Choosing a Management Strategy: Two Structured Decision-Making Methods for Evaluating the Predictions of Stochastic Simulation Models

We describe two structured decision-making methods—one using a hierarchy of goals and a second using ranking on the sum of weighted criteria—that may be useful for many practical conservation problems, particularly when advisory groups evaluate the output of simulation models. We illustrate both methods by applying them to the problem of choosing a management strategy to address the "mobbing" problem in endangered Hawaiian monk seals. Both methods require estimates of the probabilities of various outcomes, such as a population size of more than 400 seals after 20 years under a specific management regime. We used a simulation model of a small monk seal population to generate these probabilities. Both methods provide an explicit, well-documented, and reproducible decision process that helps justify the decision. Furthermore, they are easy for those untrained in decision analysis to understand and use, they focus discussion on management objectives, they facilitate an examination of trade-offs in the light of multiple and sometimes conflicting objectives, they are suitable for use in workshops, and, at least in our example, they lead to management recommendations that are not highly sensitive to minor changes in probability estimates or other factors.     

Stochastic environmental research risk assessment

In a briefly approach, sustainability can be defined as the ability to achieve economic prosperity while protecting the natural systems of the planet, and providing a higher quality of life for its people. Nowadays it is a prime and very active area of research, fundamental for human development. Several concepts based on economics, social and environmental concerns have been considered in the development of sustainability indices. The sustainability concept is, not only but necessarily, dependent on “quantification of the environment health”, necessary to determine its effectiveness in achieving or increasing the environmental capacities of ecosystems, as well as to compare alternative plans and policies, to influence decision-makers.Environmental indices are a very important tool for the analysis of some environmental assessment factors, providing quantitative criteria and synthesizing the available information. A good index should be simple to use, transparent, and expandable across other issues. In particular, environmental indices are a useful tool for several audiences, to aid environmental decision making and to allow the media to keep score of and reduce complex information to a smaller, more easily retained, amount of information [Hardi, P., DeSouza-Huletey, J.A., 2000. Issues in analyzing data and indicators for sustainable development. Ecol. Model. 130, 59–65].The goal of this work is the development of environmental indices, based on stochastically simulated scenarios, using probabilistic approaches. This study was applied to assess the impact of particulate air contamination on the Setúbal Peninsula ecosystems (South of Lisbon, Portugal).     

Stochastic theory of ecological interactions

It is possible, using the distribution of random numbers of random variables, to derive bimodal vertical distributions of phytoplankton biomass similar to those observed in nature. On the basis of the distribution of pseudorandom events, equations for the probability of individual mortality from one of several reasons, and for the capture of one of several preys by the predators were obtained. From these theoretical formulations the empirical equations of Beverton and Holt, Ricker and Ivlev were derived. An equation for the average feed intake of one individual interacting in a swarm, feeding on aggregated food, is derived from an estimate of the average interval between the random encounters of aggregates, in the nodes of an α-dimensional net.     

Stochastic models for forest fires

A stochastic model for man-caused forest fires is developed for a forest with given environmental conditions which is represented by an index. This model is then generalized to take into account both man-caused and natural fires and the mean and the variance of the number of fires is derived. Fitting procedure for given data is suggested.     

Simulation of the Effect of Spatial and Temporal Variation in Fire Regimes on the Population Viability of a Banksia Species

Populations of plants that rely on seeds for recovery from disturbance by fire (obligate seeders) are sensitive to regimes of frequent fire. Obligate seeders are prominent in fire-prone heathlands of southern Australia and South Africa. Population extinction may occur if there are successive fires during a plant's juvenile period. Research on the population biology of obligate seeders has influenced the management of fire in these heath and shrublands, but work on the effects of the spatial variability of fires is lacking. We hypothesize that extinction maybe avoided under an adverse fire frequency if fires are patchy. We present a model that simulates the effects of spatial and temporal variations in fire regimes on the viability of a plant population in a grid landscape. Seedling establishment, maturation, senescence, and seed dispersal determine the presence or absence of plants in each cell. We used values typical of serotinous Banksia species to estimate probability of extinction in relation to fire frequency and size. We examined the sensitivity of predictions to dispersal, senescence, fire frequency, spatial burning pattern and size variance, and the size of the grid. Simulations 200 years in length indicated that extinction probability was lowest when mean fire frequency was intermediate and mean fire size was large. When fire frequency was high, extinction probability was high irrespective of fire size. Senescence was more important than high-frequency fire as a cause of extinction in cells. Interactions between dispersal, fire frequency, and size were complex, indicating that extinction is governed by intercell connectivity. The model indicates that fire patchiness cannot be assumed to ensure avoidance of extinction of populations. Conservation of populations is most likely when fire patchiness is relatively low—when the size of fires is moderate to large and when burned patches are contiguous.     

Effective Population Size in Red-Cockaded Woodpeckers: Population and Model Differences

Loss of genetic variability in isolated populations is an important issue for conservation biology. Most studies involve only a single population of a given species and a single method of estimating rate of loss. Here we present analyses for three different Red-cockaded Woodpecker ( Picoides borealis ) populations from different geographic regions. We compare two different models for estimating the expected rate of loss of genetic variability, and test their sensitivity to model parameters. We found that the simpler model (Reed et al. 1988) consistently estimated a greater rate of loss of genetic variability from a population than did the Emigh and Pollak (1979) model. The ratio of effective population size (which describes the expected rate of loss of genetic variability) to breeder population size varied widely among Red-cockaded Woodpecker populations due to geographic variation in demography. For this species, estimates of effective size were extremely sensitive to survival parameters, but not to the probability of breeding or reproductive success. Sensitivity was sufficient that error in estimating survival rates in the field could easily mask true population differences in effective size. Our results indicate that accurate and precise demographic data are prerequisites to determining effective population size for this species using genetic models, and that a single estimate of rate of loss of genetic variability is not valid across populations.     

Stochastic gravity models for modeling lake invasions

Freshwater aquatic systems in North America are being invaded by many different species, ranging from fish, mollusks, cladocerans to various bacteria and viruses. These invasions have serious ecological and economic impacts. Human activities such as recreational boating are an important pathway for dispersal. Gravity models are used to quantify the dispersal effect of human activity. Gravity models currently used in ecology are deterministic. This paper proposes the use of stochastic gravity models in ecology, which provides new capabilities both in model building and in potential model applications. These models allow us to use standard statistical inference tools such as maximum likelihood estimation and model selection based on information criteria. To facilitate prediction, we use only those covariates that are easily available from common data sources and can be forecasted in future. This is important for forecasting the spread of invasive species in geographical and temporal domain. The proposed model is portable, that is it can be used for estimating relative boater traffic and hence relative propagule pressure for the lakes not covered by current boater surveys. This makes our results broadly applicable to various invasion prediction and management models.     

Risk-Based Viable Population Monitoring

Abstract:  We describe risk-based viable population monitoring, in which the monitoring indicator is a yearly prediction of the probability that, within a given timeframe, the population abundance will decline below a prespecified level. Common abundance-based monitoring strategies usually have low power to detect declines in threatened and endangered species and are largely reactive to declines. Comparisons of the population's estimated risk of decline over time will help determine status in a more defensible manner than current monitoring methods. Monitoring risk is a more proactive approach; critical changes in the population's status are more likely to be demonstrated before a devastating decline than with abundance-based monitoring methods. In this framework, recovery is defined not as a single evaluation of long-term viability but as maintaining low risk of decline for the next several generations. Effects of errors in risk prediction techniques are mitigated through shorter prediction intervals, setting threshold abundances near current abundance, and explicitly incorporating uncertainty in risk estimates. Viable population monitoring also intrinsically adjusts monitoring effort relative to the population's true status and exhibits considerable robustness to model misspecification. We present simulations showing that risk predictions made with a simple exponential growth model can be effective monitoring indicators for population dynamics ranging from random walk to density dependence with stable, decreasing, or increasing equilibrium. In analyses of time-series data for five species, risk-based monitoring warned of future declines and demonstrated secure status more effectively than statistical tests for trend.     

Population Viability Estimates: Theory and Practice for a Wild Gorilla Population

The logic of demographic modeling, the apparent simplicity of its quantifiably substantiated answers, and the ready availability of software correlate with increasing use of demographic modeling as the means of applying biology to the conservation of potentially endangered populations. I investigated that use by considering a small population (about 300 individuals) of a large, forest-dwelling mammal of the tropics, the Virunga gorilla ( Gorilla gorilla ) of Zaire, Uganda, and Rwanda. Because censuses of forest populations are so inaccurate and data on variance of some parameters takes so long to collect, models might not be broadly applicable. Therefore, simple demographic indices of potential extinction should replace sophisticated models. The current best index could be problematic, however, because it is based on detecting adult mortality, perhaps the most difficult demographic parameter to measure. Models of the Virunga gorilla population that incorporate aspects of demographic heterogeneity valuably indicate genetic and demographic persistence for several hundred years. Deterministic change in habitat is a greater threat than stochastic demographic variation, and yet our ecological ignorance is such that we could not begin to model the consequences of removal of even the main food plant. We must add to our ability to model outcomes of demographic perturbation a far greater understanding of the processes by which the perturbations occur. Demography allows us to model demographic response to demographic change, but we usually need ecology to tell us how the threat produced the demographic change in the first place. In a time of change, accurate prediction requires ecological understanding of process as well as demographic understanding of outcome.     

Stochastic growth reduces population fluctuations in Daphnia-algal systems

Deterministic, size-structured models are widely used to describe consumer-resource interactions. Such models typically ignore potentially large random variability in juvenile development rates. We present simple representations of this variability and show five approaches to calculating the model parameters for Daphnia pulex interacting with its algal food. Using our parameterized models of growth variability, we investigate the robustness of a recently proposed stabilizing mechanism for Daphnia populations. Growth rate variability increases the range of enrichments over which small-amplitude cycles or quasi-cycles occur, thus increasing the plausibility that the underlying mechanism contributes to the prevalence of small-amplitude cycles in the field and in experiments. More generally, our approach allows us to relate commonly available information on variance of development times to population stability.     

Long-Term Population Development of a Reintroduced Beaver (Castor fiber) Population in Sweden

Deliberate reintroductions of locally exterminated animal species to areas within their former ranges is an increasingly important conservation tool. Most reintroductions are fairly recent and still in an initial phase of population development. There are few long-term studies of reintroduced populations. The aim of this study was to see if the population development of the reintroduced European beaver ( Castor fiber ) population in Sweden exhibits the same pattern of population development as other introductions, in accordance with general theories, and to discuss possible management consequences. Since the European beaver was reintroduced to Sweden 70 years ago, the population has developed in a way predicted by the Riney-Caughley model for introduced ungulates, exhibiting an irruption and a subsequent decline. In two study areas, the rate of population increase (r) turned negative after 34 and 25 years and at densities of 0.25 and 0.20 colonies/km², respectively. The data suggest that management policy for an irruptive species should allow hunting during the rapid-increase phase, thus maintaining food resources and avoiding uncontrolled population decline.     

Population as an oscillating system

In this paper we present a new approach describing population dynamics based on the view of a population as an oscillating system. To develop a mathematical model of an oscillating population, we applied a third-order differential equation. Our model describes population dynamics within a parametric-temporal continuum, formed by the relative values of population growth and decrease over time. In this paper we also illustrate how our oscillative model effectively compliments the existing suite of models in population dynamics.     

Population Variability and Extinction Risk

Abstract: Population models generally predict increased extinction risk (ER) with increased population variability (  PV  ), yet some empirical tests have provided contradictory findings. We resolve this conflict by attributing negative measured relationships to a statistical artifact that arises because PV tends to be underestimated for populations with short persistence. Such populations do not go extinct quickly as a consequence of low intrinsic variability; instead, the measured variability is low because they go extinct so quickly. Consequently, any underlying positive relationship between PV and ER tends to be obscured. We conducted a series of analyses to evaluate this claim. Simulations showed that negative measured relationships are to be expected, despite an underlying positive relationship. Simulations also identified properties of data, minimizing this bias and thereby permitting meaningful analysis. Experimental data on laboratory populations of a bruchid beetle (Callosobruchus maculatus) supported the simulation results. Likewise, with an appropriate statistical approach (Cox regression on untransformed data), reanalysis of a controversial data set on British island bird populations revealed a significant positive association between PV and ER (p = 0.03). Finally, a similar analysis of time series for naturally regulated animal populations revealed a positive association between PV and quasiextinction risk (p < 0.01). Without exception, our simulation results, experimental findings, reanalysis of published data, and analysis of quasiextinction risk all contradict previous reports of negative or equivocal relationships. Valid analysis of meaningful data provides strong evidence that increased population variability leads to increased extinction risk.