Draft – CCLC Chapter 10_PVA Stanton & Akçakaya
Conservation Planning to Ensure Viability of Populations and Metapopulations
Jessica Stanton and H. Reşit Akçakaya
An important (if not the ultimate) goal of conservation planning is to preserve natural populations of species, i.e., to prevent the extinction of species. Assessing viability is the most direct way of measuring of how close to this goal your conservation plan is, or will be in the future when the planned conservation actions are in place. Viability is the likelihood that a species (or a population) will remain extant in the future. Population viability analysis (PVA) is a method for calculating this, either under current conditions, or under assumed future changes.
At this stage in your conservation planning you should have a good understanding of the landscape, what focal species you might use to represent ecosystems of conservation concern in your area, and the habitat available to those species. You may have even mapped out areas of suitable habitat and analyzed the connectivity between potential conservation areas. However, merely protecting areas of suitable habitat does not necessarily ensure that the amount and configuration of habitat patches will be sufficient for the long term survival of the focal species. Likewise, even if sufficient amounts of suitable habitat are available, species may still decline due to threats not related to habitat loss such as harvesting, introduced predators, competitors, or diseases. In order to analyze the impact of those threats information about the species’ demography should also be considered. Population viability analysis (PVA) provides a method to link demographic data with habitat maps in order to address questions about the prospects for recovery, longevity, and resilience specific to your focal species in your landscape. PVA can also be particularly useful when evaluating different management options or proposed reserve design configurations.
The ability to analyze habitat and landscape characteristics at the same time as demography in a single model is an important aspect of PVA. Populations are often faced with multiple threats that affect their long-term viability, some of which may primarily impact habitat availability (such as logging or urban sprawl), and others which may have greater impacts on demography (such as reduced survival due to pollution or hunting). These different threats combined may have synergistic impacts on the population that may not be detected if only considered singly. Similarly, some threats have effects that inherently impact both demography and habitat and cannot be adequately represented by a model that only considers habitat availability and disregards demography or vice versa. For example, road building may fragment the landscape, decrease dispersal ability, and increase mortality for some species. Methods such as PVA allow you to model multiple impacts that may have complex effects on your focal species and can be an important compliment to analyses of the habitat, landscape connectivity and reserve design.
Current Best Practices
Population viability analysis (PVA) is a process of predicting measures of population persistence, such as risk of population extinction or decline, chance of population recovery, expected population size in the future, and expected time to extinction. Most outputs from PVAs are probabilistic, and are based on three variables: the amount of expected population change (e.g., 100% decline or total extinction, or partial decline), the probability that such a decline will occur, and the time frame in which the decline is expected to take place (Akçakaya 1992, 2000a). Thus, specific PVA results may include
probability of extinction within the next 100 years;
probability of a 50% decline by the year 2060;
probability that there will be 50 or fewer mature individuals left in the population sometime in the next 40 years;
probability that the population will increase to 1000 or more individuals by the year 2050.
To predict these types of viability measures, PVA uses a variety of models (discussed below), which are parameterized with habitat and distribution data (e.g., occurrence locations and map layers describing habitat requirements) and demographic data (such as censuses, mark-recapture studies, surveys and observations of reproduction and dispersal events).
The best type of model to use depends on the conservation question being asked, the amount and type of data that are available, and the ecology of the species under consideration. The important issue of formulating a specific question will be addressed in detail below (see Guidelines). PVA is often used in the conservation and management of rare and threatened species with two broad objectives. In the short-term, the goal is to prevent extinction. In the longer-term, the goal is to promote conditions in which species not only remain extant but also retain their potential for evolutionary change without intensive management. With these objectives in mind, the specific questions addressed with a PVA may involve
(i) Assessing vulnerability: estimating the risk of extinction (an absolute measure of vulnerability), or the relative vulnerability of species and populations to extinction. These predictions can be used in ranking species (such as in the IUCN Red List of Threatened Species). When combined with other considerations such as cost effectiveness, social and cultural priorities, and taxonomic uniqueness, these results can also be used to set policies and priorities for allocating scarce conservation resources.
(ii) Evaluating management options: predicting the likely responses of species to conservation and management actions, such as reintroduction, captive breeding, prescribed burning, weed control, habitat rehabilitation, or different designs for nature reserves or corridor networks.
(iii) Impact assessment: quantifying the impact of human activities (such as urban sprawl and other types of land-use change; harvest, poaching, and other types of direct exploitation; pollution, and introduction of exotic species) by comparing results of models with and without the population-level consequences of the human activity. These assessments may involve past or current impacts (to assign blame) or projected future impacts (e.g., to evaluate proposed development plans).
(iv) Planning research: determining priorities for further data collection based on the sensitivity of model results to data uncertainties in model parameters.
(v) Improving understanding: organizing the information and assumptions about a species or a population. PVA allows a structured process that makes the assumptions explicit, and highlights the data deficiencies and uncertainties.
Although there is no single recipe to follow when doing a PVA, main components of a PVA may include identification of the question, data collection, data analysis and parameter estimation, modeling and risk assessment, sensitivity analysis and refinement of the model, monitoring and evaluation (see Figure 1 and Akçakaya et al. 1999).
After formulating the specific questions, an important step is determining the type and structure of the model consistent with the question, the available data, and the ecology of the species. The types of models include occupancy models, lattice (grid-based) models, age or stage-structured metapopulation models, and individual-based models. The details of these models are discussed by Akçakaya & Brook (2008), Akçakaya & Sjögren-Gulve (2000), DeAngelis & Mooij (2005), Grimm & Railsback (2005), Hanski (1994), and Sjögren-Gulve & Ebenhard (2000). A summary of the characteristics and examples of these model types are given in Table 1. There are also several software packages that implement these models. The most commonly used software programs include VORTEX (Lacy 1993) and the RAMAS library of programs (Akçakaya 1994, 2005; Akçakaya & Root 2003); others include ALEX (Possingham & Davies 1995), PATCH (Schumaker 1998), and META-X (Grimm et al. 2004). Of course, it is also possible to construct your own model from the ground up in any mathematical software package.
Guidelines for application
In this section we will outline some of the key issues to consider before approaching a PVA. It is important to note that because of the amount of data required, the number of variables involved and the interaction between variables, PVAs can become very complex. It is for this reason that this chapter should be thought of as a guide to the type of information and data needed and an overview of best practices. It is not a replacement for more thorough references such as Akçakaya et al. (1999), Caswell (2001) Morris & Doak (2002), and Beissinger & McCullough (2002).
Formulation of goals and questions
Before you begin a PVA it is important to clearly identify the question you wish to answer with your analysis. Clearly outlining a realistic and useful question or set of questions is not a trivial point and new questions may arise along the way as you begin to gather the data needed to construct your models. Likewise, you may find that the available data are not sufficient to address your original questions and you may need to gather more data and the process of constructing a PVA can make your data needs clearer. However, PVA can help clarify where the critical areas of uncertainty or data deficiency lie. Examples of the types of questions that are typically addressed by a PVA include predictions about future abundances or assessing vulnerabilities such as ‘What is the risk of local extinction?’ or ‘What is the chance for recovery?’; questions related to assessing the impacts or current or future threats such as ‘What is the population-level impact of harvesting?’; questions to evaluate competing management options such as ‘Which management option will reduce the extinction risk the most for the least cost?’; and questions to guide future research or data collection ‘Is the model more sensitive to uncertainty in adult survival or fecundity estimates?’.
Once your goals and questions are clearly articulated you can begin to construct the model that will serve as the backbone of your PVA. The famous quote from statistician George E. P. Box (1979), “All models are wrong but some are useful”, reminds us to think carefully about constructing a model that will be useful to address the questions you need it to address. Just as you would reach for a street map rather than a topographic map to plan a driving route, a model constructed for one type of conservation question or goal may or may not be much use to address a different type of question. Since a model is only a simplified representation of a real system, you must decide what type of model and which parameters are necessary to accurately represent the aspect of the system that is important to your goals. In addition to the nature of your conservation goals and management questions, additional considerations for deciding on what type of model to use include the amount and quality of data available, and important ecological aspects of the focal species.
Although other chapters in this volume cover predicting habitat, we briefly discuss it here, because it is an important aspect of viability analysis. In addition, habitat maps or models constructed for other conservation purposes may or may not be at the most appropriate spatial extent or resolution, or capture the characteristics of the landscape to be most useful in a PVA. A habitat map is the spatial backbone of a PVA and directly relates to many of the demographic parameters such as the number and carrying capacity of subpopulations, dispersal, and survival among others.
Methods for estimating suitable habitat that are based on either statistical correlations between environmental variables and species occurrence locations (Guisan & Thuiller 2005; Franklin 2010) or known ecophysiological tolerances (Kearney & Porter 2009) are preferable to mapping habitat from expert opinion or the boundaries of coarse landform categories (such as wetland or forest). The benefits of these approaches are that they provide a means to incorporate a number of different types of data such as climatic variables, remote sensing and digital elevation models and accommodate interactions between predictor variables. Another advantage of modeling habitat suitability in either a correlation based or ecophysiological based framework is that they allow for projecting the model to new areas or future timesteps. If possible, it is advisable to employ a few different methods to construct the habitat model and compare where they are similar and where they differ (Elith et al. 2006).
Some care ought to be taken when constructing a habitat model to be used for a PVA. During the course of gathering the GIS layers and occurrence locations for constructing a habitat model it is important to
Use a spatial scale that is relevant to the dispersal and patch size of the species (see below for more details on issues of scale).
Verify occurrence locations when constructing a correlation based habitat model. Occurrence locations from publicly available biodiversity databases can at times be problematic if the coordinates given have an unknown radius of uncertainty. For instance, coordinates given may be the location of an actual sighting, or the center of a county or township where the species is reported to occur. Species misidentification is another issue that can occur and will impact the accuracy of habitat models (Lozier, Aniello, & Hickerson 2009).
Select variables for the model that are biologically relevant to the species, and directly determine its occurrence through known eco-physiological mechanisms. Thus, indirect variables (e.g. altitude, topographic heterogeneity) should be avoided (Guisan & Zimmermann 2000).
Consider including climatic variables (derived from long-term weather data), land-use or land-cover variables (often derived from remote-sensing products such as satellite images). When the model includes climatic variables that are predicted to change in the future (see below), it may be better to include the static maps (such as land-cover) as binary masks, rather than including them in the model fitting.
When using categorical variables (such as land-cover), consider creating distance maps (e.g., distance to water) or percentage cover maps (e.g., percent of forest in a 120-meter cell, based on 30-meter cells of the original map), if such derived variables are considered to more directly affect the suitability of an area for the focal species.
Validate your model by using some form of data partitioning this will help to avoid the risk of overfitting your model (see Model parameters and assumptions).
An important consideration when constructing a model for a PVA is the spatial scale of your data, both in terms of the resolution and the extent. The scale should be relevant to the biology of the focal species, meaning it should relate to the patch size and dispersal distance. For example, too fine a resolution is needlessly data intensive, too coarse and you may not get an adequate representation of the patch structure. An approximate rule-of-thumb for vertebrate species is that the cell size of the raster map underlying the model should be about the same size or a bit smaller (but not much smaller) than the home range or territory size of the species.
Similarly, the spatial extent should be relevant to the dispersal distance of the focal species and the questions addressed by your PVA. Often times you may wish to construct a model for a subset of a species’ total range, such as to assess the viability within a national park or system of reserve areas. If your focal species is wide ranging this can cause some misleading results. Consider a situation where suitable habitat is found beyond the spatial extent of your model based on the political boundaries of the park or reserve. Subpopulations that lie on the border may be modeled as being truncated in size and therefore in carrying capacity as well. There may also be dispersal of individuals into and outside of the park or reserve system. These issues can affect the outcome of the model in terms of estimated viability, time to decline or recovery, and the rate at which individual patches within the metapopulation structure turn over.
It is equally important to consider an appropriate time-scale for your model. Population models projected for only a few years or generations may not show the longer-term trends inherent in the model. If the initial conditions of the population are not at the stable age distribution or sex ratio it may take time equivalent to several generations for the populations to stabilize. Models with time-scales that are very long will carry a high amount of uncertainty as the uncertainty is compounded through time. Also assuming a lack of significant changes to the landscape or climatic conditions as well as assumptions about lack of adaptive changes or genetic drift of the population may be valid assumptions in the short term, but are very difficult to predict over long time scales.
Model parameters and assumptions
The issues of scale mentioned above illustrate just a few of the common mistakes that can be made when constructing a population model. This is not meant as a discouragement; the process of constructing a model is an opportunity to think carefully about important dynamics of your focal species and all the factors which may be influencing the population in critical ways. It is important to be mindful of what explicit assumptions you are making in your model as well as the assumptions which are implied through the model parameters. For instance, mapping the available habitat on the present landscape as a static variable is making the implicit assumption that the landscape will not change. Sometimes, because of lack of data (or lack of a crystal ball), we are forced to make assumptions which we know are not entirely accurate. By being aware of the assumptions you are making with your model you can evaluate whether or not they seem reasonable or supportable within the context of the questions you are trying to address.
Modeling a population as scalar with no age or stage-based structure, as a single panmictic population, with closed population boundaries, or with habitat patches of uniform quality and discrete boundaries are all parameters keep the model straightforward and understandable. However, how useful or accurate your model will be depends entirely on how well those assumptions describe the actual behavior of the population you are trying to describe (Lindenmayer et al. 2003) or the questions you are addressing. In some cases, a simple model may be adequate. Models may also be overly simplified when they are missing important interactions between the population and the particular landscape such as natural catastrophes, fragmentation, disease spread, or edge effects when such factors significantly alter the trajectory of a population. But just as models can be too simple, they can also be overly complex by fitting many parameters to only a few data points (Ginzburg & Jensen 2004).
A good way to test the fit of a model is to use separate (ideally independent) data for model building and for model validation. This separate training data and testing data can come from partitioning a single data set spatially or temporally (while controlling for spatial or temporal autocorrelation). So for example, a model of habitat suitability might be constructed using one half of a landscape and tested for accuracy by seeing how well it can predict the occurrences in the other half. This can be done with time series data of population trends as well where some portion of the time series is retained for evaluation. Using this approach, Brook et al. (2000) validated probabilistic predictions of PVAs—they found that the predicted risk of population decline closely matched observed outcomes, there was no significant bias, population size projections did not differ significantly or importantly from reality, and the predictions of five software packages they tested were highly concordant.
Demographic structure refers to the categorizations of individuals within a population according to their age, size, sex, or physiological state (such as immature, breeding, etc.). Models should have an age or stage structure if the demographic characteristics (fecundity, survival, growth, dispersal) depend on the age, size, or other characteristics of the individual. These models, also referred to as "matrix models" because of the way the demographic rates can be organized in a matrix equation, are commonly used in conservation biology; and many techniques have been developed to parameterize them (Caswell 2001). The data that can be used for estimating the parameters of these models (e.g., age-specific survival rates and fecundities) include mark-recapture data (White & Burnham 1999), and population censuses in which individuals of different ages or stages are counted separately.
Models that lack age or stage-based structure are called scalar models (they are also known as "count-based models" and "diffusion approximation"). Scalar models assume that all individuals in the population are functionally identical, and they are used in cases where the only available data are a time series of total population size estimates. If the population being modeled has age structure, a scalar model of this population may overestimate the variability in the population size, and hence overestimate the risks faced by the population (Holmes 2004; Dunham, Akçakaya, and Bridges 2006). A set of simulations has indicated that the bias increases as a function of the generation time of the species, and that correcting the bias seems difficult if not impossible, because the bias is not a simple function of generation time, and because any deviation of the initial age structure from the stable age structure adds uncertainty (Dunham et al. 2006).
Most models of vertebrate populations include only females. In many cases this is appropriate (as long as sex ratio is properly incorporated into fecundity estimates; see Akçakaya et al. 1999), because total reproduction is often limited by the number of breeding females. However, there are some cases where it is necessary to model both males and females, by developing matrix models with different stages or age classes for males and females. If, for example, the purpose of building a model is to evaluate the consequences of different hunting regimes, and only males (and perhaps only males over a certain age) are hunted, then the model obviously needs to have both male and female age classes (e.g., see Sezen et al. 2004). Regardless of the model objective, if males have higher mortality than females (causing a skewed sex ratio), and the mating system is (or is close to) monogamous, then the number of breeding females (and thus, overall population productivity) may be limited by the availability of males; in such cases, the model should include both females and males, in separate stages.
Density dependence refers to how the population growth depends on population size. In many species, both survival and fecundity decrease as a function of population size (i.e., more crowded populations have lower population growth). The mechanism for this is usually intraspecific competition for limited resources, such as food, light, and space (i.e., nesting or hiding sites). However, at very low populations, the reverse of this can also happen: because of factors collectively known as Allee effects, survival or reproduction may be lower when population size is very low (because of, for instance, difficulty in finding mates, or breakdown of social structures).
Density dependence can have important effects on extinction risks (e.g., see Ginzburg et al. 1990), therefore it is necessary to use caution in selecting the type of density dependence, and specifying its parameters. Most types of density dependence are modeled with two main parameters: the maximum population growth rate, and carrying capacity. Carrying capacity, the population size that can be supported by the available habitat and resources, provides an important link between the suitability of habitat (see above) and population dynamics. Thus, for example, projected habitat loss is often translated as a decline in the population's carrying capacity in the population model.
Most PVA models represent the landscape as discrete patches of suitable habitat, surrounded by a "matrix" which does not support populations, but may allow dispersal. Each discrete habitable patch is assumed to support one biological population (sometimes called a subpopulation of a metapopulation). A biological population can be defined as a group of regularly interbreeding (i.e. panmictic) individuals. How these populations are delineated (i.e., the number, size, shape, and location of these populations in the landscape) determines the model's spatial structure.
One approach to delineating populations is to identify clusters of cells in the habitat suitability map (see above) that have high values (high suitability). Clusters are identified based on a distance parameter called "Neighborhood distance"; suitable cells within this distance of each other are grouped into one patch (see Figure 2 for an example). Thus, individuals (or territories) that are farther apart than the neighborhood distance are considered to be in different populations. This approach, combined with modeling and prediction of suitable habitat as described above, is used in habitat-based metapopulation models to delineate populations (Akçakaya 2000b; 2005).
Dispersal and connectivity
Dispersal is the movement of individuals in the landscape. Dispersal between populations allows extinct populations (unoccupied patches) to become recolonized, and decreases the probability of local extinction of extant but small populations ("rescue effect"). Thus, in many cases increased dispersal increases viability. However, this is not always true (see Stacey et al. 1997; Beier & Noss 1998; Lecomte et al. 2004); in some cases, increasing dispersal, e.g., by building or maintaining habitat corridors, may not be the best option. Whether or not such conservation actions are useful depends on many factors, including the behavior of the species in corridors, risk of spreading diseases or attracting predators, and cost of, and alternatives to, corridors (Akçakaya et al. 2007). Thus, defining connectivity as a conservation goal by itself may be counterproductive; instead the role of dispersal should be studied in the context of the whole metapopulation, and in terms of its effect on the overall viability of the species in the landscape.
How connectivity is incorporated into a PVA depends on model type (see above). Parameters commonly used to model connectivity include dispersal rate (proportion of individuals moving from one habitat patch to another), and dispersal probability (probability off an individual moving from one patch or cell to another). Estimation of these parameters can be based on mark-recapture data. Relative rates of dispersal can be based on landscape-based approaches such as least cost path (or friction) maps (Haines et al. 2006), gravity models (Beaudry, deMaynadier, & Hunter 2008) or circuit-theoretic methods (McRae et al. 2008). However, to be useful in a PVA, these relative measures must be combined with estimates of the actual number or proportion of individuals dispersing.
Variability and uncertainty
Variability is a pervasive characteristic of natural populations, and an important determinant of risk of extinction or decline in population models. Some variability in population sizes arises from the internal dynamics of the population; these include deterministic changes such as fluctuations in age composition due to departure from the stable age distribution, and random changes caused by demographic stochasticity. Demographic stochasticity is the sampling variation in the number of survivors and the number of offspring that occurs (even if survival rates and fecundities were constant) because a population is made up of a finite, integer number of individuals. Demographic stochasticity is often modeled by sampling the number of survivors from a binomial distribution and the number of offspring from a Poisson distribution (Akçakaya 1991). Relative to other factors, demographic stochasticity becomes more important at small population sizes.
Variability is also caused by fluctuations in environmental factors, causing stochastic changes in demographic rates such as survival, growth, fecundity, and dispersal. Environmental stochasticity is often modeled by selecting these demographic rates from random probability distributions, with specified mean, variance and distribution type (such as normal, lognormal, beta, etc.). For examples of incorporating environmental variability into PVA models, see Akçakaya et al. (2004).
Estimating temporal variability for a PVA is often complicated because, for unbiased estimates, the components due to sampling and demographic stochasticity must be subtracted from total observed variance. Otherwise, variability may be overestimated, which may cause overestimated risks, as well as truncation (and, consequently, bias) in vital rates. There are several ways to obtain unbiased estimates:
If survival rates are based on a mark-recapture analysis, see Gould & Nichols (1998), White et al. (2002), or the help file of Program MARK on how to remove demographic/sampling variance.
If survival or fecundity estimates are based on age-structured census data, subtract the expected demographic variance from the observed variance (Akçakaya 2002).
If the data are from a census of the total (or part of the) population, use methods discussed by Holmes (2001, 2004).
If you have repeated or parallel estimates of the same population, the covariance of the parallel measurements or the within-year variance estimates can be used to subtract observation error from total observed variance (see Dunning et al. 2002; and Morris & Doak 2002, Chapter 5).
An important consideration is the correlation among the demographic rates over time. This can be either different demographic rates in the same population (e.g., the correlation between survival and fecundity), or in different populations (e.g., the spatial correlation of population growth rate). Correlation increases the variability of the population size, and hence increases the risks of decline or increase (LaHaye et al. 1994). Thus, assuming no (or zero) correlation often gives results that are not precautionary.
Landscapes change according to seasons, climatic fluctuations (e.g., droughts, El Niño events), disturbances (e.g., fire and windthrow) and succession, as well as human impacts (e.g., urban sprawl, global climate change, and agricultural expansion). For a species in such a dynamic landscape, these changes cause changes in the spatial structure of the population (e.g., populations may become more fragmented or more isolated), as well as in the characteristics of populations (e.g., habitat loss may mean a declining carrying capacity). These changes have important effects on the viability of the species, which depends on the interaction between landscape change (the pattern, scale, rate and direction of habitat changes in size, structure and quality) and the species' ecology (its ability to disperse between and function within the habitat patches).
For many species, habitat loss and global climate change are two important threats that cause reduction, shifts, and fragmentation of their habitats. To adequately analyze these threats, a PVA should allow a dynamic spatial structure; in other words, it should simulate temporal changes in the location and number of populations that arises from habitat patches splitting, merging, appearing and disappearing as the species' habitat changes (Akçakaya 2001; Akçakaya & Root 2003). PVA approaches that link a dynamic habitat to metapopulation models with dynamic spatial structure have been applied to study climate change (Keith et al. 2008; Anderson et al. 2009; Brook et al. 2009), timber harvest, succession and natural disturbances (Akçakaya et al. 2004, 2005; Wintle et al. 2005).
Model parameters used in a PVA always contain some level of uncertainty. This uncertainty may be a consequence of measurement error, not knowing how different model parameters interact with one another, natural variability in the environment, and/or not knowing how parameters may change in the future. The relative effects of uncertainty in model parameters on model results can be evaluated by conducting a sensitivity analysis. A sensitivity analysis can help to identify important parameters in which small changes in estimated values or assumptions have relatively large effects on conclusions drawn from the model. Sensitivity analysis can also help to prioritize resource allocation to collecting field data in the future as it will allows for identifying parameters whose more precise estimation will have the largest effects on improving model confidence (Akçakaya & Sjögren-Gulve 2000). PVAs, particularly when constructed as spatially explicit demographic or individual based models, can include complicated interactions between multiple variables. Ideally, sensitivity analysis should include tests of multiple parameters at once rather than one-at-a-time parameter tests especially if spatial and non-spatial parameters may be interacting (Naujokaitis-Lewis et al. 2009).
Guidelines for implementing conservation using this approach
Evaluating Conservation Options
Population viability models naturally lend themselves to address questions related to available conservation management options. It may be that you wish to evaluate a proposed plan in terms of how effective it may be over time or how the focal species might be expected to respond. You may have multiple management options on the table and you wish rank to them in terms of expected effectiveness. For example, reserve design often involves selecting the network of reserve areas that will represent the greatest number of species. This approach does not examine whether the arrangement and connectivity of the selected reserve areas will be sufficient to support the long term survival of any those species. By looking at the total species pool and selecting a subset of focal species that are representative of the range of dispersal abilities, life history traits, and habitat preferences and conducting a PVA for those focal species you would be able to evaluate the proposed reserve designs with an eye toward long-term viability of the species represented. Within a PVA framework each reserve can be evaluated as one or more patch or subpopulation for each focal species. Other examples of how PVA can inform conservation planning include simulating habitat corridor design by modeling increased dispersal between patches and simulating translocation or reintroduction by modeling a set number of individuals being moved or reintroduced to a patch.
When making decisions between competing management options, very often the final decision ends up being a combination of both biological and non-biological considerations. The biological aspects are those related to the long-term viability of the focal species (but see discussion in Formulation of Goals and Questions section). The non-biological aspects are those that are related to the societal, cultural, or financial constraints or costs associated with each proposed action. Hopefully, any proposed management option with unacceptably high costs or serious constraints would have been ruled out early in the decision making process. Among the remaining management options PVA can be useful by providing a biologically-based risk assessment criterion to rank competing options. Decision makers can then decide if it is more important to maximize viability for the species (subject to cost constraints) or minimize the costs (as long as the species viability is above some threshold).
Climate change has the potential to pose a threat to a great number of species, particularly those already being impacted by habitat loss and fragmentation, hunting, pollution, disease, and competition from invasive species. PVA provides a method to examine the impact of climate change that goes beyond predicting net changes in amount and location of suitable habitat available under future climate scenarios. The linkage between species demography and the landscape available with PVA models allows for examining how a species’ dispersal and colonization abilities will be able to keep pace with the rate of change. Recent work by Brook et al. (2009) and Keith et al. (2008) demonstrates how a species risk of extinction under climate change depends on complex interactions between life history characteristics and the landscape.
The method of linking PVA to future climate scenario models involves generating or interpolating the future climate predictions to create a dynamic variable of available habitat through time. At this point, a spatially explicit demographic model for the species can play out on the changing landscape (Keith et al. 2008). However, it is important when constructing the dynamic habitat model under predicted future climate condition to be careful to consider how correlations between present environmental conditions may change in the future. For example, if elevation is shown to be an important predictor of habitat suitability for a species presently it may be that the species is not responding to elevation per se, but rather the temperature and precipitation regimes associated with elevation which may change with future climate conditions. Changing habitat in response to climate change can often result in a more fragmented spatial structure of the metapopulation. In such cases, the factors that affect survival of small populations (Alee effects and demographic stochasticity) and those that affect connectivity (dispersal rates) may be expected to play more important roles in the future.
In addition to changing habitat suitability in time (and the resulting change in the spatial structure of the species’ metapopulation), climate change can also affect other aspects of a species’ ecology. These can be incorporated into a PVA through changes in average survival or fecundity of affected populations (if climatic conditions in those populations are predicted to become less suitable for the species), in the variability of survival and fecundity (if the frequency or strength of extreme weather events such as hurricanes, droughts, or fires are predicted to increase in the future).
An important advantage of PVA compared to alternative methods of assessment is that it can incorporate the effects of multiple impacts and conservation measures. Thus, a model can simulate effects of habitat loss (through decrease in carrying capacity of affected populations), harvest or poaching (through reduced survival rates in populations targeted), climate change (by changes in several model parameters, as discussed above), as well as conservation actions that are designed to mitigate against these threats, such as reintroductions, translocations, protected areas, habitat corridors and habitat restoration and improvement. In some cases, different threats may exacerbate each other’s impact. For example, habitat loss may result in smaller populations, which may make them more vulnerable to affects of hunting (e.g., due to Allee effects) or climate change. Thus, it is important to build PVAs that incorporate all known threats to the populations of the species, rather than focusing on one threat or one conservation measure.
This material is based in part upon work supported by the National Aeronautics and Space Administration under Grant No. NNX09AK19G issued through the NASA Biodiversity Program.
Akçakaya, H.R. 1991. “A method for simulating demographic stochasticity..” Ecological Modelling 54:133-136.
Akçakaya, H.R. 1992. “Population cycles of mammals: evidence for a ratio-dependent prediction hypothesis..” Ecological Monographs 62:119-142.
Akçakaya, H.R. 1994. RAMAS Metapop: viability analysis for stage structured metapopulations. Setauket, NY: Applied Biomathematics.
Akçakaya, H.R. 2000a. “Population viability analyses with demographically and spatially structured models.” Ecological Bulletins 48:23-38.
Akçakaya, H.R. 2000b. “Viability analyses with habitat-based metapopulation models.” Population Ecology 42:45-53.
Akçakaya, H.R. 2001. “Linking population-level risk assessment with landscape and habitat models.” Science of the Total Environment 274:283-291.
Akçakaya, H.R. 2002. “Estimating the variance of survival rates and fecundities.” Animal Conservation 5:333-336.
Akçakaya, H. R. 2005. RAMAS GIS: linking spatial data with population viability analysis. Setauket, NY: Applied Biomathematics.
Akçakaya, H.R., and B.W. Brook. 2008. “Methods for determining viability of wildlife populations in large landscapes.” in Models for Planning Wildlife Conservation in Large Landscapes, edited by J.J. Millspaugh and FR Thompson, III. Burlington, MA: Elsevier Academic Press.
Akçakaya, H.R., and W.T. Root. 2003. RAMAS Landscape: integrating metapopulation viability with LANDIS forest dynamics mode. Setauket, NY: Applied Biomathematics.
Akçakaya, H. R., and P. Sjögren-Gulve. 2000. “Population Viability Analyses in Conservation Planning: An Overview.” Ecological Bulletins 9-21.
Akçakaya, H.R., M.A. Burgman, and L.R. Ginzburg. 1999. Applied Population Ecology. Sunderland, MA: Sinauer Associates.
Akçakaya, H.R., M.A. Burgman, O. Kindvall, C. Wood, and P. Sjögren-Gulve, eds. 2004. Species Conservation and Management: Case Studies. New York: Oxford University Press.
Akçakaya, H.R., J. Franklin, A.D. Syphard, and J.R. Stephenson. 2005. “Viability of Bell's sage sparrow
(Amphispiza belli ssp. belli): altered fire regimes.” Ecological Applications 15:521-531.
Akçakaya, H.R., G. Mills, and C.P. Doncaster. 2007. “The role of metapopulations in conservation.” Pp. 64-84 in Key Topics in Conservation Biology, edited by D.W. Macdonald and K. Service. Blackwell.
Anderson, B. et al. 2009. “Dynamics of range margins for metapopulations under climate change.” Proceedings of the Royal Society B: Biological Sciences 276:1415-1420.
Beaudry, F., P.G. deMaynadier, and M.L. Hunter. 2008. “Identifying road mortality threat at multiple spatial scales for semi-aquatic turtles.” Biological Conservation 141:2550-2563.
Beier, P., and R.F. Noss. 1998. “Do habitat corridors provide connectivity?” Conservation Biology 12:1241-1252.
Bekessy, S.A. et al. 2009. “Modelling human impacts on the Tasmanian wedge-tailed eagle (Aquila audax fleayi).” Biological Conservation 142:2438-2448.
Box, G.E.P. 1979. “Robustness in the strategy of scientific model building.” in Robustness in Statistics, edited by R.L. Laurner and G.N. Wilkinson. Elsevier Science & Technology Books.
Breininger, D.R., M.L. Legare, and R.B. Smith. 2004. “Eastern Indigo Snakes (Drymarchon couperi) in Florida: Influence of edge effects on population viability..” Pp. 299-311 in Species Conservation and Management: Case Studies, edited by H.R. Akçakaya et al. New York, NY: Oxford University Press.
Brito, D., & F.A.S. Fernandez. 2000. “Metapopulation viability of the marsupial Micoureus demerarae in small Atlantic forest fragments in south-eastern Brazil.” Animal Conservation 3:201-209.
Brook, B.W., D.M.J.S. Bowman, C.J.A. Bradshaw, B.M. Campbell, and P.J. Whitehead. 2006. “Managing an Endangered Asian Bovid in an Australian National Park: The Role and Limitations of Ecological-Economic Models in Decision-Making.” Environmental Management 38:463-469.
Brook, B.W., J.J. O'Grady, A.P. Chapman, M.A. Burgman, H.R. Akçakaya, & R. Frankham. 2000. “Predictive accuracy of population viability analysis in conservation biology.” Nature 404:385-387.
Brook, B.W., H.R. Akcakaya, D.A. Keith, G.M. Mace, R.G. Pearson, & M.B. Araujo. 2009. “Integrating bioclimate with population models to improve forecasts of species extinctions under climate change.” Biology Letters 5:723-725.
Brown, K.A., S. Spector, and W. Wu. 2008. “Multi-scale analysis of species introductions: combining landscape and demographic models to improve management decisions about non-native species.” Journal of Applied Ecology 45:1639-1648.
Caswell, H. 2001. Matrix population models. MA, USA: Sinauer Associates Sunderland.
Cooley, H.S., R.B. Wielgus, G.M. Koehler, H.S. Robinson, & B.T. Maletzke. 2009. “Does hunting regulate cougar populations? A test of the compensatory mortality hypothesis.” Ecology 90:2913-2921.
DeAngelis, D.L., & W.M. Mooij. 2005. “Individual-Based Modeling of Ecological and Evolutionary Processes.” Annual Review of Ecology, Evolution, and Systematics 36:147-168.
Dunham, A.E., H.R. Akcakaya, & T.S. Bridges. 2006. “Using scalar models for precautionary assessments of threatened species.” Conservation Biology 20:1499-1506.
Dunning, D.J., Q.E. Ross, S.B. Munch, & L.R. Ginzburg. 2002. “Measurement Error Affects Risk Estimates for Recruitment to the Hudson River Stock of Striped Bass.” The Scientific World Journal 2:238-253.
Elith, J., C.H. Graham, R.P. Anderson, M. Dudik, S. Ferrier, A. Guisan, R.J. Hijmans, et al. 2006. “Novel methods improve prediction of species' distributions from occurrence data.” Ecography 29:129-151.
Franklin, J. 2010. Mapping Species Distributions: Spatial Inference and Prediction. Cambridge University Press.
Fryxell, J.M., J.F. Wilmshurst, A.R.E. Sinclair, D.T. Haydon, R.D. Holt, and P.A. Abrams. 2005. “Landscape scale, heterogeneity, and the viability of Serengeti grazers.” Ecology Letters 8:328-335.
Gilioli, G., A. Bodini, J. Baumgartner, P. Weidmann, & J. Hartmann. 2008. “A novel approach based on information theory to rank conservation strategies: an application to amphibian metapopulations.” Animal Conservation 11:453-462.
Ginzburg, L.R., S. Ferson, and H.R. Akçakaya. 1990. “Reconstructibility of Density Dependence and the Conservative Assessment of Extinction Risks.” Conservation Biology 4:63-70.
Ginzburg, L.R., & C.X.J. Jensen. 2004. “Rules of thumb for judging ecological theories.” Trends in Ecology and Evolution 19:121-126.
Gould, W.R., and J.D. Nichols. 1998. “Estimation of temporal variability of survival in animal populations.” Ecology 79:2531-2538.
Grimm, V et al. 2004. “META-X: generic software for metapopulation viability analysis.” Biodiversity and Conservation 13:165-188.
Grimm, V., and S.F. Railsback. 2005. Individual-based modeling and ecology. Princeton University Press.
Guisan, A., and W. Thuiller. 2005. “Predicting species distribution: offering more than simple habitat models.” Ecology Letters 8:993-1009.
Guisan, A., and N.E. Zimmermann. 2000. “Predictive habitat distribution models in ecology.” Ecological Modelling 135:147-186.
Haines, A.M., M.E. Tewes, L.L. Laack, J.S. Horne, and J.H. Young. 2006. “A habitat-based population viability analysis for ocelots (Leopardus pardalis) in the United States.” Biological Conservation 132:424-436.
Hanski, I. 1994. “A Practical Model of Metapopulation Dynamics.” Journal of Animal Ecology 63:151-162.
Hodgson, J.A., A. Moilanen, N.A.D. Bourn, C.R. Bulman, and C.D. Thomas. 2009. “Managing successional species: Modelling the dependence of heath fritillary populations on the spatial distribution of woodland management.” Biological Conservation 142:2743-2751.
Holmes, E. E. 2004. “Beyond theory to application and evaluation: Diffusion approximations for population viability analysis.” Ecological Applications 14:1272-1293.
Holmes, E.E. 2001. “Estimating risks in declining populations with poor data.” Proceedings of the National Academy of Sciences of the United States of America 98:5072-5077.
Hraber, P.T., and B.T. Milne. 1997. “Community assembly in a model ecosystem.” Ecological Modelling 103:267-285.
Kearney, M., and W. Porter. 2009. “Mechanistic niche modelling: combining physiological and spatial data to predict species' ranges.” Ecology Letters 12:334-350.
Keith, D.A. et al. 2008. “Predicting extinction risks under climate change: coupling stochastic population models with dynamic bioclimatic habitat models.” Biology Letters 4:560-563.
Kindvall, O., and K.-O. Bergman. 2004. “Woodland brown butterfly (Lopinga achine) in Sweden: viability in a dynamic landscape maintained by grazing.” Pp. 171-178 in Species Conservation and Management: Case Studies, edited by H.R. Akçakaya, M.A. Burgman, O. Kindvall, C. Wood, and P. Sjögren-Gulve. New York: Oxford University Press.
Lacy, R.C. 1993. “VORTEX - A computer-simulation model for population viability analysis.” Wildlife Research 20:45-65.
Lahaye, W.S., R.J. Guitierrez, and H.R. Akçakaya. 1994. “Spotted owl Metapopulation dynamics in southern California.” Journal of Animal Ecology 63:775-785.
Larson, M.A., F.R. Thompson, J.J. Millspaugh, W.D. Dijak, and S.R. Shifley. 2004. “Linking population viability, habitat suitability, and landscape simulation models for conservation planning.” Ecological Modelling 180:103-118.
Lecomte, J., K. Boudjemadi, F. Sarrazin, K. Cally, and J. Clobert. 2004. “Connectivity and homogenisation of population sizes: an experimental approach in Lacerta vivipara.” Journal of Animal Ecology 73:179-189.
Li, Y., G. Zhongwei, Y. Qisen, W. Yushan, and J. Niemelä. 2003. “The implications of poaching for giant panda conservation.” Biological Conservation 111:125-136.
Lindenmayer, D.B., H.P. Possingham, R.C. Lacy, M.A. McCarthy, and M.L. Pope. 2003. “How accurate are population models? Lessons from landscape-scale tests in a fragmented system.” Ecology Letters 6:41-47.
Lozier, J.D., P. Aniello, and M.J. Hickerson. 2009. “Predicting the distribution of Sasquatch in western North America: anything goes with ecological niche modelling.” Journal of Biogeography 36:1623-1627.
McRae, B.H., N.H. Schumaker, R.B. McKane, R.T. Busing, A.M. Solomon, and C.A. Burdick. 2008. “A multi-model framework for simulating wildlife population response to land-use and climate change.” Ecological Modelling 219:77-91.
Morris, W.F., and D.F. Doak. 2002. Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis. 1st ed. Sinauer Associates.
Murrow, J.L., J.D. Clark, and E.K. Delozier. 2009. “Demographics of an Experimentally Released Population of Elk in Great Smoky Mountains National Park.” Journal of Wildlife Management 73:1261-1268.
Naujokaitis-Lewis, IR, JMR Curtis, P Arcese, and J Rosenfeld. 2009. “Sensitivity Analyses of Spatial Population Viability Analysis Models for Species at Risk and Habitat Conservation Planning.” Conservation Biology 23:225-229.
O'Regan, H.J., A. Turner, and D.M. Wilkinson. 2002. “European Quaternary refugia: a factor in large carnivore extinction?” Journal of Quaternary Science 17:789-795.
Ozgul, A., K.B. Armitage, D.T. Blumstein, D.H. Vanvuren, and M.K. Oli. 2006. “Effects of patch quality and network structure on patch occupancy dynamics of a yellow-bellied marmot metapopulation.” Journal of Animal Ecology 75:191-202.
Pellet, J., G. Maze, and N. Perrin. 2006. “The contribution of patch topology and demographic parameters to population viability analysis predictions: the case of the European tree frog.” Population Ecology 48:353-361.
Possingham, H.P., and I. Davies. 1995. “ALEX - A model for the viability analysis of spatially structured populations.” Biological Conservation 73:143-150.
Quintana-Ascencio, P.F., I. Caballero, J.M. Olano, A. Escudero, and M.J. Albert. 2009. “Does habitat structure matter? Spatially explicit population modelling of an Iberian gypsum endemic.” Population Ecology 51:317-328.
Ranius, T., and O. Kindvall. 2006. “Extinction risk of wood-living model species in forest landscapes as related to forest history and conservation strategy.” Landscape Ecology 21:687-698.
Schumaker, N.H. 1998. A users guide to the PATCH model. Corvallis, Oregon: Environmental Protection Agency, Environmental Research Laboratory.
Sezen, Z., H. R. Akçakaya, and C.C. Bilgin. 2004. “Turkish Mouflon (Ovis gmelinii anatolica) in Central Anatolia: Population Viability under Scenarios of Harvesting for Trophy.” Pp. 459-468 in Species Conservation and Management: Case Studies, edited by H.R. Akçakaya, M.A. Burgman, O. Kindvall, C. Wood, and P. Sjögren-Gulve. New York: Oxford University Press.
Shimada, M., and F. Ishihama. 2000. “Asynchronization of local population dynamics and persistence of a metapopulation: a lesson from an endangered composite plant, Aster kantoensis.” Population Ecology 42:63.
Sjögren-Gulve, P., and T. Ebenhard. 2000. The use of population viability analyses in conservation planning. Wiley-Blackwell.
Southwell, D.M., A.M. Lechner, T. Coates, and B.A. Wintle. 2008. “The sensitivity of population viability analysis to uncertainty about habitat requirements: Implications for the management of the endangered southern brown bandicoot.” Conservation Biology 22:1045-1054.
Spromberg, J.A., and L.L. Johnson. 2008. “Potential effects of freshwater and estuarine contaminant exposure on lower Columbia River chinook salmon (Oncorhynchus tshawytscha) populations.” in Demographic Toxicity: Methods in Ecological Risk Assessment, edited by H. R. Akcakaya, J. D. Stark, and T.S. Bridges. New York, NY: Oxford University Press.
Stacey, P.B., V.A. Johnson, and M.L. Taper. 1997. “Migration within metapopulations: the impact upon local population dynamics.” Pp. 267-291 in Metapopulation biology: ecology, genetics, and evolution, edited by I Hanski and M.E. Gilpin. San Diego, CA: Academic Press.
White, G.C., A.B. Franklin, and T.M. Shenk. 2002. “Estimating parameters of PVA models from data on marked animals.” Pp. 169-190 in Population Viability Analysis, edited by S.R. Beissinger and D.R. McCullough. University Of Chicago Press.
White, G.C., and K.P. Burnham. 1999. “Program MARK: survival estimation from populations of marked animals.” Bird Study 46:120-139.
Wintle, B. A., S.A. Bekessy, L.A. Venier, J. L. Pearce, and R. A. Chisholm. 2005. “Utility of Dynamic-Landscape Metapopulation Models for Sustainable Forest Management.” Conservation Biology 19:1930-1943.
Table 1: Types of PVA models (modified from Akçakaya and Brook 2008)
High rate of local extinction and recolonization
Limited demographic data
Small, short-lived organisms (e.g., invertebrates)
Large number of patches
Alpine Rhine valley amphibians (Gilioli et al. 2008)
Saproxylic invertebrates (Ranius & Kindvall 2006)
Heath Fritillary butterfly (Melitaea athalia) (Hodgson et al. 2009)
Yellow-bellied Marmot Marmota flaviventris (Ozgul et al. 2006)
Lattice (grid-based) models
Relatively uniform or undisturbed landscapes
Landscapes with continuous environmental gradients
Locally abundant organisms
Serengeti grazers (Fryxell et al. 2005)
Helianthemum squamatum (Quintana-Ascencio et al. 2009)
Aster kantoensis (Shimada & Ishihama 2000)
Asian Water Buffalo (Brook et al. 2006)
Demographically (age- or stage) structured metapopulation models
Locally abundant organisms
Vertebrates and plants
Large or dynamic landscapes
Survival or fecundity depends on age or size
Sufficient demographic data
Invasive tree Syzygium jambos (Brown et al. 2008)
Woodland Brown Butterfly (Kindvall & Bergman 2004)
Chinook Salmon (Spromberg & Johnson 2008)
Tree Frog (Pellet, Maze, & Perrin 2006)
Eastern Indigo Snake (Breininger, Legare, & Smith 2004)
Ovenbird (Larson et al. 2004)
Tasmanian Wedge-tailed Eagle (Bekessy et al. 2009)
Cougar (Cooley et al. 2009)
Southern Brown Bandicoot (Southwell et al. 2008)
Very small populations
Abundant demographic and behavioral data
Large-bodied, territorial species
Modeling impact of genetic threats
Determining emergent behaviors
Micoures demerarae (Brito & Fernandez 2000)
Panthera gombaszoegensis (O'Regan, Turner, & Wilkinson 2002)
Community assembly (Hraber & Milne 1997)
Giant Panda Ailuropoda melanoleuca (Li et al. 2003)
Elk Cervus elaphus (Murrow, Clark, & Delozier 2009)
Figure 1. Main components of a Population Viability Analysis (from Akçakaya et al 1999).
Figure 2. Detail of the spatial structure of the PVA model of the California Gnatcatcher. Shades of green represent habitat suitability (the lighter the color, the higher the suitability), the white outlines are the approximate outer borders of patches, identified based on a neighborhood distance parameter of 300 meters (Akçakaya & Atwood 1997). Cell (pixel) size of the underlying habitat map is 100 meters. Each patch represents one population of the metapopulation model. In this small section of the study area, there are 3 small patches and part of a large patch (identified as "6"). The smallest patch ("2") consists of 70 cells. Smaller clusters of suitable cells are not identified as populations, because they are too small to support a population.