When should we save the most endangered species?

Ecology Letters, (2011) doi: 10.1111/j.1461-0248.2011.01652.x LETTER When should we save the most endangered species? Howard B. Wilson,1* Liana N Joseph,2 Alana L. Moore3 and Hugh P. Possingham4 1 The University of Queensland, St Lucia, QLD 4072, Australia 2 Wildlife Conservation Society, 2300 Southern Boulevard, The Bronx, NY 10460, USA 3 University of Melbourne, Parkville, Victoria 3010, Australia 4 Abstract At the heart of our efforts to protect threatened species, there is a controversial debate about whether to give priority to cost-effective actions or whether focusing solely on the most endangered species will ultimately lead to preservation of the greatest number of species. By framing this debate within a decisionanalytic framework, we show that allocating resources solely to the most endangered species will typically not minimise the number of extinctions in the long-term, as this does not account for the risk of less endangered species going extinct in the future. It is only favoured when our planning timeframe is short or we have a long-term view and we are optimistic about future conditions. Conservation funding tends to be short-term in nature, which biases allocations to more endangered species. Our work highlights the need to consider resource allocation for biodiversity over the long-term; Ôpreventive conservationÕ, rather than just short-term fire-fighting. The University of Queensland, St Lucia, QLD 4072, Australia *Correspondence: E-mail: [email protected]. Keywords Anti-triage, decision theory, endangered species, time-frames. Ecology Letters (2011) INTRODUCTION Conservation budgets are limited and inadequate to conserve the worldÕs biodiversity and there is increasing pressure for prudent investment (Balmford et al. 2003; Hoffmann et al. 2010). However, conservation practitioners and the public alike are often polarised as to what constitutes the wise use of a limited budget. On one side, proponents of triage, the process of prioritising the allocation of limited resources to maximise conservation returns, claim that resources are limited and the threatened species problem is sufficiently large that, to maximise the number of species that we save, the management of species must be prioritised based on concepts of cost-efficiency (Weitzman 1998a; Possingham et al. 2002; Bottrill et al. 2008; McCarthy et al. 2008; Joseph et al. 2009; Schneider et al. 2010). This may, under certain circumstances, result in the decision to not invest in managing highly endangered species. Iconic or charismatic species, for example, often receive a disproportionate amount of spending (Male & Bean 2005; Christie 2006), whereas the majority of threatened species receive no, or very little, funding (Male & Bean 2005). This represents an opportunity cost; a large number of species could be individually managed with the money that has been allocated to a few. Resigning some endangered species to extinction is, however, socially and politically unpalatable. The alternative point of view is that this is a defeatistsÕ strategy and that allows policy makers to give up on highly threatened species that may be expensive to manage (Mittermeier et al. 1998; Pimm 2000; Marris 2007; Jachowski & Kesler 2009). The adversaries of the triage philosophy propose that focusing on the most urgent species now will maximise our chances of saving the greatest number of species in the long-term. These two philosophies are not mutually exclusive. Focusing on the most urgent species may also be the most cost-effective strategy. Here, we uncover the conditions under which spending money on the most endangered of all threatened species may succeed in conserving the greatest number or nearly the greatest number of species. To do this we place the debate within a decision-analytic framework, where we model a set of species and determine the optimal strategy for allocating resources for a range of conditions. We show that allocating resources solely to the most endangered species will typically not minimise the number of extinctions in the long-term as this does not account for the risk of less endangered species going extinct in the future. It is only favoured when our planning time frame is short or we have a long-term view and we are optimistic about future conditions. MATERIALS AND METHODS We defined a model in which every species is in one of three states: extinct, endangered or recovered. Species that have gone extinct stay extinct indefinitely, species in the recovered category remain recovered indefinitely. At every time step, a species i in an endangered state can (in this order): recover with probability ri if management intervention is enacted at a cost hi; recover by chance with a low generic probability q; or go extinct with probability, pi. After each time step, any species still in an endangered state goes through the same process. The recovery by chance or serendipitous event can represent a multitude of different possibilities; including a reduction of anthropogenic pressures on that species, technical advances or evolving immunity to a disease. This has been proposed as one argument for focusing resources on highly endangered species, namely that urgency is a catalyst for scientific innovation (Pimm 2000) and that scientists should retain hope for breakthroughs that could lead to recovery (Jachowski & Kesler 2009). The probability of species i being extant at time t, Ai,t, is the sum of being in states endangered or recovered at t. This probability will depend on the species parameters pi, q and ri. No management is when ri = 0. So, the increase in the probability of being extant or benefit Bi,t at time t as a consequence of spending on recovery is: Bi,t = Ai,t( pi, q, ri) ) Ai,t(pi, q, 0). The benefit to species i after t time steps is:  2011 Blackwell Publishing Ltd/CNRS 2 H. B. Wilson et al. Letter   1  ð1  ri Þt ð1  qÞt ð1  pi Þt Bi;t ¼ ðri þ ð1  ri ÞqÞ 1  ð1  ri Þð1  qÞð1  pi Þ þ ð1  ri Þt ð1  qÞt ð1  pi Þt   1  ð1  qÞt ð1  pi Þt  ð1  qÞt ð1  pi Þt :  qi 1  ð1  qÞð1  pi Þ RESULTS ð1Þ The first quantity in equation (1) is the probability of recovery via intervention alone plus recovery via serendipity if intervention fails (ri + (1 ) ri)q), summed over all time steps up to time t (multiplied by the factor in square brackets). The second quantity is the probability of being in an endangered state at time t, which is the probability of not having recovered or died: (1 ) ri)t(1 ) q)t( ) pi)t. The third and fourth quantities are the same except for the case where no resources are spent on recovery (i.e. r = 0). The cumulative cost at time t is: Ci;t ¼ hi  1  ð1  ri Þt ð1  qÞt ð1  pi Þt 1  ð1  ri Þð1  qÞð1  pi Þ  ð2Þ and the cost-effectiveness, Ri,t, is the benefit divided by the cost. When t = 1 : Ri,1 = (1 ) q)(pi ⁄ ci), where ci = hi ⁄ ri, which is the expected total cost of a successful recovery (the cost of a recovery programme divided by the likelihood of success). As t fi ¥: Ri,¥ = (1 ) q)(1 ⁄ ci) + (q ⁄ hi)(1 ) [1 ) (1 ) ri)(1 ) q)(1 ) pi)] ⁄ [1 ) (1 ) q) (1 ) pi)]). Two key parameters were estimated for 32 endangered species from New Zealand (Joseph et al. 2009), the probability of extinction, pi and the expected total cost of a successful recovery, ci (= hi ⁄ ri). These parameters spanned a range of values from highly endangered, but expensive to recover, to a smaller probability of extinction, but less costly to recover (Fig. 1). The data for the 32 endangered species are listed in table 1 in Joseph et al. 2009, from which we also use the cost (=hi), the probability of success (=ri) and the benefit, Bi. The annual probability of extinction used here, pi, is calculated as 1 ) (1 ) pi,50)1 ⁄ 50, where pi,50 is the probability of extinction within 50 years (=Bi). The recovery probability, ri, equals the probability of success, although we assume here that the whole recovery plan can be enacted in 1 year. We wished to determine how to allocate resources between these species solely to maximise the number of species extant at time horizon tH, for a given budget. We also explored a different objective function; maximise the total number of species alive in every year up to time horizon tH. This places value on a species being alive for some time, even if they are not alive at the time horizon. An objective such as this may be particularly politically palatable, as species alive now may ÔbenefitÕ citizens now, even if the species subsequently go extinct. This objective function is equivalent to maximising the total number of Ôspecies yearsÕ or, equivalently, maximise the sum of the number of species alive in each P year up to time horizon tH. In this case, the benefit at time t is Bi,j, where the sum is over j = 1 to t, and the cost is the same as before (see Supporting Information). We have not employed a discount factor, so that species alive in any year have the same value. Whether discounting is relevant here, and what level and type of discounting to use, is contentious for such problems with a social concern (Heal 1998; Weitzman 1998a; Moore et al. 2008), although there is evidence that people would rather have benefits now as opposed to the future. None of our results would be qualitatively changed if a discount factor was employed, although there would be more emphasis on keeping species alive in the short-term.  2011 Blackwell Publishing Ltd/CNRS Consider a fixed allocation of resources, i.e. the cost-efficiency of directing resources solely at one species when compared with another. Maximising the total number of species extant at tH for a fixed budget, is achieved by spending on those species with the highest costeffectiveness, Ri,t. When we ignored the possibility of fortuitous serendipitous events (i.e. q = 0) and we considered only one time step (i.e. tH = 1), then Ri,1 = pi ⁄ ci (Materials and Methods). When the timeframe was short, the benefit gained was the probability of extinction (without management) divided by the expected cost, and the optimal strategy was to allocate resources to the species with the highest pi ⁄ ci (Fig. 1a), i.e. species that have high extinction probabilities and low expected recovery cost. In the short-term, at least for species with equal cost, the benefit was weighted to species that are more endangered, as there is little benefit to recovering a species with a low probability of extinction as it would be very likely to survive even without management. However, even for short-time horizons, when there are differential costs between species, allocating resources based on risk of extinction alone will not maximise the number of species extant. As the time horizon of the planning process increased, the optimal strategy was to allocate resources to the species with the lowest expected cost of recovery (Fig. 1b). When ri = 1 (and q = 0) and species only differed in the cost of recovery, then Ri,t = [1 ) (1 ) pi)t] ⁄ hi. When t is large, even species with a low risk of extinction were likely to become extinct within the timeframes considered and Ri,t converged to 1 ⁄ hi, converging quicker for higher pi (when ri „ 1, then Ri,t converged to 1 ⁄ ci, Materials and Methods). As the time horizon increased, species with a high probability of extinction, but also high cost became relatively less cost-effective. There was a switch to spending on less endangered and easier to recover species, and a focus on maximising the total number of recovered species as opposed to minimising the number of short-term extinctions (Fig. 1c). When this switch occurred depended on the precise distribution of costs and extinction probabilities (see also Hartig & Drechsler 2008). Spending on less endangered species meant a shortterm loss for a long-term gain; in the short-term, there would be relatively fewer species extant when compared with spending on more endangered species, whereas at longer time periods, there would be relatively more species extant (Fig. 2). A focus on a longer planning horizon changed some of the allocation of resources away from the more endangered New Zealand species to the less endangered, but cheaper to recover species (Fig. 1d). The extent of this difference (i.e. which species are funded) between short- and long-time horizon strategies depends on the precise specifics of species costs and probabilities of extinction. When there was optimism about the future, i.e. q > 0, for shorttime horizons the optimal allocation between species remained the same, but the benefit gained was weighted by the probability of no serendipitous event; Ri,1 = (1 ) q) pi ⁄ ci (Materials and Methods). For longer time horizons, there were benefits to keeping as many species extant as possible in the hope that they will recover. The result is a species allocation intermediate between short (Fig. 1a) and long (Fig. 1b) time horizons (Fig. 3a). An objective function that seeks to maximise the total number of species alive in every year up to time horizon tH also results in allocating resources to more endangered species in a very similar way to optimism about the future (Fig. 3b). When resources can be switched from one species to another dynamically with time, determining the optimal solution required Letter Saving endangered species 3 (a) (b) (c) (d) Figure 1 The allocation of resources for strategies with different time horizons. (a) Contour plots of lines of equal cost-effectiveness for a 1-year time horizon with no species recovery by chance. All points (or species) that fall on the same line have equal cost-effectiveness, species below the line are more cost-effective and species above are less costeffective. (b) A 100-year time horizon with no species recovery by chance. (c) Schematic showing how the allocation of funds moves from more endangered, but expensive to recover species when only a short-time horizon is considered (the area under the straight diagonal line with hatching at 45o) to less endangered, but cheaper to recover species when a longer time horizon is considered (the area under the curve with hatching at 135o). A linear scale for the probability of extinction is used to more clearly show the differences. Species in the cross-hatched area in the bottom right are allocated resources under both time horizon scenarios. The graph assumes a uniform distribution of species across the parameter space, so that the total area hatched under each curve is proportional to the total number of species-allocated resources (there is an equal budget for both strategies). (d) The New Zealand species allocated resources under a fixed budget of $80 million. All species under the curves are funded. The straight line assumes a planning horizon of 1 year and the curve a 100-year planning horizon. The points on graphs a, b and d are 32 endangered species from New Zealand (Joseph et al. 2009), and the expected recovery cost is in NZD$M. Stochastic Dynamic Programming (Supporting Information). We found very similar results to when looking at a fixed allocation of resources; namely, when there was a long time to the time horizon, then resources were spent on less endangered, but cheaper to recover species, but as the time horizon approached, resources were switched to spending on more endangered, but expensive to recover species. The only scenarios when resources were directed first at highly endangered, expensive species were when the original time horizon was short or when the budget was very large compared with the cost of recovering all species (so that all species could be recovered). DISCUSSION Our results highlight two basic strategies: for short time horizons, minimise the number of extinctions in the short-term by allocating resources to the species with the highest ratio of the probability of extinction to cost; for long-time horizons, recover as many species as possible by allocating resources based on the lowest expected cost of recovery. Allocating resources to the most endangered species will not typically maximise the number of species saved, as this does not take into account the risk of less-endangered species going extinct in the future. This result has parallels in the dynamic conservation planning literature (e.g. Naidoo et al. 2006), although conservation planning also incorporates concepts such as dependencies and complementarity, and in reserve site selection studies that include the likelihood of unprotected land parcels being converted to alternative uses other than conservation (Costello & Polasky 2004; Meir et al. 2004; Harrison et al. 2008); analogous to an unrecovered species going extinct here. Allocating resources to the most endangered species will be closer to optimal when: (1) the time-period considered is short; (2) we are optimistic about the future conditions for management of biodiversity; (3) if the conservation resources are large relative to the number of threatened species; and (4) if we value species that are alive now even if they then go extinct. Conditions (1) and (2) do not act synergistically though, as optimism over future conditions is only beneficial when considering long time-scales. More generally, these conditions are unlikely as: (1) long time-frames must be considered if species are to be conserved in perpetuity; (2) the threats to biodiversity are increasing and conservation efforts for threatened species are not sufficient (Stokstad 2010), despite major gains in conservation spending and international  2011 Blackwell Publishing Ltd/CNRS 4 H. B. Wilson et al. Letter (a) Figure 2 The number of species extant under different resource allocation scenarios. An $80 million budget is allocated in year 1 based on three different allocation scenarios for the New Zealand species, and each curve then represents the number of species extant each year over the next 100 years. (a) The full line allocates resources to the species with the highest cost-effectiveness assuming a 100-year planning horizon (typically species with low expected recovery costs). (b) The dotted, light line allocates resources assuming a planning horizon of only 1 year (species that have high extinction probabilities and low expected recovery costs; the highest pi ⁄ ci first). (c) The dashed, heavy line (lowest) allocates resources to the most endangered species first (highest probability of extinction first). In each year, species still in the endangered state go extinct with probability pi. The curves are the average over 1000 simulations. The variances around these curves are very small, so for clarity are not shown. targets for protected areas; and (3) resources for conservation are grossly inadequate (Balmford et al. 2003; Hoffmann et al. 2010). There are other arguments for directing resources to highly endangered species not considered here. These principally include that citizens often place greater value on charismatic species; many of the most endangered species are large animals with large ranges, and so conservation of their habitat spills over into conservation benefits for other species, and conservation budgets focused on the most charismatic will tend to grow with time. Assigning a cultural, economic or ecological value to a species is a notoriously difficult task. However, if each species was assigned a value or weighting, wi, then these can be simply included within our framework by weighting the cost-effectiveness of each species, Ri,t, i.e. Ri,t (new) = wi Ri,t, exactly as in the NoahÕs Ark framework (Weitzman 1998b). The result is that more resources would be directed to the more valued species. Some endangered species will indeed act as umbrella species, but this is not a trait restricted solely to charismatic species. Furthermore, many conservation actions are species-specific and site-specific, as endangered species often do not overlap in range and do not necessarily require the same management actions. Finally, growing conservation budgets are also not restricted to charismatic species (Joseph et al. 2011). Consequently, some of these issues will direct more funding to highly endangered species, whereas others are not restricted to highly endangered species or may not applicable. None of them invalidate the general results presented here. One last point concerns uncertainty and risk. A possible justification for spending on highly endangered species is that protecting species that are most likely to go extinct now is a risk-averse strategy. By keeping more species alive in the short-term, it provides the best environment to take advantage of future unseen events. We have  2011 Blackwell Publishing Ltd/CNRS (b) Figure 3 Contour plots of lines of equal cost-effectiveness. (a) The effects of positive events in the future. The full lines assume a time horizon of 100 years and no species recovery by chance, and the dotted lines assume a time horizon of 100 years and a probability of recovery by chance of 0.05 each year. The effect of serendipity is to allocate more resources to species with a high probability of extinction and high recovery cost at the expense of species with a lower probability of extinction and lower recovery cost. (b) The effect of a different objective function. All the lines are for a time horizon of 100 years with no species recovery by chance. The full lines are for an objective function which maximises the number of species alive at 100 years. The dotted lines are for an objective function that maximises the total number of species alive in every year up to 100 years. The effect of valuing extent species even if they do not survive to the time horizon is to allocate more resources to species with a high probability of extinction and high recovery cost at the expense of species with a lower probability of extinction and lower recovery cost, as in (a). The expected recovery costs are in NZD$M and the diamond points are 32 endangered species from New Zealand. attempted to look at this through the use of a probability of future unseen events helping to recover a species by chance, which results in a greater weighting of resources to more endangered species. However, there are clearly more issues around uncertainty than addressed here. Conservation funding tends to be short-term in nature, which biases allocations to more endangered species. However, our results show that, as in medicine (Messonnier et al. 1999), more emphasis should be Letter placed on long-term Ôpreventive conservationÕ rather than short-term Ôfire-fightingÕ. Allocating resources to the most endangered of all threatened species, regardless of cost, may be a logical consequence of short-term thinking and great optimism about the future. ACKNOWLEDGEMENTS We thank Richard Fuller and Madeleine Bottrill for helpful comments. The work was supported by the Centre for Applied Environmental Decision Analysis, a Commonwealth Environmental Research Facility Hub funded by the Australian Government Department of Environment, Water, Heritage and the Arts. 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SUPPORTING INFORMATION Additional Supporting Information may be found in the online version of this article: Appendix S1 Derivation of the benefit function with the alternative objective function and details of the the stochastic dynamic programming. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer-reviewed and may be reorganized for online delivery, but are not copy edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors. Editor, Stephen Polasky Manuscript received 21 March 2011 First decision made 1 May 2011 Manuscript accepted 9 June 2011  2011 Blackwell Publishing Ltd/CNRS