3 Structured decision making for designing complex ...

3 Structured decision making for designing complex release strategies Stefano Canessa

Summary The release of individuals at a chosen location is the defining feature of reintroduction programmes. However, the choice of an adequate release protocol for translocated individuals can be complicated, particularly for programmes with multiple objectives, such as maximising release numbers while minimising impacts on the source population. Limited resources and the biology of species can also generate trade-offs, such as where older individuals have greater survival but are more expensive to translocate or breed. Uncertainty will surround many of these aspects: yet decisions must be made, often within strict time frames. This chapter illustrates how a structured decisionmaking framework can be used to guide the choice of release strategies in complex reintroduction programmes. This approach focuses on clearly specifying objectives, comparing the available actions by their expected outcomes and explicitly considering uncertainties and trade-offs. An example is provided using the release programme for the endangered southern corroboree frog Pseudophryne corroboree. For a 10-year release programme for this species, mixed releases of eggs and sub-adults are expected to maximise the persistence of both wild and captive populations, while meeting budget constraints. Decision-analytic methods can help managers design transparent and effective release strategies, making rational decisions in the face of uncertainty.

Release strategies as complex decision problems The movement of individuals between populations is a defining moment for most reintroduction programmes, often representing the result of arduous efforts to recover small populations, or to restore previously degraded habitats, and attracting attention from media and public. Although most reintroduction programmes do not end with the release of individuals, this is a key step in ensuring that the long-term objectives of the reintroduction are met,

and the choice of the optimal strategy for release is therefore particularly important. For example, assuming releases aim to establish a viable population of the target species (IUCN 2013), the probability that they are successful may depend on several biological factors, such as the number of individuals released, their fitness, the suitability of the release site or the chosen method of release (Fischer and Lindenmayer 2000; Griffith et al. 1989; Griffiths and Pavajeau 2008; Letty et al. 2000; Wolf et al. 1996). Incomplete information about the direction and magnitude of these

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Advances in Reintroduction Biology of Australian and New Zealand Fauna

influences is likely to generate uncertainty: which of the available release sites is best? How many individuals should be released? Should the releases incorporate an ‘acclimation time’ or post-release support such as supplementary feeding? The real difficulties that such factors entail when choosing a release strategy may not become clear until one considers the variety of possible objectives and constraints of most reintroduction programmes (Converse et al. 2013b). For example, captive populations can be intended as reserves of individuals for reintroduction, but also as insurance against the risk of extinctions in the wild, as a tool for preserving genetic diversity, for learning about threatening processes, for leveraging funds for other activities, or for community engagement and education (Bowkett 2009; Clarke 2009; Conde et al. 2011; Hutchins and Thompson 2008; Zimmermann et al. 2007). In addition to these ‘conservation objectives’, programmes also need to meet other requirements: minimising costs, or maintaining them within the available budget, will be an inevitable constraint for most managers. The management of release strategies needs to be considered against this range of complex objectives and their relative importance, particularly in light of the trade-offs that may arise among objectives. For example, managers of a given species might expect that increasing the number of individuals released from captivity (founder population size) will increase the likelihood of them establishing and persisting in the wild. However, removing too many individuals from the captive population might reduce its insurance value in case the releases fail, and ultimately decrease the chance of success in the fundamental objective of avoiding extinction of the species. Such trade-offs have been considered for at least 20 years in the Australian reintroduction programmes for the helmeted honeyeater (Lichenostomus melanops cassidix) (McCarthy 1995) and orange-bellied parrots (Neophema chrysogaster) (Brown et al. 1995), but the full complexity they entail for managers has not been explored. Indeed, such trade-offs can become increasingly complicated, depending on the characteristics of individual programmes. For species with complex life

histories, releasing older individuals might provide greater chances of establishment, since their survival is generally higher than that of juveniles, sometimes by orders of magnitude (see, for example, Sarrazin and Legendre 2000). However, being maintained in captivity for longer may imply a lack of natural selection of individuals by avoiding exposure to wild conditions – for example, during dispersal of juvenile stages – and ultimately reduce the average fitness of a given cohort upon release (Clubb and Mason 2003; Mathews et al. 2005). Several studies have reported on post-release reductions in survival and fecundity of captive-bred individuals (Jule et al. 2008; McCarthy et al. 2012). As mentioned, non-biological objectives must also be considered. Where costs are a constraint, cheaper release options can appear desirable, but may prove less effective than other strategies. For example, Bright and Morris (1994) found that when translocating dormice in the United Kingdom, released individuals that were not provided supplementary feeding lost body mass at an excessive rate, due to inefficient foraging behaviour. For species with multiple life stages, keeping individuals in captivity until they reach later life stages may require the maintenance of a larger captive population, thus increasing costs. Different life stages may also have different maintenance costs (e.g. where adults need complex enclosures or large spaces and require social interactions). Objectives other than costs may also play an important role, such as where zoos need to balance communication and education targets – for example, by maintaining displays (Veltman 2009) – and to efficiently rear animals for release. Again, uncertainty will surround most of these dynamics, particularly with respect to biological aspects, and will complicate the choice of the optimal strategy by decision makers.

Decision analysis as a tool to design release strategies To approach this range of decisions under uncertainty, managers can find help in the array of methods collectively known as decision analysis (also

3 – Structured decision making for designing complex release strategies

referred to as structured decision making: Gregory et al. 2012). Decision analysis provides a framework to approach decisions by carefully stating the problem at hand, formulating clear and measurable objectives, identifying the available courses of action, evaluating their expected outcomes in the face of uncertainty and negotiating trade-offs and constraints. These methods have been successfully employed in several branches of conservation biology (Possingham et al. 2001), and have long been advocated for reintroduction biology (Maguire 1986; Maguire et al. 1988). However, their application in real-world reintroduction programmes has only recently gained momentum (see, for example, Collazo et al. 2013; Converse et al. 2013a). Decision analysis is naturally suited for dealing with the uncertainties and trade-offs that can arise in the design of release strategies for reintroductions. The rest of this chapter illustrates the concepts behind its application; the text boxes describe a practical example, focusing on the design of a release

SDM process

Key concepts

Problem

- Choice of release strategy

Objectives

Actions

Outcomes

Trade-offs

strategy for the endangered southern corroboree frog in Australia (summarised in Fig. 3.1).

Objectives The decision-analytic approach is value-based, focusing on the preferences and values of the decision makers and stakeholders to identify the optimal decision. Focusing on preferences does not negate the desire for objective, rational decisions: rather, it reinforces it, because it recognises that a strategy is simply a way of achieving a given objective – no ‘best’ strategy can thus be defined unless the objective is clear. Therefore, the first step in selecting the optimal release strategy is to clearly define the objective of the reintroduction programme. It is important not to confuse the fundamental objectives of a programme (the general goal that we are trying to achieve) with the so-called means objectives: these represent aspects that are important to the programme, but only insofar as they affect the chance of achieving

- Fundamental and means - Value functions and weights - Risk and utility functions

- Discrete or continuous alternatives - Needs creative thinking - Maintain focus on objectives -

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Predictive model Measure in terms of objectives Quantitative/qualitative Data analysis and/or expert opinion

- Multiple objectives - Methods for solving trade-offs (from MCDA to optimisation) - Sensitivity analysis

Case study: southern Corroboree frog

- Problem: identify optimal release strategy for P. corroboree - Reintroduction: maximise average number of wild individuals over ten years - Insurance: avoid decline in captive population - Cost: meet yearly budget for captive populadon

-

Release eggs and/or subadults Release variable proportions Tools: stage-structured population model and PVA Elicited vital rates, accounting for uncertainty Matrix of release rates

- Optimisation of release rates, constrained by insurance objective and cost

Figure 3.1: Summary of the structured decision-making process: the key concepts in regard to release strategy design and the corresponding sections in the corroboree frog example.

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attract little preference. Decision-analytic methods can easily handle variable preferences (Converse et al. 2013b). Moreover, ignoring aspects of the decision problem that are perceived as irrelevant or uncomfortable will simply create an unrealistic definition of the problem, potentially leading to a poor decision. For example, costs may be considered of little importance when dealing with the ethical issues of species extinction: however, limited resources are likely to exist for most conservation programmes, and disregarding them may lead to the selection of sub-optimal strategies (Stewart et al. 2003; Wilson et al. 2010). Objectives should be assigned a measurable attribute and a criterion of success to allow evaluation. For example, a programme can have the valid fundamental objective of ‘establishing a viable population’. However, in itself, such a statement is not sufficient to evaluate the relative merits of potential release strategies. For example, the viability of the reintroduced population, for a given timeframe, may be measured by its probability of extinction, or indirectly by its size or genetic diversity. Non-biological aspects can also be incorporated, by using direct metrics (such as dollars for costs) or indirect or constructed scales (arbitrary definitions such as ‘low’, ‘medium’ and ‘high’ outcomes). Again, see Table 3.1 for an example. Caution should be exercised when choosing objectives and success criteria for release strategies: statements such as ‘to achieve a probability

the fundamental objective (Gregory et al. 2012). For example, if the fundamental objective of a programme is the persistence of a species in the wild, achieving a viable captive population could be considered as a means objective: that is, the persistence of the captive population is important only because it provides individuals for reintroduction in the wild. But the captive population might be abandoned if a more effective alternative were available that did not require captive individuals. Table 3.1 provides an example of how multiple objectives might be arranged to reflect their hierarchy. Even when multiple fundamental objectives exist, they may not be considered equally important. Where persistence of the target species and community outreach (for example) are both fundamental objectives, managers may still decide that ensuring the species persists is much more important, and therefore choose a release strategy that is more effective in pursuing this objective, even though it may be less effective in terms of community outreach. Since decision analysis largely focuses on value-based decisions, several methods exist to account for unequal preferences for objectives. For example, objectives may be assigned proportional weights reflecting their importance, and the outcomes of a given strategy in regard to each objective are compared accounting for such preferences. It is important to incorporate all objectives that are recognised as important, even though they may

Table 3.1. Example of consequence table for a hypothetical recovery plan Objective

Performance measure (desired trend)

Fundamental: population persistence

Alternative actions A1: no action

A2: release captive-bred adults

A3: release captive-bred juveniles

A4: manage source population

Means: population size

Number of individuals (maximise)

55

125

102

88

Means: number of populations

Number of populations (maximise)

1

2

2

1

Fundamental: cost

A$ spent (minimise)

0

250 000

170 000

95 000

Fundamental: community engagement

Constructed scale (maximise)

None

High

Medium

Low


of persistence greater than 99%’ can lead to anchoring to a specific value, forgetting its biological importance and the relative desirability of different outcomes (is 99% the only acceptable solution, meaning that release strategies that yield 50% and 90%, respectively, are equally unacceptable?). Clearly separating the fundamental objectives from means objectives and criteria of success can help in this sense. Box 3.1 illustrates how a decision problem can be set up, defining objectives and measures of success.

Alternatives and outcomes Once the overall objectives of the reintroduction are clearly established, it is possible to define and evaluate the possible release strategies. Given the biological

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and non-biological complexity of most reintroduction programmes, release strategies can be a combination of an infinite array of factors, such as the location, timing and duration of releases, the size and composition of the released cohorts, and the method of release. Depending on these aspects, the alternatives available may be entirely discrete strategies (such as the release of either juveniles or adults, or release at different locations), or continuous variations of single aspects, such as the relative proportion of a given life stage in the release cohort, or the number of individuals released at each of a given number of sites. The candidate release strategies can then be compared in terms of their expected outcomes in regard to the different objectives of the programme

Box 3.1: Defining the problem and objectives Background The southern corroboree frog Pseudophryne corroboree Moore (Anura: Myobatrachidae), which is endemic to south-eastern Australia, is considered at imminent risk of extinction after declining continuously since the late 1980s, mainly due to the disease chytridiomycosis (Hunter et al. 2010). To prevent the overall extinction of the species and support reintroduction attempts, several Australian institutions are successfully maintaining a captivebreeding programme for this species (McFadden et al. 2013). At the current stage, releases of individuals in the wild are being used to maintain presence of breeding individuals to allow the possible development of tolerance to the pathogen, and to allow researchers to continue their investigation into the dynamics of decline. However, the design of the release strategy is complicated by several factors. First, given the risk of extinction to the species, releases should not deplete the captive population to the extent of reducing its viability, to maintain its insurance value and allow future full-scale reintroductions. The selection of the life stage to release is also important: although adults of the species have relatively higher survival in the wild, maturity is only reached at 4 years of age (Hunter 2000). Therefore, releasing mature individuals can improve the chances of establishing a population, but will require a larger captive population to be maintained, greatly increasing maintenance costs. The following sections will illustrate how a decision-analytic approach can help in designing a release strategy that deals with these trade-offs. For a full description of the case study, see Canessa et al. (2014). Objectives For the purpose of this example, it is assumed that the reintroduction programme for P. corroboree has three equally weighted fundamental objectives: reintroduction, insurance and cost management. The fundamental ‘reintroduction objective’ of this decision problem is to ensure the presence of a breeding population of P. corroboree in the wild. Assuming the release programme will last for 10 years, the general objective can be measured by the average number breeding individuals in the wild over a 10-year period. At the same time, the programme also involves an ‘insurance objective’, reflecting the desire to avoid a decline in the captive population. This can be measured using a threshold criterion: over the 10-year release program, the size of the captive population should not decrease under its initial size. Finally, the ‘cost objective’ reflects the resources required to maintain the captive population during the programme (for simplicity, I assume the cost of releases remains the same independent of the release strategy chosen). In the decision problem, this can also be modelled as a fixed constraint, with a yearly maximum budget of A$250 000, reflecting actual resources in the years 2008–2012 (D. Hunter pers. comm.).

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(Table 3.1). These outcomes can be estimated from a model of the system: again, the form of this model is impossible to generalise, and will depend on the structure of the programme and on the available information and skills. Its complexity may range from simply relying on expert knowledge (experts may be asked to provide a reasonable guess of these expected outcomes, taking into account the known limitations of this approach, and adopting best-practice protocols: Martin et al. 2012) to a quantitative model that incorporates complex system dynamics. For some objectives, the calculations may be straightforward and require a very simple model (such as the sum of estimated costs). However, for many objectives, the estimated outcomes may require consideration of more complex dynamics. For example, since the biological aspects of reintroductions are mostly concerned with demographic and genetic dynamics, population models are commonly used to produce viability analyses (PVA; for an example, see Bach et al. 2010). A wide body of literature exists on how to build PVA simulations to evaluate alternative management strategies for reintroductions, such as the number of individuals to release, their age and sex and the configuration of release sites (for reviews of population modelling for reintroductions, see Armstrong and Reynolds 2012 and Chapter 8). Box 3.2 illustrates how to formulate a decision problem to allow explicit evaluation of the consequences of alternative strategies, identifying the optimal solution.

Uncertainty and trade-offs As acknowledged in the previous sections, the choice of release strategy may be affected by the uncertainty that surrounds the estimated outcomes of the candidate strategies. Such uncertainty should be explicitly acknowledged and described to allow a complete assessment: the methods used will depend on the model used to estimate outcomes and on the type and structure of uncertainty. For example, projections from population viability analyses can incorporate uncertainty about demographic parameters in the model (McGowan et al. 2011), the effect of which can be expressed as confidence intervals or ranges of predicted outcomes. Even for simpler models, such as

direct elicitation of expert opinion, there exists a wide array of tools to account for uncertainty (Martin et al. 2012). In addition to uncertainty, predictions should also consider stochasticity: the outcomes of a given release strategy may vary across time and space, simply due to the variability of the target system, and to semi-random events such as equipment failure or disease breakouts. Stochasticity in demographic and genetic dynamics is naturally incorporated in simulations such as PVA (Akcakaya 1991). In general, acknowledging and quantifying uncertainty and stochasticity, and evaluating their influence on the expected outcomes of release strategies, can improve transparency and provide decision makers with a more complete assessment of the problem. Finally, the existence of multiple objectives may also determine the existence of trade-offs among strategies. This could be the case for releases of different life stages, where juveniles can be cheaper to produce than adults, but might have greater mortality. This could result in a trade-off between the cost of a strategy and its effectiveness. When the candidate release strategies are discrete, such as releasing juveniles rather than adults, a simple comparison of the estimated outcomes under each strategy, including a measure of uncertainty (such as confidence intervals around estimated persistence) may be sufficient to identify the solution to the trade-off. On the other hand, when candidate strategies are particularly complex, or continuous (e.g. when aiming to find the optimal age distribution of a set of released individuals), then specific approaches such as mathematical optimisation may prove more effective in finding an optimal solution under uncertainty. Boxes 3.2 and 3.3 illustrate how such optimisation methods can be used and their results interpreted. Again, the careful definition of objectives and their relative importance can help in correctly describing such trade-offs and evaluating their outcomes in a transparent way.

Conclusions The choice of a release strategy can influence the short- and long-term outcomes of a reintroduction programme. In particular, managers that


Box 3.2: Comparing alternatives After defining the problem and objectives for the reintroduction of P. corroboree, the alternative actions available were evaluated. In this case, managers can choose between the release of eggs, sub-adults (4-year-old individuals), or both. The stages chosen can then be released in variable proportions: a larger release rate can reduce the size of the captive population, and increase the number of wild individuals, whereas a small release rate will be more effective in meeting the ‘insurance objective’. Rather than defining and comparing several discrete release strategies, optimisation was used to identify the matrix of release rates that gave the best outcome for all objectives, maximising the size of the wild population over 10 years, maintaining the size of the captive population at least at its initial value, and maintaining the cost of the captive population under the A$250 000 yearly budget. To evaluate the outcomes under each objective, I used a stage-structured population model (Caswell 1989) to define a system of a captive and a wild population. I modelled female individuals in six stages (eggs, 1-, 2- and 3-year-olds, 4-year-old sub-adults and adults of 5+ years of age). In this formulation, the size of each stage in a population (N(t+1)) is given by the product of the population at the previous time step (N(t)) and the Leslie matrix of vital rates L:

N(t+1) = LN(t) =

0 f2 ... fj s11 s21 ... si1 s12 s22 .. .. . . s1j s2j

... si2 .. .. . . ... sij

N(t)

where fi and sij indicate, respectively, the fecundity of stage j and the survival rate from stage i to j. The two populations communicate through the release rates: at every time step, a proportion r of individuals in a given stage is retained in the captive population, and the complementary proportion 1–r is transferred to the wild population. In this sense, the rate r can be interpreted as a multiplier of the vital rates (the Hadamard product of the matrices of release and vital rates respectively), for the captive population: 0 r1(t) C(t+1) = Lc ° R(t) C(t) = Lc °

1 r2(t)

r1(t) r2(t) .. ... . r1(t) r2(t)

1 ...

1 rn(t)

... rn(t) .. ... . ... rn(t)

C(t)

where C is the size of the captive population, Lc is the matrix of vital rates for the captive population and R is the matrix of the release rates. This formulation assumes that releases are carried out after reproduction: therefore, in captivity, multipliers for fecundities are equal to 1, and the release rate of the first captive life stage changes the probability of transitioning to the second stage. Correspondingly, the size of the wild population can be calculated as: W(t+1) = Lw(t)W(t) + [(1–R)(t) ° Lr]C(t) where W is the size of the wild population at a given time step, Lw is the matrix of its vital rates, and Lr is the matrix that describes the vital rates of individuals post-release. To parameterise the model, experts provided estimates of vital rates for the wild and captive population. To account for uncertainty, experts estimated the maximum, minimum and most-likely value for each parameter: these were used to define a full probability distribution for each parameter (Vose 1996). The models were implemented in a MS Excel spreadsheet, using the Solver add-in to optimise the release rates. The process was repeated 10 000 times, drawing a random value from the distribution of each parameter, to account for uncertainty in the estimated vital rates.

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Box 3.3: Evaluating outcomes and trade-offs The results of the simulation for the release of P. corroboree showed that the release of single life stages was unlikely to meet the multiple objectives of the program. On one hand, the release of eggs alone, even at the maximum sustainable rate (the maximum rate that did not allow a decline in the captive population), was unlikely to produce a large wild population (Fig. 3.2). On the other hand, releasing sub-adults was more effective in regard to the ‘reintroduction objective’, being predicted to result in a large wild population, due to their higher survival rates (Fig. 3.2). However, the captive population required to sustain the release of sub-adults was too large for the available budget, exceeding A$250 000 in most years of the programme even when releasing the largest possible proportion of individuals (~98%; Fig. 3.2). The most effective solution was a mixed release of eggs and sub-adults (Fig. 3.2). In its optimal configuration, this required that in the first 2 years some eggs be retained (averaging 20 to 70%), to increase the captive population to capacity, that some sub-adults be retained in years 3 and 4 (39% and 40%) to maintain the desired number of captive adults, and finally that both stages be released in large proportions in years 5–9 (> 80%). This strategy provided better outcomes than egg releases alone, and although in the last 5 years it produced fewer individuals than a sub-adult-only strategy, its total cost was 68% lower, without exceeding the yearly budget (Fig. 3.2). This solution to the release strategy trade-offs reflects the biological and non-biological configuration of the programme and, perhaps most importantly, the relative weight of each objective. For example, if insurance was considered the most important aspect, the requirements in this sense could be changed (i.e. a larger captive population may be required). More realistic population dynamics could be incorporated, such as genetic composition (Lees et al. 2013), density dependence and environmental stochasticity; the last in particular appears to influence both reproductive survival and disease dynamics in P. corroboree (Hunter et al. 2009; Kriger 2009). Costs may be allowed to vary between years, to reflect fluctuations and uncertainties in the available budget. For these reasons, risk-seeking managers with strict budget constraint might tend to favour strategies that focus more on releasing eggs, whereas larger budget could allow managers to retain eggs and increase the captive population, in order to focus on more effective sub-adult releases. The flexibility of the decision-analytic approach would allow transparent and rigorous consideration of such scenarios.

700

3000

SA

Yearly cost (A$1000)

Size of wild population

3500

2500 2000 1500

M

1000 500

1

2

3

4

5

6

500 400 300

M

200

E

100

E

0

SA

600

7

8

9

10

1

2

3

4

5

6

7

8

9

10

Year of program

Figure 3.2: Outcomes of releases for southern Corroboree frogs, for releases of eggs or sub-adults only (E and SA), and for a mixed release of both life stages (M). The top plot shows the outcome for the ‘reintroduction objective’ of maximising the size of the wild population (the shaded area indicates 95% confidence intervals); the bottom plot shows the yearly cost of the captive population (the dashed line indicates the maximum available yearly budget). Figure adapted from Canessa et al. 2014.


pursue multiple objectives and act within complex socio-ecological systems need to balance biological and non-biological aspects, all under considerable uncertainty. The adoption of a structured decisionmaking approach does not guarantee success: however, it can make the process of selecting a release strategy more rational and transparent. It can help in clarifying the objectives of the releases, defining carefully the options available and evaluate their expected outcomes, uncertainties and trade-offs, to ensure the eventual decision reflects the preferences of managers and the reality of the reintroduction programme.

Acknowledgements The preparation of this chapter was supported by funding from the University of Melbourne and the ARC Centre of Excellence for Environmental Decisions. The corroboree frog case study was developed in collaboration with experts D. Hunter, M. McFadden, G. Marantelli and M.A. McCarthy, whose contribution is gratefully acknowledged. I am grateful to A. Morán Ordóñez for useful comments and advice. M. Hayward and T. Martin provided helpful comments on an earlier version of this chapter.

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