
function with D, with
. The square of the observed deviations from the
expected yields, i.e. the residuals of equation 6, represents the yield variance and thus can be used to
estimate the relationship with species diversity:
where represents the yield variance function that is expected to satisfy and
, i.e. a convex function with D. Based on the assumptions made, these regression models
exhibit heteroscadasticity, i.e. the variance of the error term () is changing with the level of species
diversity. This needs to be accounted for in the estimation process. Here, we use weighted regression
approaches, with weights being equal to the inverse of the variance at a specific point. The applicability
of this approach can be limited because the estimated variance of may not be necessarily positive. In
cases where the estimated variance is indeed negative, Di Falco and Chavas (2006) suggest to use White
heteroscedasticity corrected standard errors. This, however, would lead to different estimation methods
used in the different equations and differences in estimation results may occur simply due to the different
approaches used. To avoid this potential inconsistency, we use log-squared residuals to estimate a
relationship between the variance and the explanatory variables. A re-transformation using
exponentiation ensures consistent variance estimates used in the weighted regression scheme. To
account for location and time effects, we add dummy variables in all estimation steps
We consider two easy to calculate indices representing species diversity D, namely the Shannon and the
Simpson indices. Both indices are frequently used in ecological applications (e.g. Krebs, 1999, Hooper
et al., 2005 for overviews), but weigh species abundances or biomass production slightly differently.
The Shannon index is defined as
, with being the share of the biomass of
i (i=1,…K) that is present in the investigated grassland. The Simpson index is defined as
. Both indices approach zero if the relative abundance of one species approaches unity (as in a
monoculture). While the Shannon index is known to give greater weight to rare species by correcting
species richness for differences in evenness, the Simpson index gives greater weight to abundant species
(Roscher et al., 2013 and references therein). Nevertheless, both indices have been found to be useful in
the Jena Experiment, as for many other studies before. For example, Roscher et al. (2013) studied the
effect of species diversity on the spontaneous colonization over several years and found the temporal
variability of the (relatively simple) Shannon index to be very similar to that of a (much more complex)
Location is captured using a block dummy, which distinguishes four main homogeneous areas (i.e., blocks with
respect to soil and water conditions) in the experimental set-up (see section 4 and Weigelt et al., 2010, for
We focus on diversity at species level because this tends to be the standard unit of conservation and
measurement (e.g. in the experimental data used here). But we are aware that also within-species genetic
diversity can play an important role (e.g. Di Falco and Chavas, 2008).
functional trait index. Here, we use both indices in our ecological economic assessment. This implies
that we focus on realized instead of on sown diversity. Even though these measures are usually expected
to show similar patterns, realized diversity may be influenced by a wider range of factors, comprising,
for instance, local management and availability of resources (e.g. Fridley, 2002, Vogel et al., 2012), and
thus may be the better indicator for (controllable) species diversity levels in the respective field or
experimental site. In the Jena Experiment, which is base for our empirical analysis, sown and realized
plant species richness/diversity are closely related (Marquard et al., 2009).
The econometric specification of equations 6 and 7 includes the choice of appropriate functional forms.
To allow for sufficient flexibility and based on assumptions on the shape of these functions (e.g.
Koellner and Schmitz, 2006, Marquard et al, 2009) , we consider three options with the diversity index
entering the regression either in linear or square root form as well as in a combination of both. Different
model selection criteria (AIC, BIC, adjusted coefficient of determination) indicate that the square root
specifications are superior for both equations.
In a second estimation approach, we additionally control for the presence of legumes in the experimental
plots using a dummy variable in all estimation steps since legumes are expected to increase productivity
(see section 2). Accounting also for this variable, we aim to identify whether effects of species diversity
on mean and variance of grassland production solely originate from the presence of legumes or from a
more general species diversity effect.
3.3 Implementation and analysis
In a next step, we combine the results from the ecological economic framework developed above with
the econometric analysis. More specifically, the empirical relationships estimated according to equations
6 and 7 are used to derive absolute and marginal relationships between species diversity and benefits as
well risk premia at different levels of species diversity. In this respect, assumptions on risk preferences
of the farmer have to be made. To ensure flexibility in terms of the representation of these risk
preferences in our analysis, we assume a power utility function , so that .
Thus, this choice implies that the decision maker exhibits decreasing absolute risk aversion. Initially,
we assume a specification of the utility function with , reflecting a moderate level of risk aversion
(Chavas, 2004). Furthermore, we assume a price of yield equal to 150 €/t (of drymatter yield) (taken
from http://www.proplanta.de). This analysis will result in point estimates of the absolute and marginal
benefits and risk premia arising from different levels of species diversity.
However, the interpretation of such results as point estimates may be misleading because it does not
reflect uncertainties and assumptions underlying our analysis. To overcome this problem, we conduct
sensitivity analyses with respect to three aspects
: First, we aim to reflect the uncertainties underlying
In addition, we conducted a similar analysis using the Simpson index and come to qualitatively similar results
as presented here for the Shannon index.
our econometric analysis. Thus, a bootstrap approach is chosen where we repeat the estimation process
for 999 bootstrap samples that have been randomly selected with replacement. The resulting 999
different estimates for mean and variance yield functions are used to estimate risk premia (at and
p=150 €/t) and the resulting values for the benefits, risk premia, marginal benefits and insurance values
are used to derive 95% confidence intervals. Second, we investigate uncertainties with respect to the
assumptions made for the economic parameters, i.e. price levels and levels of risk aversion. Here, we
repeat our analysis for a total of fifty specifications of the utility function, with ranging from 0 to 5 (at
p=150 €/t). This range reflects the variation from risk neutral to very risk-averse behavior that has been
revealed by German farmers (e.g. MaartNoelck and Musshoff, 2014). Third, we repeat our analysis (at
) using price levels ranging from 100 to 200 €/t, representing the range of price fluctuations over
recent years. The results of the latter two sensitivity analyses are presented using contour plots for
revenue certainty equivalents and insurance values.
We use biomass data obtained from the Jena Experiment, a large scale biodiversity experiment
conducted in Germany (50°55’N,11°35E, 130 m altitude, see e.g. Roscher et al., 2004, and Weigelt et
al., 2010 for details). For the period 1961-1990, the mean average temperature has been 9.3°C, and the
average annual precipitation in this period was 587 mm. The experiment uses 82 main plots (which
cover 20 m x 20 m each), in which different combinations of species are used, belonging to four plant
functional groups (grasses, legumes, tall herbs, small herbs). More specifically, the species pool
comprised 16 grasses, 12 legumes, 20 tall and 16 small herbs (see Roscher et al., 2004, for details). The
species selection reflects the typical Central European flora found in semi-natural, species rich, hay
meadows, traditionally used in the region (Roscher et al., 2004). All monocultures and mixtures, ranging
from 2-species to 60-species mixtures, have been used in our assessment. To account for differences in
soil and water conditions, the experimental site (in total about 10ha) was divided in 4 blocks and the 82
plots distributed equally across these blocks. We focus our analysis on data obtained from these 82 main
plots, where 3-4 randomly selected sub-plots (each 0.2 x 0.3 m) were used for biomass harvests twice a
year (typically late May and late August). Management conditions are constant across time and space
and comprise biannual weeding and mowing (early June and early September), but no fertilization. The
dataset used comprises 1455 observations and is taken from Weigelt et al. (2010); we employ
observations for the period 2003-2008
. Total target species biomass (dry matter yield) is used in our
analysis. The mean biomass is 5.21 t/ha (SD=3.81 t/ha). The average Shannon and Simpson indices
across sub-plots are 0.91 (SD=0.56) and 0.47 (SD=0.24), respectively.
Data for 2002, the establishment year of the Jena Experiment, was not used because only one harvest took
place and was thus not comparable with the management in the following years.
Table 1 summarizes the estimation results following equations 6 and 7. In this first estimation approach,
diversity effects are not controlled for the specific effect of legumes, but the focus is laid on species
diversity effects in general. For both indices, we find evidence for the expected properties of species
diversity to increase the mean and decrease the variance of grassland yields
. F-tests allow us to reject
null hypotheses that the explanatory variables do not explain variation in the dependent variables.
Table 1. Estimation results of grassland produczion.
Species Diversity (D)
a) Expected yields (Equation 6)
b) Variance of yields (Equation 7)
Numbers in parentheses are t-values. * and *** denote significance levels at the 10% and 1% level, respectively.
xxx denotes that the null hypothesis, i.e., the explanatory variables do not explain variation in dependent variables
could be rejected by the F-test at the 1% level. D0.5 indicates the square root of the diversity index used (either
Shannon or Simpson index).
is the adjusted coefficient of determination. Note that plot location and year of
the experiment have been accounted for using dummy variables (coefficients not shown), df=1436.
In Table 2, estimation results are presented for which we took also the presence of legumes in the plots
into account in both estimation steps. As expected, the presence of legumes has a significant positive
effect on the mean yield levels. Even though the remaining effect of species diversity on mean yield
levels is still positive, it is smaller compared to the estimation without accounting for legume presence
(Table 1a). For the Simpson index, the effect is no longer significant (Table 2a). On the other hand, the
results for the yield variance (Table 2b) show that the positive effect of legumes on mean yield levels
also implies a significantly higher yield variance. In contrast, species diversity in general (expressed as
Shannon or Simpson index) still has a significant negative effect on yield variance. It shows that this
effect is even more distinct if controlling for the effects of the presence of legumes (comparing Tables
1 and 2).
As indicated above, other model specifications (e.g. linear) have been rejected in favour of the square root
Table 2. Estimation results – controlling for the effects of legumes.
Species Diversity (D)
a) Expected yields (Equation 6)
b) Variance of yields (Equation 7)
Numbers in parentheses are t-values. * and *** denote significance levels at the 10% and 1% level, respectively.
xxx denotes that the null hypothesis, i.e., the explanatory variables do not explain variation in dependent variables,
could be rejected by the F-test at the 1% level. D0.5 indicates the square root of the diversity index used (either
Shannon or Simpson index). Legumes is a dummy indicating the presence of legumes.
is the adjusted
coefficient of determination. Note that plot location and year of the experiment have been accounted for using
dummy variables (coefficients not shown), df=1435.
In summary, we find that species diversity increases expected levels of grassland production yields and
decreases their variance, i.e. reduces production risks. The effect on expected yield levels is caused to a
large extent by the presence of legumes in the (more diverse) species mixtures. In contrast, the risk
reducing property of species diversity is even more distinct if controlling for the presence of legumes.
However, since we aim quantifying the effects of species diversity in general and not only the functional
group of legumes plays a special role in the Jena Experiment (Roscher et al., 2004, Marquard et al.,
2009), we will proceed with the results displayed in Table 1. Furthermore, as the results presented above
are similar for both diversity indicators, and to ensure clarity of presentation, we thus proceed in using
one index only, i.e., the Shannon index.
Figure 1 shows certainty equivalent (of revenues) and risk premium (evaluated at and p=150 €/t)
in relation to the Shannon index for realized species diversity in the grassland as well as the 95%
confidence intervals around the estimates (dotted lines), which have been derived using non-parametric
bootstrap. The confidence intervals represent the uncertainties underlying the results, arising from
estimation errors for production yields and yield variance functions. Certainty equivalents of revenues
are increasing with species diversity. As shown in Table 1, a higher Shannon index implies both higher
and more stable yield levels, with both effects leading to increasing utility for a risk-averse decision
maker. The latter property is furthermore illustrated by the fact that the risk premium is decreasing with
increasing species diversity. The confidence intervals indicate that the findings presented in Table 1, i.e.
that species diversity increases yield and decreases yield variance, are robust with respect to the sample
Figure 1. Certainty equivalents and risk premium in relation to realized species diversity expressed
with the Shannon index.
Dotted lines represent 95% confidence intervals derived from non-parametric bootstrap.
The marginal benefits and insurance values of species diversity are shown in Figure 2. Again, 95%
confidence intervals derived from non-parametric bootstrap are presented (dotted lines). Due to the
concavity of the production function and the convexity of the yield variance function, both values are
decreasing with increasing values of the Shannon index. If the Shannon index approaches zero, i.e. in
cases when the relative abundance of a single species approaches unity, as in a monoculture, marginal
benefits and insurance values are highest. For instance, increasing the species diversity expressed by the
Shannon index at a point where it is close to zero by one unit would imply a risk reducing effect
(insurance value) being equivalent to more than 200€/ha. Note, however, that an increase of the Shannon
index by one unit reflects a substantial change in species diversity; for comparison, the interquartile
range of the Shannon index in our sample is 0.53-1.29. The confidence intervals indicate that inference
on the marginal effects of species diversity is subject to high levels of uncertainty as introduced by the
estimations steps. In particular, it shows that inference drawn for low levels of species diversity is
associated with a higher level of uncertainty than for high levels of diversity. However, the levels of
marginal benefits and insurance values resulting from the resampling procedure are consistently
positive, underlining the conclusion that species diversity is clearly associated with both positive
marginal benefits and positive insurance values.
Figure 2. Marginal benefits and insurance values of species diversity.
Dotted lines represent 95% confidence intervals derived from non-parametric bootstrap.
Next, we present results of the sensitivity analysis with respect to the level of output prices, summarized
using contour plots. Figure 3 shows the levels of certainty equivalents (Of revenues) in relation to both
the output price and the species diversity level. Lines represent iso-certainty equivalent curves,
indicating all combinations of price levels and species diversity that lead to the identical level of
certainty equivalent for the farmer. Certainty equivalents increase with both output prices and species
diversity. For instance, at a price of 150€/t, increasing from 0.5 to 1.5 increases the certainty
equivalents from about 800 to about 975 €/ha (Fig. 3). The iso-certainty equivalent curves are convex
to the origin, indicating that output price and species diversity are substitutes in terms of farmers’ utility,
while the marginal rate of substitution (the slope of iso-certainty equivalent curves) is decreasing. The
results displayed in Figure 3 underline that benefits from grassland production can vary substantially in
the range of observed prices and species diversity.
Figure 3. Results from sensitivity analysis: contour lines of certainty equivalents (in €/ha) for different
combinations of species diversity and prices.
Figure 4 shows the contour plots for the insurance value of species diversity derived from the sensitivity
analysis with respect to output price levels. Supporting the theoretical findings presented in section 3, it
illustrates that the insurance value of species diversity is increasing with the output price and decreasing
with species diversity. But even for conditions with high species diversity and low output prices (i.e.,
the bottom right corner of Figure 4), these insurance values are clearly above zero, i.e. even at these
points, there is a significant insurance value of species diversity. However, to what extent farmers would
be willing to invest in species diversity in those situations depends on the costs of its provision.
Price in €/t
0.5 1.0 1.5
100 120 140 160 180 200
Figure 4. Results from sensitivity analysis: contour lines of insurance values of species diversity (in
€/ha) for different combinations of species diversity and prices.
Next, we conduct a sensitivity analysis with respect to the level of risk aversion. Figure 5 shows that
certainty equivalents are (again) increasing in species diversity, but decrease with increasing risk
aversion. For instance, for a situation when equals to one, a shift from risk neutrality ( ) to very
high risk aversion ( ) leads to a reduction of certainty equivalents from about 1150 to about
800€/ha, representing the increase of the risk premium. The shape of the iso-certainty equivalent curves
also indicates that gains in certainty equivalents due to increasing species diversity are higher for more
risk-averse decision makers.
Price in €/t
0.5 1.0 1.5
100 120 140 160 180 200
Figure 5. Results from sensitivity analysis: contour lines of certainty equivalents (in €/ha) for different
combinations of species diversity and coefficients of risk aversion.
This property is also illustrated by the fact that the insurance value of species diversity is higher for
more risk-averse decision makers, while the insurance value of species diversity is equal to zero if the
farmer is risk neutral, as shown in Figure 6. Furthermore, for a fixed level of risk aversion, the insurance
value is decreasing with the Shannon index. Figure 6 also illustrates the earlier stated finding (e.g.
section 3) that the insurance value increases with the level of risk aversion.
Coefficient of Risk Aversion
0.5 1.0 1.5
Figure 6. Results from sensitivity analysis: contour lines of insurance values of species diversity (in
€/ha) for different combinations of species diversity and coefficients of risk aversion.
6 Discussion and Conclusion
As often reported in the ecological literature, species diversity in grasslands increases expected
production levels and decreases the variability of grassland yields, with the Jena Experiment, the
empirical base for our analysis, being no exception. Note that our assessment of risk-reducing effects of
species diversity is thus based on a data set with an extensive management regime (biannual mowing
and no fertilization), which may limit the transferability of results. However, the overall biodiversity-
productivity relationship is in line with many other studies (e.g. Cardinale et al. 2012, Hector et al.,
1999, Hooper et al., 2012, Isbell et al., 2011, Tilman et al., 2005), including North American prairies
(e.g. Tilman et al., 2006) and intensively managed grasslands across Europe (e.g. Kirwan et al., 2007),
and thus applies to many different species compositions, environmental settings and management
intensities. Increasing yields with increasing species diversity are typically explained by the niche
complementarity concept (see section 2 for details). In addition, not only grassland yields and their
stability increase with increasing biodiversity, but also many other beneficial ecosystem functions which
provide relevant ecosystem services in agriculture, such as pollination, efficient soil nitrogen use (and
thus less nitrate leaching), and insurance against weed pressure (e.g. Balvanera et al., 2006, Allan et al.,
2013), adding to a basic (but critical) conservation aspect when maintaining grassland species diversity
Coefficient of Risk Aversion
0.5 1.0 1.5
(Hoekstra et al., 2005). Overall, we conclude that biodiversity might be considered an additional
production factor in grassland management.
In our analysis, we expand this ecological perspective, develop an ecological economic and an
econometric framework, and quantify the (monetary) value of this stabilizing and thus risk reducing
effect from the perspective of a risk-averse farmer. We find species diversity to have a significant
monetary insurance value for risk-averse decision makers, a result which is robust to the boundary
conditions considered in various sensitivity analyses. In practice, farmers can influence species diversity
with a wide range of management practices, such as sown diversity as well as adjustments of fertilization
and mowing practices. Not accounting for the here revealed yield stabilizing property would lead to an
underestimation of the values of on-field species diversity from a farmer’s perspectives. Taking into
account that the risk reduction property of plant diversity is perceived as an important risk reducing
factor by farmers and farm advisors (e.g. Lugnot and Martin, 2013), this finding has important
implications both at the farm and at the aggregated level
. For instance, our results underline that
farmers’ reliance on diversity can be an essential part of their ex-ante risk management strategies (e.g.
Di Falco and Chavas, 2009). Moreover, our results suggst that farmers’ risk preferences may shape
agroecosystem diversity (e.g. Di Falco, 2012, Mouysset et al., 2013). This is particularly important
because on-farm diversity has positive external effects (see above and e.g. Baumgärtner and Quaas,
2010, Marggraf, 2003). These external effects have not been considered in our analysis, but may
introduce a potential rationale for governmental support of management practices leading to species-
rich grasslands. In future research, the investigation presented here should be extended in the following
directions: i) The yield perspective should be extended by also considering energy values of grassland
yields (e.g. for fodder or bio-energy use) or grassland nitrogen use, not solely focusing on physical yield
levels. ii) Further evidence is needed if and how farmers perceive the relationships revealed here in
agricultural practice and how this influences management decisions. iii) Decisions under uncertainty
regarding on-farm species diversity should be considered at larger scales, e.g., at farm- or regional levels.
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