Ecol Res (2011) 26: 687–695 DOI 10.1007/s11284-011-0849-9
R EV IE W
Doug P. Armstrong • Heiko U. Wittmer
Incorporating Allee effects into reintroduction strategies
Received: 7 October 2010 / Accepted: 20 May 2011 / Published online: 11 June 2011 Ó The Ecological Society of Japan 2011
Abstract Allee effects, the reduction of vital rates at low population densities, can occur through several mechanisms, all of which potentially apply to reintroduced populations. Reintroduced populations are initially at low densities, hence Allee effects can potentially lead to reintroduction failure despite habitat quality being sufficient to allow long-term persistence if the population survived the establishment phase. The probability of such failures can potentially be reduced by releasing large numbers of organisms, by reducing post-release dispersal or mortality through management, or by directly managing the Allee effects, e.g., by implementing predator control or food supplementation until population size increases. However, such measures incur costs, as large releases have a greater impact on source populations, and management actions require financial and other resources. It is therefore essential to compare the costs and benefits of attempting to reduce Allee effects in reintroduction programs. Here we advocate the use of structured decision-making frameworks whereby alternative strategies are nominated, probability distributions of outcomes obtained under different strategies, and utilities assigned to different outcomes. We illustrate the potential application of such decision frameworks using projections from a stochastic population model including Allee effects. As there will seldom be estimates of Allee effects available from the species or system involved, it will be necessary to predict these effects based on the biology of the species and data from other systems. In doing so, it is important to identify mechanisms for proposed Allee effects, and to avoid misleading inferences from correlations subject to confounds. In D. P. Armstrong (&) Wildlife Ecology Group, Massey University, Private Bag 11222, Palmerston North, New Zealand E-mail:
[email protected] Tel.: +64-6-3569099 H. U. Wittmer School of Biological Sciences, Victoria University of Wellington, PO Box 600, Wellington 6140, New Zealand
particular, naive interpretations of correlations between numbers released and reintroduction success may exaggerate the benefits of releasing large numbers. Keywords Reintroduction Æ Translocation Æ Allee effects Æ Population modeling Æ Structured decision-making
Introduction The term ‘‘Allee effect’’ can refer to any reduction in vital rates (per capita survival and reproduction) at low density, and such effects have also been referred to as ‘‘positive density dependence’’, ‘‘inverse density dependence’’ or ‘‘depensation’’ (Courchamp et al. 2008). Allee effects have long been recognized as determinants of the dynamics of small populations (Allee 1931), but until recently have tended to be ignored or dismissed as of minor importance. The lack of attention to Allee effects can be at least partially attributed to the skeptical attitude toward all forms of density dependence for several decades of the 20th century (e.g., Andrewartha and Birch 1954). The inevitable role of density dependence, however, became widely accepted by the early 1990s (e.g., Turchin 1990), and there has subsequently been an exponential increase in the number of publications on Allee effects (Courchamp et al. 2008). Allee effects are currently a major focus of ecological research, hence the scope and significance of Allee effects should become much clearer over the next decade. Given the growing awareness of potential Allee effects in populations, it is prudent to consider the implications for practical population management of rare and threatened species. Reintroduction, defined as any attempt to restore a species to a site where it formerly occurred (IUCN 1987), has become an important and widely applied tool for managing species threatened by extinction (e.g., Armstrong and Seddon 2008). Since the number of organisms released in reintroductions is usually much lower than the site-specific carrying capacity, Allee
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effects are potentially quite relevant to reintroduced populations (Deredec and Courchamp 2007). It is therefore surprising that Allee effects are not even mentioned in the current IUCN Guidelines to Reintroduction (IUCN 1998), and that there is minimal cross referencing between the growing bodies of literature on reintroduction and Allee effects (Deredec and Courchamp 2007). The fact that reintroduced populations are initially small to some extent means that all facets of the ‘‘small population paradigm’’ (Caughley 1994) come into play, i.e., inbreeding depression, loss of heterozygosity, demographic stochasticity (variation in vital rates due to chance fates of individuals) and environmental stochasticity (variation in vital rates due to environmental conditions) as well as Allee effects. Genetic problems are likely to decrease gradually over time (unless the population consists of very few closely related individuals), and are most relevant in populations that remain chronically small rather than those that grow rapidly from a small founder group (Frankham et al. 2010). In contrast, impacts of stochasticity and Allee effects can happen immediately, potentially causing extinction before reintroduced populations have a chance to grow. These impacts will likely be synergistic, making them difficult to distinguish. Optimal reintroduction strategies may depend on whether small populations are most vulnerable to demographic stochasticity, environmental stochasticity, or Allee effects. What is most important, however, is to distinguish the factors that may threaten the establishment of populations from those threatening long-term persistence (Armstrong and Seddon 2008). If the reintroduction site has suitable habitat for the species, then the population will persist in the long term as long as it successfully establishes. In such cases, it makes sense to manage the reintroduction to minimize the establishment risks posed by stochasticity and/or Allee effects, and therefore avoid a failed reintroduction to suitable habitat. On the other hand, if the habitat is unsuitable for long-term persistence, then attempts to maximize establishment success will be misplaced, and only serve to maximize the waste of money and lives of the translocated organisms. Although reintroduction should never be attempted if the habitat is unsuitable for the species (IUCN 1998), there is often tremendous uncertainty about site suitability, and reintroduction strategies need to take this uncertainty into account. In this paper, we attempt to create a decision framework for incorporating Allee effects into reintroduction strategies in the face of uncertainty about habitat quality. We first outline potential strategies for minimizing Allee effects, and discuss the costs of these strategies as well as their potential benefits. We then create a decision framework for comparing alternative strategies in light of these costs and benefits, and illustrate the potential use of the framework using a stochastic population model incorporating uncertainty in parameter estimates. Finally, we discuss issues involved
in estimating the strength of Allee effects. We particularly advocate the importance of sound theory and the danger of naive interpretation of empirical trends subject to confounds.
Strategies for minimizing Allee effects Deredec and Courchamp (2007) proposed several strategies for minimizing Allee effects in reintroductions, and these can be divided into three categories: (1) improving size and composition of the release group; (2) management to reduce post-release mortality and dispersal; and (3) management of Allee effects. Size and composition of release group The most obvious strategy is to avoid Allee effects by releasing large numbers of individuals at reintroduction sites, and this is the main strategy that Deredec and Courchamp (2007) focus on. Although Allee effects have received little attention in reintroduction, the ideal number of individuals to release has been a major focus in the reintroduction literature (e.g., Griffith et al. 1989; Towns and Ferreira 2001), and is usually a major point of discussion when planning reintroductions. Increasing the number released should reduce the impacts of both Allee effects and demographic stochasticity, but probably not at the same rate. For example, larger numbers might be needed to substantially reduce Allee effects than are needed to substantially reduce demographic stochasticity, but this will depend on the biology of the species and the environment. As shown below, the quality of the release site is a particularly important factor affecting the benefits gained from large releases. Releasing large numbers of individuals has an equally obvious cost, i.e., the loss of those individuals from source populations. One aspect of this cost is the tradeoff between the number of possible reintroduction sites and the number released per site (Deredec and Courchamp 2007), but removal of individuals can also significantly impact the viability of the source populations themselves, regardless of whether they are captive or wild. These impacts vary greatly among programs, ranging from situations where every individual is highly valuable to those where large numbers of surplus individuals are produced. Deredec and Courchamp (2007) also proposed several methods of altering the composition of the release group to increase its effective size, e.g., by choosing the optimal sex ratio, choosing attractive individuals, or maximizing genetic diversity. However, it is important to remember that the costs of these strategies may be proportional to the intended benefits, i.e., individuals thought to be of greater value to a reintroduced population will also tend to be valuable to the source population.
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Where possible, the ideal strategy for reducing Allee effects may be to increase the local density or average group size rather than the total number released. Initial densities are easily manipulated in reintroductions of plants or sessile animals, and in some cases densities of mobile animals can be increased by confining them to fenced areas. Group size may be particularly important in social predator or prey species. For example, individuals in smaller groups face higher predation risk in situations where predators usually kill one animal per group per attack irrespective of the group size (McLellan et al. 2010). Thus, animals that are likely to depend on social groups for survival are sometimes held together in captivity pens before release in an attempt to increase group cohesion. For example, groups of unrelated lions Pathera leo were held in bomas for several months to promote group formation (Hayward et al. 2007), and African wild dogs Lycaon pictus groups are artificially formed before reintroductions using this method (Davies-Mostert et al. 2009; Somers and Gusset 2009). Unlike increases in numbers, if local density or group sizes could be increased, this could potentially reduce Allee effects without increasing costs to the source population. Also, unlike increases in numbers, there would not be a simultaneously reduction in demographic stochasticity.
Stephens and Sutherland (1999) and Deredec and Courchamp (2007) suggest that Allee effects can be reduced by penning animals at release sites to prevent dispersal, this has been ineffective or detrimental in many cases (e.g., Short et al. 1992; Castro et al. 1994; Clarke et al. 2002; Hardman and Moro 2006) although there are examples of penning reducing both post-release dispersal (e.g., Bright and Morris 1994; Tuberville et al. 2005) and mortality (e.g., Bright and Morris 1994; King and Gurnell 2005; Hamilton et al. 2010). Other methods for reducing post-release mortality include both predator training (Biggins et al. 1999) and anti-predator training (van Heezik et al. 1999; Shier and Owings 2006). Other potential methods for reducing post-release dispersal potentially include ‘‘acoustic anchoring’’, where calls are broadcast near the release site (Molles et al. 2008), and release of captive-reared rather than wildcaught individuals (Berry 1998). However, there is so far no clear evidence that acoustic anchoring actually reduces dispersal (L. Molles pers. comm.; Bradley et al. 2011), and captive-reared animals often have higher post-release mortality than wild animals (Snyder et al. 1996). Ongoing research in this area will hopefully improve our predictive capabilities, but it would be rash at present to assume that any management will effectively reduce post-release dispersal or mortality unless this has been demonstrated in a similar species and system.
Management to reduce post-release mortality and dispersal
Direct management of Allee effects
An alternative to increasing the size or density of the release group is to undertake management designed to reduce post-release dispersal and mortality, which can be defined as the dispersal and mortality occurring during the acclimation period immediately after release (Hamilton et al. 2010). Organisms are subject to stresses associated with the translocation process and adjustment to the novel environment at this stage, so it is common to have significantly elevated mortality (e.g., Tavecchia et al. 2009; Hamilton et al. 2010) and/or dispersal (e.g., Hardman and Moro 2006; Le Gouar et al. 2008; van Heezik et al. 2009) during the acclimation period. The initial population (N0), which is often defined as the number of individuals surviving to the first breeding season, is therefore often much lower than the number of individuals released (Nr). It is important that the two are not confused. Releasing more individuals or reducing post-release mortality and dispersal are both strategies for increasing N0, so achieve the same benefits in terms of reducing Allee effects and demographic stochasticity. However, the costs will probably be different, so it is necessary to weigh the costs to source populations incurred through larger releases with the costs incurred through post-release management. The other difference between the two strategies is that we can control the numbers released whereas attempts to reduce post-release mortality and dispersal are often ineffective. For example, while
The third option is to directly manage the Allee effects rather than avoiding them by increasing N0. Undertaking such management requires having a clear theory in place about the mechanisms for the assumed Allee effects. For example, if a species is thought to be vulnerable to predation or unable to forage efficiently at low density, then predator control or food supplementation, respectively, could be undertaken until density reached some critical level. Similarly, if a plant species is projected to have low pollination rates at low density, hand pollination could initially be undertaken. When considering such management, it is important to distinguish between component and demographic Allee effects (Stephens et al. 1999). For example, although pollination may be reduced at low density (component effect), reduced pollination may not translate into lower recruitment, hence there may be no effect on population growth rate (demographic effect). Unlike strategies that increase N0, direct management of Allee effects does not simultaneously target demographic stochasticity. However, any increase in population growth rate through management is likely to reduce negative impacts of demographic stochasticity, as those impacts are greatest at low growth rates (i.e., k close to 1). Similar to management of post-release mortality and dispersal, direct management of Allee effects imposes additional financial costs on reintroduction programs,
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but avoids the need to increase impacts on source populations through large releases. Making sensible decisions about which option(s) to pursue requires not only comparing these costs but also considering how confident we are that the management will have the desired effect.
Using structured decision-making to compare strategies Structured decision-making (SDM) involves three components: envisioning possible outcomes; estimating the probabilities of those outcomes occurring under different possible actions; and assigning utilities that take into account both the values of the outcomes and the costs of the actions (Clemen 1996; Williams et al. 2002). The standard approach is to calculate the average utility expected under each action. For example, if there are two or more discrete outcomes x, the average utility of action a is given by RðaÞ ¼
X
ð1Þ
pðxjaÞRða; xÞ
x
where p(x|a) is the probability of a possible outcome occurring under the action and R(a,x) is the utility of that combination of action and outcome. Uncertainty about the probabilities can be accounted for by treating alternative sets of probabilities as hypotheses. For example, the expected average utility is given by E½RðaÞ ¼
X i
" pðHi Þ
X
# pðxjaÞRða; xÞ
ð2Þ
x
where Hi represents one of several discrete hypotheses. Alternative strategies for addressing Allee effects can potentially be discrete. For example, we might choose between: (1) a large release group; (2) a small release group with management to reduce post-release mortality; or (3) a small release group with direct management of Allee effects. However, given that there is a continuum of possible release group sizes, it may be better to estimate the optimum rather than simply choose between a small or large group. Similarly, management strategies may fall on a continuum in relation to intensity, e.g., intensity of predator control. Reintroduction outcomes can also be divided in the discrete categories of ‘‘success’’ and ‘‘failure’’, but this simple dichotomy is problematic, and we suggest that it is better to use measures such as expected population size after some time period. The probabilities of different outcomes occurring can be generated from stochastic population models, and these are equivalent to the alternative hypotheses in Eq. (2). There may be discrete alternatives into terms of model structure. However, the main uncertainty may be in the parameter estimates included in the models, and this uncertainty is best represented by continuous distributions.
Creating a population model A range of model structures have been proposed for incorporating Allee effects into population dynamics (Boukal and Berec 2002; Courchamp et al. 2008), and the best model(s) to use will depend on the species and system concerned. For illustrative purposes, we use a discrete-time version of Wang et al.’s (1999) model, which provides a good combination of simplicity and biological realism. Under this model, the population size 1 year into the future is given by Nt Nt Ntþ1 ¼ Nt sa þ Nt b 1 ð3Þ R Nt þ h where Nt is current population size, sa is the annual survival probability of current individuals in the population, b is the number of recruits per current individual per year at low density without Allee effects, R is the maximum population size where recruitment occurs, and h is the strength of the Allee effect (reproduction is halved when Nt = h). The key features of the model are that survival is density-independent, whereas recruitment is subject both to compensation of a logistic form and depensation of a rectangular hyperbolic (RH) form. The RH form was suggested by Dennis (1989) for modeling increases in mating probability as a function of density, but it could also approximate other Allee effects such as increased brood survival due to protection from predators at higher density. It is essential to include demographic stochasticity in any model used to make population projections for different-sized released groups. It is also essential to include uncertainty about parameter values in any projections for reintroduced populations to reflect uncertainty about the quality of habitat at the release site. In our projections, we incorporated demographic stochasticity by sampling the survivors from a binomial distribution with probability sa and sample size Nt, and sampling the number of recruits from a Poisson distribution with t mean Nt b 1 NRt NNt þh : We incorporated parameter uncertainty by specifying both a mean and standard error for each parameter, and sampling the values from a log-normal (b, R, h) or logit-normal (s) distribution for each run of the model. Given that reintroduced populations are also strongly affected by post-release mortality and dispersal, we included a first step where N0 was sampled from a binomial distribution with probability sr (probability of surviving from release to first breeding season) and sample size Nr (number released). The parameter sr was also subject to uncertainty. We constructed the model as a Microsoft ExcelÒ spreadsheet, and ran all projections using this spreadsheet. The formula for calculating N0 took the form ¼ CRITBINOM(B11,$B$5,RAND()) where B11 is the number of animals released and $B$5 is parameter sr. Formulas for calculating Nt+1 for
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subsequent years took the form
Hypothetical decision scenarios
¼ CRITBINOMðC11,$C$5,RAND()Þ þ dPoissonDev(C11 $D$5 ð1 C11=$E$5Þ C11=ðC11 þ $F$5ÞÞ
We considered a hypothetical scenario in which sr, sa, and b were all estimated to be 0.75, and R estimated to be 500. This is a favorable scenario, as the population is expected to grow by 50% per year (i.e., k = 1.5) at low density in the absence of Allee effects, and to reach a carrying capacity of 333 individuals. We created four variations on this scenario (Table 1) to assess the effects of adding Allee effects and the effect of uncertainty about the strength of the Allee effect and the survival and recruitment rates. For each scenario, we used the spreadsheet model to calculate mean population sizes and probabilities of growth after 10 years with different release strategies (in increments of ten), with or without Allee effects being managed. The spreadsheet also counted the number of years that Allee effects were managed (i.e., until n = 60). We then used these projections to calculate the average utility under the above frameworks. The optimal number of individuals released ranged from 10 to 120 depending on the scenario and on whether Allee effects were managed (Fig. 1). Not surprisingly, the optimal number to release increases when the Allee effect is added to the model, and decreases again if the Allee effect is prevented through management. The net benefits were fairly similar with and without management of the Allee effects if the optimal numbers were released, but this result will depend on the relative costs incurred per animal released and for management of Allee effects. The results were fairly insensitive to uncertainty about the strength of the Allee effect (i.e., the value of h). However, they were highly sensitive to uncertainty in survival and reproduction rates, the optimal numbers released being much smaller under high uncertainty. The optimal numbers released were also generally smaller if benefits were valued in terms of probability of growth rather than population size after 10 years. These results are specific to the hypothetical scenario and population model used, and should not be interpreted as general rules. Further modeling could
where C11 is Nt, $C$5 is sa, $D$5 is b, $E$5 is R, and $F$5 is h. The dPoissonDev function is part of the PopTools (Hood 2010) add-into Excel, but a Poisson distribution can also be approximated using the GAMMAINV function. We did 10,000 runs of the model under each scenario using an Excel macro attached to the spreadsheet, and used this macro to collate probability distributions for outcomes. Assigning utilities Utilities of outcomes can be measured as a monetary value, requiring the economic evaluation of non-monetary outcomes such as environmental attributes (Martı´ nLo´pez et al. 2008). Alternatively, utilities can be expressed as an arbitrary but consistently measurable real number, for example from 0 to 1 or 0 to 100 (Clemen 1996; Hastie and Dawes 2010). Utilities are then measured by weighting different types of outcomes according to their relative importance to the decision-maker (Clemen 1996; Hastie and Dawes 2010). For illustrative purposes, we considered two different attributes by which the benefit of the reintroduction could be measured. The benefit was considered to be proportional to either: (1) the expected size of reintroduced population after 10 years or (2) the probability of population growth after 10 years, where growth is defined as exceeding the number of individuals released (we chose 10 years, as this is a typical time frame used for planning and assessing reintroduction projects). Under the first framework, we assumed utility increased linearly with population size, and assigned a utility of 1 to a population of 300 since this was just below the expected carrying capacity with the population parameters chosen (see below). Under the second framework, we assumed utility increased linearly with the probability of growth, and assigned a utility of 1 to 100% certainty of growth after 10 years. We assumed the monetary costs of translocation were $2,000 per individual released and $10,000 per year of management undertaken to prevent Allee effects. We assumed that such management would completely remove the Allee effects (i.e., h becomes 0) and would be undertaken any year that the population was less than 60 individuals. To express the monetary cost as a utility and enable trade-offs between the costs and benefits, we assumed utility increased linearly with money, with a utility of 1 equivalent to $300,000 (i.e., $300,000 has a utility of 1). Although we chose arbitrary weights for the costs and benefits, there are several rigorous methods for measuring a decision-maker’s utilities for different outcomes (Clemen 1996; Dawes and Smith 1985).
Table 1 Means and standard errors for parameters used in the stochastic population model for scenarios A–D in Fig. 1 sr A B C D
0.75 0.75 0.75 0.75
sa (0.075) (0.075) (0.075) (0.75)
0.75 0.75 0.75 0.75
b (0.075) (0.075) (0.075) (0.75)
0.75 0.75 0.75 0.75
h
R (0.075) (0.075) (0.075) (0.75)
500 500 500 500
(50) (50) (50) (50)
0 20 (2) 20 (20) 20 (2)
Values were sampled from log- or logit-normal distributions defined by these means and standard errors for each run of the model: sr, probability of survival from release to first breeding season; sa, subsequent annual survival probability; b, mean number of recruits per individual per year at low density with no Allee effects; R, compensation parameter giving maximum population size where recruitment occurs; h, depensation parameter whereby recruitment is halved when Nt = h
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0.4
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50
(B) Allee effect known precisely
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0
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0
350
(C) Allee effect uncertain
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250 200
0.6
150
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0.8
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50 0
0
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1
vital rates uncertain
250
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150 0.4
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0
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60
Number released
potentially be done to establish a more general theory about optimal strategies for incorporating Allee effects into release strategies. However, our main goal is to illustrate how a structured decision framework incorporating a relatively simple population model could be used on a case-by-case basis.
Incorporating empirical evidence into decision-making The most challenging aspect of developing a decision framework for any reintroduction will be estimating the parameters in the population model. Although models of reintroduced populations constructed from post-release data are used to make management decisions (e.g., Armstrong et al. 2007), it is particularly challenging to derive realistic distributions for population parameters before release to a new site (McCarthy et al. 2011). This applies to all reintroductions, regardless of whether Allee effects are likely to occur, but here we will focus on the particular problem of estimating Allee effects.
80
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(D) Allee effect known precisely
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0.4 0.2 0
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1 0.8
0.4 0.2 0
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1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
0.4 0.2 0
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1 0.8 0.6
Utility
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1
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(A) No Allee effect
300
Utility
Mean N after 10 years
Mean N after 10 years
Mean N after 10 years
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Mean N after 10 years
Fig. 1 Population projections (grey) for different release strategies under four different scenarios (A–D), and utilities of these strategies (black) under two hypothetical decision frameworks (left and right). Dotted lines indicate strategies where Allee effects are nullified through management until N (size of reintroduced population) reaches 60. This management is assumed to cost $10,000 for each year undertaken, and each individual released is assumed to incur a cost of $2000. Utilities are calculated by adding either 1/300 units for each individual at year 10 (left) or the probability of growth at year 10 (right), and subtracting 1/150 units per dollar spent. Projections are from a stochastic simulation model based on Eq. (3), and the parameters used in the four scenarios are shown in Table 1. In scenario A, there is no Allee effect and the other parameters are known precisely (SE 10% of mean). In scenario B, an Allee effect is added through the depensation parameter h, and h is also known precisely. Scenario C is the same as scenario B but with great uncertainty about the value of h (SE = mean). Scenario D is the same as scenario B but with great uncertainty around survival and reproduction rates
0.4 0.2
0
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Number released
One potential source of information is correlations between numbers of individuals released and reintroduction success (Griffith et al. 1989; Wolf et al. 1996). Deredec and Courchamp (2007) noted that the correlations observed may partially reflect Allee effects, but that other small-population issues such as demographic stochasticity will also be involved. The mechanism underlying the relationships may not matter if the only strategies considered involve manipulation of the initial population size. However, the mechanism clearly makes a difference if the strategies considered include direct management of the hypothesized Allee effects. The more important issue is that correlation does not equal causation, and that naive interpretation of correlations may give a distorted impression of the effect of numbers of individuals released on reintroduction success. Interpreting correlation as causation requires the highly unrealistic assumption that numbers of individuals released are chosen at random with respect to the probability of success. As shown above, the optimal
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Probability of growth
Optimal number relased
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λ =1.150 λ =1.125
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Fig. 2 Optimal number of individuals to release (Nr) in relation to expected population growth. The relationship shown is from a stochastic population model based on Eq. (3), with sr = 0.75, sa = 0.75, R = 500, h = 0 (i.e., no Allee effect), and b (recruitment rate) varied to change the expected growth rate (see Table 1 for definitions of parameters). The expected rate of increase at low density (kmax) is given by sa + b, i.e., adult survival rate plus recruitment rate. The optimal Nr is defined as the number giving the maximum probability of population growth after 10 years (i.e., N10 > Nr). The dots show the values transferred to Fig. (3)
Fig. 3 Potential misinterpretation of the effect of numbers released on reintroduction success through naive interpretation of correlations. The lines show the true effect of number released on the probability of the population growth over 10 years (N10 > Nr) under different expected growth rates (kmax). The relationships are based on the same stochastic model and parameter values as in Fig. 2. The dots show the pattern that would be observed if managers choose the optimal number of individuals released based on an accurate a priori assessment of the expected growth rate (see Fig. 2), and the dashed line connecting those dots shows the incorrect cause-and-effect relationship that could be inferred from this pattern
number to release can be strongly affected by expected population growth rate (Fig. 2), and also by uncertainty about the expected growth rate (Fig. 1). Although reintroduction practitioners are rarely trained in theoretical population ecology, they are generally highly experienced and will realize that it does not make sense to risk large numbers of individuals if it seems marginal whether the population will grow or is highly uncertain. If practitioners were able to accurately guess the population growth rates expected, and chose the optimal numbers to release based on this (Fig. 2), data subsequently collated from the reintroductions would show a very gradual increase in probability of success in relation to the number released (Fig. 3). However, this gradual increase would not reflect the true effect of the numbers released on probability of success (Fig. 3), so naive interpretation of the observed pattern would greatly exaggerate the benefit of releasing large numbers (Fig. 3). For example, the observed pattern in Fig. 3 (dots and dashed lines) suggests that >50 individuals need to be released to get to 90% of the maximum probability of successful reintroduction, whereas in reality no more than 15 are needed to reach this 90% level under any expected growth rate. Although it is preferable to examine relationships between demographic rates and population density (e.g., Sinclair et al. 1998), these can also be subject to confounds, so also need to be interpreted with caution. For example, slow initial growth of reintroduced populations due to post-release mortality and dispersal will also be associated with low initial density, so could easily be misinterpreted as an Allee effect. Where multiple reintroductions are considered, populations reintroduced to poor sites will inevitably tend to have smaller population sizes, hence the effect of habitat quality on population
growth rate among sites can again be easily misinterpreted as Allee effects. We suggest that it is best to consider Allee effects in reintroductions where there is good theoretical reason to expect them, and to treat correlations suggesting Allee effects with appropriate caution even when observed in single populations. For example, predation-driven Allee effects were implicated in the decline of the Channel Island fox (Urocyon littoralis) (Angulo et al. 2007), a species which forms breeding pairs but not larger social groups. There is currently no plausible mechanism to explain the occurrence of predation-driven Allee effects in species that do not occur in social groups (McLellan et al. 2010), and a more comprehensive analysis of the island fox data by Bakker et al. (2009) suggested that the positive density dependence was most likely due to emigration. There is therefore no good reason to expect that releasing more individuals will reduce per capita predation by foxes, and such releases might simply sacrifice valuable individuals by releasing them at an unsuitable site. In contrast, the positive correlations between vital rates and density in populations of woodland caribou (Rangifer tarandus caribou) in British Columbia (Wittmer et al. 2007) can be given more weight because a mechanism has been identified for predator-driven Allee effects in this species (McLellan et al. 2010). It would still be rash to assume that releasing large numbers of caribou would reverse observed population declines given that extinction probabilities are correlated with habitat loss (Wittmer et al. 2010). However, it is prudent to estimate Allee effects, and include these effects in candidate models used to develop conservation strategies including possible reintroductions and/or augmentations. In at least one species, the black-faced impala (Aepyceros melampus petersi), there already appears to
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be good evidence that large releases increase probability of establishment by reducing per capita predation by cheetahs (Acinonynx jubatus) (Matson et al. 2004). Such effects are expected in social ungulates in the presence of predators, and the existing data should clearly be used to incorporate Allee effects into models used to decide strategies for further translocations. The pack-hunting African wild dog (Lycaon pictus) is another reintroduced species known to be affected by Allee effects, with two different mechanisms operating. First, Courchamp and Macdonald (2001) have shown that successful rearing of pups in these highly social canids is closely related to pack size, with small packs unsuccessful. Second, Somers et al. (2008) have shown that the establishment of translocated populations can be hindered by low probability of finding mates following post-release dispersal, an effect that should be reduced by releasing multiple groups. This information should again be used to make population projections as a function of release strategy, although at this stage it is unclear how well managers are able to manipulate the sizes of packs formed after release. Of course there will seldom be estimates of Allee effects available for a particular species proposed for reintroduction, and there will never be estimates of Allee effects for the species in the particular ecosystem where it is being reintroduced. It will therefore be necessary to derive estimates from other species and systems with similar attributes, so a clear theoretical framework is needed to anticipate the circumstances where different forms of Allee effects are expected. Working out the appropriate degree of uncertainty around the estimates derived will be a particular challenge. The recent focus on Allee effects in academia has rightly raised awareness of the potential relevance of Allee effects for conservation management actions such as reintroduction. However, this strong focus could have given the impression that Allee effects always play an important role in population dynamics, leading to uncritical adoption of strategies designed to reduce these effects. As there are costs associated with any strategy for either avoiding or managing Allee effects, strategies should be based on sensible decision frameworks weighing costs and benefits. The apparent importance of Allee effects has already been reduced somewhat through meta-analysis of demographic data available for multiple taxa (Gregory et al. 2010). Further research will hopefully lead to a much stronger evidence base that can be used to further develop the types of decision frameworks we have proposed. Acknowledgements DPA thanks Gaku Takimoto and Tadashi Myashita for the invitation to speak on this topic at the Allee effects symposium at the 57th Annual Meeting of the Ecological Society of Japan, and to the Japan Society for the Promotion of Science KAKENHI (21770091 and 21310149) for funding this visit to Japan. We thank Tracy Rout for help with the decision analysis, and M. Hayward, J. Ewen, and two anonymous reviewers for comments on the manuscript.
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