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1Factors that have been considered when deciding how to invest resources in conservation of species include the efficacy and cost of management, the importance of the species, the level of threat, and the timeframe over which results are to be achieved. However, it is unclear how each of these different factors should be weighted and combined when making a decision.
2We examine how the probabilities of species changing in IUCN Red List categories are influenced by expenditure of resources. We use these relationships to determine optimal investment strategies, using Australian birds as a case study.
3The optimal level of investment in different species depends critically on whether managers wish to minimize the number of extinct species or a weighted average of all threatened species, and on the available budget. The level of investment should not necessarily reflect the level of threat. In our case study, the timeframe of management had little influence on the investment decision.
4Our results show that extinctions of Australian birds can be largely avoided over the next 80 years given current expenditure, but greater investment in conservation is required to reduce the number of threatened species.
5Synthesis and applications. The most efficient allocation of resources to conserve species is difficult to determine intuitively; therefore, this decision demands the use of formal decision theory. The influence of the particular management objective on the optimal decision means that this feature needs careful consideration. Our approach can be used to determine the level of investment that is required to reduce the number of threatened species.
In the face of the continuing decline of biodiversity, conservation biology requires decisions about the investment of finite resources for the protection of species. The efficacy and cost of management, the importance of the species, the level of threat, and the timeframe over which results are to be achieved have been considered when deciding how to invest resources in conservation of species (Millsap et al. 1990; Weitzmann 1993; Avery et al. 1994; Restani & Marzluff 2001; Hughey, Cullen & Moran 2003; Rodriguez, Rojas-Suarez & Sharpe 2004; Marsh et al. 2007). However, it is unclear how each of these different factors should be weighted and combined when making a decision, with each previous method using a different approach. The wide range of different methods can lead to very different priorities for investment in species conservation. It is often not possible to decide which method should be used in a particular case because the goal of management is rarely considered explicitly by defining an objective function (Hughey et al. 2003).
Decision theory provides a rigorous basis for making decisions about ecological management (Possingham et al. 2001). An objective function states the management goal explicitly in terms of a set of variables that define the state of the system. A model describes how these variables change and the influence of management on these changes. Any constraints on the state of variables or the role of management are defined, as are the range of uncertainties. This model is then analysed to determine the management option or set of options that provides the optimal value for the objective function (Possingham et al. 2001). Applied ecological problems need to be framed in terms of decision theory to be able to help managers make decisions.
Protocols for prioritizing species for conservation action routinely ignore the role of decision theory (Possingham et al. 2002). In particular, the goal of management is rarely stated explicitly. We show that the optimal strategy for investment in species conservation is highly sensitive to the choice of the objective function; therefore, using decision theory instead of intuition is essential for making wise decisions about the investment of resources in conservation of species. We show how conservation of species can be analysed using decision theory, presenting a case study of investment in the conservation of threatened Australian birds. This study represents the first application of decision theory to investment in threatened species programmes.
We developed a probabilistic model of changes in the conservation status of species. We define the state of the system by the number of species in different IUCN Red List categories (IUCN 2001), and the management decision is how much money to spend on each of the species. The level of funding influences the probabilities of changing from one IUCN category to another over time. An annual budget limits how much can be spent in total across all species. The solution is obtained by minimizing an objective function that reflects the extinction and endangerment of species in the future. Uncertainty in the estimation of the probabilities of transition and in the effects of management is propagated through to considering uncertainty in the optimal allocation of funds to species. Details of the methods are presented below, by first describing a general solution, and then introducing a particular case study.
the general case
We model changes in the conservation status of species using a transition matrix M that defines the probability of moving among different IUCN categories over a particular time period. Elements of this matrix are a function of the amount of money spent on species in each category i (xi). We recognize four ordered categories for threatened species (extinct, critically endangered, endangered, and vulnerable) and one category of non-threatened species that might nevertheless be of conservation concern (e.g. pooling the IUCN categories of near threatened and least concern). These five categories are represented by the indices 0, 1, 2, 3, and 4, being ordered from extinct (category 0) to non-threatened species (category 4).
The elements of the matrix M (mi,j) define the probabilities of a species moving to category i from category j in a single time period, which will be a function of how much money is spent on species in category j (xj). Thus, the model of transitions among conservation categories is similar to a stage-based model of population dynamics (Caswell 2001), but note that Σj mi,j = 1. If N(t) is a vector with elements ni(t) defining the number of species in category i at time t, then
N(t) = MtN(0).
For a single time period, the expected number of extinct species is n0(1) = n0(0) + Σ m0,ini(0), assuming that extinct species remain extinct (but see Keith & Burgman 2004). The expected number of extinct species after two time periods is
n0(2) = n0(0) + Σi[(m0,i + Σjm0,j mj,i) ni(0)].
Iteration of the matrix M provides the expected number of species in each of the different IUCN categories over any specified number of time periods t for a given level of expenditure on species in each category.
Allocation of funds to species of different conservation status should be based on how best to achieve a particular objective function. Let xi be the amount of money spent per period on each species in IUCN category i. Then, subject to the constraint that the total amount spent in the first time period is equal to the available budget B [Σi xini(0) = B], and assuming the amount spent on each species in each IUCN category is the same from one period to another, the expected number of extinct species at time t can be minimized.
Because the amount spent per species in each IUCN category is the same from period to period, the expenditure on each species will change as it changes category. Further, the actual budget in subsequent periods will change as the number of species changes in each category. In our case study of Australian birds (see below), the total expected budget in all subsequent periods remained relatively stable despite the changes in the expected number of threatened species.
An analytical solution can be obtained when the objective is to minimize the expected number of extinct species after one time period. Using Lagrange minimization, the Lagrangian is
L = n0(0) + Σim0,ini(0) – λ(x1n1(0) + x2n2(0) + x3n3(0) + x4n4(0), and dL/dxi = ni(0) dm0,i/dxi – λni(0),
where λ is the Lagrange multiplier, an arbitrary constant used in Lagrange minimization.
Setting the derivatives to zero to obtain the minimum, and assuming the function L is convex at this point (implying there are diminishing reductions in extinction risk as more money is spent),
λ = dm0,i/dxi.(eqn 1)
This solution means that money should be allocated to all species such that the rates at which the probability of extinction changes per dollar spent are equal.
A solution to minimizing the expected number of extinct species at time t = 2 can be obtained in a similar manner, leading to
This is less easily interpreted than the one-time-step case, and closed-form solutions for xiare unlikely. However, note that if the values of mi,j (i ≠ j) are small (close to zero), then the above solution (equation 2) can be approximated by λ = 2dm0,idxi, which leads to the same solution as for the one-time-step (equation 1). In general, the one-time-step solution is the first-order approximation of the t-time-step solution, and will be a good approximation if the probabilities of changing IUCN category are low. The analytical solutions highlight the structure of the solution, but numerical solutions are easily obtained.
If we assume that the probability of extinction is m0,2 = exp(–a – bx2) for endangered species, m0,1 = exp(–c – dx1) for critically endangered species, and zero for other species, the expected number of extinct species after one time period will equal:
For this parameterization of the model, the optimal allocation of resources to species can be solved analytically. In other cases and for objectives other than minimizing the expected number of extinct species, solutions can be obtained numerically, as in the following case study.
threatened australian birds
We present a case study based on resource allocation for threatened Australian birds. We considered not only extinction but also objective functions that included the expected number of species in different conservation categories. The probabilities of transition among IUCN categories over an 8-year period as a function of resources spent were modelled using exponential functions. The parameters were estimated from data collected for the period 1992–2000 (Table 1; see Garnett, Crowley & Balmford 2003 for details of the methods of data collection) using multinomial regression.
Table 1. Change in status of Australian birds in different conservation classes. Number of bird taxa in each IUCN category that decline two conservation categories (Down 2), decline one conservation category (Down 1), remain the same (Same), or increase by one conservation category (Up 1) over an 8-year period (based on the data used in Garnett et al. 2003). The numbers are the fitted values based on the model, with bracketed values being the observed number. The data are separated depending on whether species received any funding or not, demonstrating that the model is a good fit for both unfunded and funded species. The IUCN categories are critically endangered (CR), endangered (EN), vulnerable (VU), and non-threatened, which combines near-threatened (NT) and least concern (LC)
Initial conservation status
Change in conservation status
A total of 772 bird species occur in Australia and its territories, of which approximately 600 breed (Olsen et al. 2003). Of these species, 180 taxa (mainly species but some subspecies) are threatened, with a further 81 taxa of conservation concern (Garnett & Crowley 2000). Major threats to Australian birds include destruction and fragmentation of native vegetation, grazing, inappropriate fire regimes, intensification of agriculture, changed hydrology, reduction in coarse woody debris, introduced animals, longline fishing and climate change (Olsen et al. 2003). Conservation actions undertaken in Australia have aimed to mitigate the impact of these threats. Actions include, among other measures, captive breeding programmes, controlling competitors and exotic predators, provision of supplementary food, and protection and enhancement of habitat (Garnett & Crowley 2000).
In our case study of threatened Australian birds, declines of more than two categories or an increase of more than one category within an 8-year period were not observed (Garnett et al. 2003); thus, these transition rates were set to zero. The probability of declining by one or two categories and the probability of increasing by one conservation category, for a given expenditure, were assumed to be identical for all threatened bird species. Further, non-threatened birds never declined beyond the vulnerable category; thus, we only permitted declines by one category for this group of species. We used exponential functions to model how the probability of changing IUCN category varied among species as a function of expenditure. Thus,
mi–2,i = exp(–a–bxi) i = 2, 3
mi–1,i = exp(–c–dxi) 1 ≤ i ≤ 3
mi+1,i = exp(–f + gxi) 1 ≤ i ≤ 3
m3,4 = exp(–y–zx4),
where the parameters a, b, c, d, e, f, g, y and z were estimated from data. The probabilities of remaining in the same IUCN category were simply the complements of the above functions:
m1,1 = 1 – (m0,1 + m2,1)
mi,i = 1 – (mi–2,i + mi–1,i + mi+1,i) i = 2, 3
m4,4 = 1 – m3,4
The functions for the probabilities of transition among conservation classes (mi,j) were estimated using a Bayesian model in WinBUGS (Spiegelhalter et al. 2006; see Appendix). Vague priors were used for the parameters to ensure that the posterior distributions had the same shape as the likelihood functions, but with the caveat that parameter values were constrained to ensure that spending money decreased the probabilities of decline, and the probabilities of transition were less than 1. Further, it was assumed a priori that the risk of extinction of critically endangered species was greater than that for endangered species. These constraints on the priors had very little influence on the results. Uncertainty in the estimation of parameters a, b, c and d was propagated within WinBUGS to assess the uncertainty in the optimal resource allocation values and .
The objective of minimizing the number of extinct species does not consider the ecological costs of species being threatened. Conservation programmes aim to maintain representative populations of species across their range, rather than only preventing extinction. The aim is usually to keep threatened species as far as possible from extinction. In this case, an alternative objective function might be the number of threatened species, weighted by their conservation status:
E = n0(t) + w1n1(t). w2n2(t) + w3n3(t),(eqn 3)
which weights species according to a prescribed level of concern. For example, if having two critically endangered species concerned us as much as having one extinct species, w1 would equal 0·5. Closed form solutions for this objective function are not available, but it is relatively easy to solve using numerical methods. Note that the previous objective function for minimizing extinctions is simply equation 3 with all the weights wi equal to zero. As an alternative, we also consider an objective function (3) with the weights w1 = 0·5, w2 = 0·05, w3 = 0·005, reflecting the risk of extinction of different IUCN categories (Butchart et al. 2004).
Many jurisdictions aim to reduce the list of threatened species. At the same time, managers would be reluctant to accelerate the extinction of other species. This management goal could be reflected in an objective function that equals the number of non-threatened species minus the number of extinct species. It is easy to show that maximizing this objective function is equivalent to minimizing the objective function (3) with all weights wi equal to 0·5. We also present results for this objective function.
Finally, the model of changes in transition probabilities (values of mi,j) was used to predict the expected number of species in the different IUCN categories in 80 years time as a function of the budget, assuming that the money was spent to maximize the single period (8-year) objective. This analysis reveals how changes in the budget can achieve different conservation objectives, demonstrating the value of extra investment in species conservation.
the general case
If it is assumed that critically endangered and endangered species are the only species immediately vulnerable to extinction, then expenditure on vulnerable or non-threatened species will not influence the expected number of extinct species after a single time step. In this case, the expected number of extinct species will be minimized by spending money on critically endangered species, endangered species or both. The optimal amount to spend on each critically endangered species is
Then the remainder of the budget is spent on endangered species:
For some parameterizations, the above equation for leads to negative numbers, in which case and (assuming that it is inappropriate to sacrifice the viability of critically endangered species to further fund endangered species). The same consideration applies if the equation for is negative. At least some money is spent on critically endangered species if the available budget B is sufficiently large:
Similarly, at least some money is spent on endangered species if the budget is sufficiently large:
Threatened Australian birds
The estimated functions for how the probabilities of transition among conservation categories for threatened Australian birds change with the amount of money spent show explicitly the value of management (Fig. 1). Probabilities of decline are reduced with increases in expenditure. Although positive, the probability of improving the conservation status of species increases very little as more money is spent. This model fits the observed number of transitions among different IUCN categories remarkably well, both for those species that received conservation funding and those that did not (Table 1). The main discrepancy is the number of unfunded vulnerable species that became critically endangered (down two categories). These observed transitions were all for taxa from Christmas Island; thus, they are not strictly independent, inflating the variation from the model. Therefore, it appears to be a reasonable model of how the probability of changing conservation status is influenced by funding for threatened Australian birds.
If the budget is small and the aim is to minimize the number of extinct species in the future, then resources should only be spent on endangered species. Once the budget is sufficiently large (approximately $7 million; Australian currency used throughout), it is optimal to spend more money on critically endangered than endangered species (Fig. 2). Numerical solutions for five time periods (40 years) lead to almost identical results, so the one-time-step solutions are good approximations of the optimal expenditure on threatened Australian birds for any time period (up to at least 40 years) where the aim is to minimize the expected number of extinct species in the future. The 1-year solution is valid when the probabilities of changing conservation classes are small.
When minimizing a weighted average of the number of threatened Australian bird species, the five-period (40-year) solution is again very similar to the one-period (8-year) solution, simplifying the question about how to allocate funds (Fig. 3). However, the solution when minimizing the number of threatened species weighted by their conservation status is very different from the solution when minimizing the number of extinct species (cf. Figs 2 and 3). In this example, we should invest in all threatened species if the budget is greater than approximately $13 million.
The optimal management strategy is again different when the aim is to maximize the number of non-threatened Australian bird species minus the number of extinct species (Fig. 4). As the budget increases, we first invest in endangered species before investing in critically endangered species. With further increases in the budget, we invest in non-threatened species prior to investing in vulnerable species. In this case, the 40-year and 8-year solutions are again similar, although we invest more in vulnerable species when considering the longer time horizon (Fig. 4). The difference presumably arises because the probabilities of reaching undesirable states via the vulnerable class are non-trivial for longer management timeframes.
As the budget increases, the order in which we spend money on threatened Australian species is not necessarily correlated with the level of threat. For example, when minimizing a weighted average of the number of threatened species (Fig. 3), we first invest in endangered species, then in vulnerable species, and then in critically endangered species (Fig. 3). This order of investment is somewhat counterintuitive and unpredictable, a priori, and depends on the objective function. At some levels of funding (< $40 million per 8 years), it was optimal to invest less money in critically endangered species than in endangered species, and at some values (< $21 million) even less than in vulnerable species (Fig. 3). However, once we start spending money on critically endangered species, the amount we invest per species increases relatively quickly with increases in the budget until such time that we allocate more money to critically endangered species than endangered species (Figs 2–4). This occurs because investing in one group of species leads to an opportunity cost for other species, and the balance point is a function of the available budget. For example, it is cheaper to prevent endangered species becoming extinct, a reduction of two IUCN categories, than it is to prevent extinction of critically endangered species, a reduction of one category (Fig. 1). Therefore, critically endangered species are only protected when the total budget is sufficiently large.
There is uncertainty about the optimal investment strategy due to uncertainty in the estimated transition rates and how these change in response to funding. For example, at a budget of $28·7 million (the budget for the period 1992 to 2000), the 95% credible interval for the optimal amount to spend on each critically endangered species is ($310 000, $940 000) and on each endangered species is ($150 000, $520 000) when the objective was to minimize the number of extinct species. This high level of uncertainty suggests that learning about the estimated transition rates, for example, by purposefully changing the level of investment in different species and monitoring the response using adaptive management (Walters 1986; McCarthy & Possingham 2007), may be beneficial.
The model predicted that without investment in species conservation, 46 species of Australian birds (17% of those of conservation concern) are expected to become extinct in the next 80 years. If resources are allocated to minimize the expected number of extinct species over each 8-year period, the expected number of extinct species in 80 years approximately halves with each additional 8-year budget of $8 million ($1 million per year) (Fig. 5). Only one species is expected to be extinct when the annual budget is $5 million. However, the number of threatened species remains relatively stable at 148 under this objective regardless of the budget, with reduction in the number of extinct species balanced by increases in the number of endangered species (Fig. 5). This emphasizes the difficulty of improving the conservation status of threatened species (Fig. 1). If resources are allocated to minimize the objective function that includes other threatened species (wi = 0·5), an annual budget of $5 million reduces the expected number of threatened species in 80 years time from 148 to 138 (Fig. 6). This modest reduction requires the trade-off that extinct species comprise five of these 138 species (Fig. 6). Reducing the expected number of threatened species without increasing the expected number of extinctions is expensive. For example, an annual budget of $10 million can reduce the expected number of threatened species to 127 (from 148) while ensuring that the expected number of extinct species is only one. This level of investment is approximately three times that spent in 1992–2000.
Our analysis directly addresses the triage debate (McIntyre et al. 1992; Towns & Williams 1993; Possingham et al. 2002; Hobbs, Cramer & Kristijanson 2003) about whether we should invest money in conserving those species that are already critically endangered. If the resources spent on these species were directed to other declining species, we may be able to reduce the number of threatened species in the future. The contrary view is that we should protect the most endangered species, because they are most imperiled now. Both positions can be justified, depending on the level of resources available for conservation and the objective of overarching policy. In contrast, the timeframe of management appears relatively unimportant, at least in the case study.
We suggest that there is no agreement yet about the particular objective of species conservation among conservation practitioners, let alone society more generally. Legislation commonly emphasizes the avoidance of extinction (e.g. US Endangered Species Act 1973, European Union's Habitats Directive 92/43), but declines of species are also of concern in some jurisdictions (e.g. European Union's Birds Directive 79/409, New Zealand's Conservation Act 1987, Australia's Environmental Protection and Biodiversity Conservation Act 1999). The objective of species conservation needs to be clearly agreed upon and defined, or weights placed on multiple objectives, before it is possible to determine the optimal investment in conservation of species. We advocate using formal decision theory methods to help support decisions about allocating money to threatened species, because optimal investment decisions are not intuitively obvious.
An important point is that previous methods for prioritizing investment in threatened species conservation have not considered the interaction between the objective and budget on the optimal allocation of funds. Our results demonstrate that this interaction could have profound implications for decision-making. Essentially, the relative level of funding of species in different conservation categories changes as the size of the budget increases. Similar changes occur with relatively small changes to the objective function. These changes are difficult to predict in the absence of formal decision theory methods. Therefore, explicit statements of the objective of conservation and the constraints on what can be achieved are required for sensible decision-making.
For Australian birds, our analysis indicates that an annual budget of $10 million (an average of $37 000 per species of conservation concern, approximately three times the current level) can be expected to reduce the number of threatened species in 80 years time by approximately 15% while limiting the number of extinct species to one. Such a modest reduction in the number of threatened species is perhaps not surprising given the relatively modest level of investment for each species, but this level of funding is predicted to come close to preventing extinctions. However, the budget needed to reduce the number of threatened birds is far greater.
The relationship between the optimal investment per species and the available budget is approximately piece-wise linear; hence, reasonably good approximations for the results in Figs 2–4 can be obtained by using Taylor series expansions around the points at which funding for each group of species commences (results not shown). However, the numerical solutions can be obtained from a wide range of numerical software packages; thus, there is little value in obtaining the linear approximations.
For our model, the probability of extinction of critically endangered species was the same as the probability of moving from endangered to critically endangered, and vulnerable to endangered. While this is unlikely to be true, it provided a good fit to the data (Table 1), and was a necessary assumption to estimate how expenditure influenced the probabilities of transitions for all IUCN categories. This assumption emphasizes that decisions about optimal investment in conservation of species require information on how extinction risks change with the level of investment. It is unlikely that predictions would be any more precise if an alternative method for determining this relationship, such as using population models that predict extinction risk, were used, but this is a potential avenue for further research.
An assumption made in this analysis is that species respond independently to management, such that conservation actions in one place and on one species do not influence other species. Where conservation actions have complementary or adverse influences, the model would need to be modified, although the basic approach to the analysis would remain unchanged.
Our approach can accommodate the greater value placed on some species over others (Vane-Wright, Humphries & Williams 1991; Weitzmann 1993; Nee & May 1997; Marsh et al. 2007), and that the relationship between the resources spent and the probability of changing conservation status is likely to vary among species. This may be especially important when considering investment among species in very different taxonomic groups (e.g. plants vs. vertebrates vs. invertebrates). For example, species with a more distinct evolutionary history or those more highly valued by humans (Vane-Wright et al. 1991; Nee & May 1997) could be given more weight in the objective function by specifying different transition matrices (M) for each group of species, and summing with appropriate weighting over these different species. More resources would then be spent on those species that have greater value and for which conservation outcomes were most efficient. In the extreme case, the probability of changing IUCN category as a function of resources spent would be different for each species. In most cases, however, it would be difficult to support such a detailed model with empirical evidence. Even in our case study, where we obtained good fits and pooled across species, there was considerable uncertainty about the probabilities of transition between different IUCN categories.
Perhaps the most important point arising from this study is that decisions about how to reduce the number of species in different threat categories requires information about how the probabilities of changing status are influenced by investment of resources. Management efficiency has been considered in a previous prioritization scheme (Marsh et al. 2007). However, our analysis shows that a single metric of management efficiency is not sufficient, given the dependence of the result on the budget and objective function. Instead, the entire function (e.g. Fig. 1) is required. Our model of how changes in conservation status are influenced by the level of investment, while admittedly simple, is, as far as we are aware, the first such study based on empirical data. In all cases, these relationships are uncertain, and the influence of this uncertainty on management decisions is a possible avenue of future research.
We do not envisage our analysis being used prescriptively. Rather, it can help guide decisions. Deviations from the level of investment suggested by our analysis could be justified by differences in management efficiency, the value of species (for phylogenetic, social or some other reason) or the possible synergistic benefits of managing species. Synergistic benefits include cases where matching funding for conservation efforts might be available for particular species, or where a single conservation action assists multiple species. However, deviations ought to be justifiable, and these details could be accommodated in the analysis with relatively minor changes.
Overall, our analysis suggests that, for greatest efficiency in the allocation of resources to species conservation, governments need to make overt decisions about the objective function, something that is at best simply implied in legislation, and is usually ambiguous in either statutes or in policy. As it is, decisions are being made in the triage debate by default without a strategy for achieving long-term objectives that have been open to public debate. The allocation of resources should also be undertaken in a considered way across all species, taking into account the diverse values placed on species by society, not piecemeal across various levels of legislature as is the case within most jurisdictions. Finally our analysis suggests that allocating resources today based on an agreed objective function is likely to have the desired benefit for a substantial period into the future.
We are grateful to Hugh Possingham for ongoing discussions about triage, and Doug Armstrong, Barry Brook, Michael Brooke, Stuart Butchart, Adam Drucker, Cindy Hauser, David Keith and Robert May for helpful comments of an earlier draft of the manuscript. Our research was supported by the Australian Research Council, the Applied Environmental Decision Analysis Hub of the Commonwealth Environment Research Facility, and the Australian Centre of Excellence for Risk Analysis.