A model for behavioral regulation of metapopulation dynamics

Habitat fragmentation can decrease local population persistence by reducing connectivity, which is a function of dispersal of individuals among habitat fragments. Dispersal is often treated as diffusion in population models, even though for many species it is a result of a series of behavioral decisions. We developed a metapopulation model to explore the potential importance of dispersal behaviors in driving metapopulation dynamics. We incorporated types of behavior that affect dispersal—colonization inhibiting, colonization enhancing, extinction inhibiting, extinction enhancing, rescue enhancing, rescue inhibiting—into Levins’ (1969) metapopulation model and projected occupancy rates for a variety of parameter values. Examples from the literature of behaviors associated with each of these parameters are provided. Our model simplifies into previously published metapopulation models that incorporate only a single behavior, and we present a density-dependent rescue function that leads to multiple non-zero equilibria. We found a variety of behavioral effects on metapopulations. Rescue enhancement fills patches faster than does colonization enhancement or extinction inhibition, and declines in patch occupancy are moderate with extinction enhancement, but colonization inhibition causes metapopulation extinction. We also found that with colonization and extinction inhibitions, equilibrium patch occupancy is inversely related to patch turnover rate. With density-dependent rescue, persistence depends not only on the strength of the strong rescue effect, but also on having a sufficient initial fraction of patches occupied; the stronger the rescue effect, the lower this fraction can be. This study suggests that dispersal behavior can have strong influences on metapopulation dynamics. It confirms the importance of understanding the relationship between landscape structure and dispersal behavior in understanding population persistence.     

Robust optimal observation of a metapopulation

We consider a two-parameter continuous-time Markovian model for patch occupancy in metapopulation, and address the question of when to observe the population in order to obtain the most accurate and precise estimator of the parameters. Using the likelihood obtained from a diffusion approximation we derive a robust procedure for determining the optimal observation schedule, which is considerably simpler than would otherwise be possible. We investigate the performance of two optimality criteria, ED-optimality and a particular form of maximin-optimality. Both allow one to incorporate prior belief about the parameter values before any data is collected. Kernel density estimates of the maximum likelihood estimator are compared under the various combinations of optimality criteria and prior distributions. Our methods are illustrated with reference to a model for the spread of crown of thorns starfish (Acanthaster planci) among the 55 islands comprising the Ryukyu group in Japan.     

Analytical methods for a stochastic mainland-island metapopulation model

We study a class of chain-binomial metapopulation models, giving special attention to the ‘mainland-island’ configuration, where patches receive immigrants from an external source. We evaluate the distribution of the number n_t of occupied patches at any census time t and establish a law of large numbers that identifies a deterministic trajectory which can be used to approximate the process when the number of patches is large. We also establish a central limit law, which shows that the fluctuations about this trajectory are approximately normally distributed. We describe briefly much finer results that can be used for model calibration.     

Incorporating natural enemies in an economic threshold for dynamically optimal pest management

The control of pests by their natural enemies represents an important regulating ecosystem service that helps maintain the stability of crop ecosystems. These services, however, are often ignored in pest management decision making. In addition, the use of broad-spectrum insecticides can damage the populations of natural enemies, reducing the cost-effectiveness of insecticide investment if unaccounted for in treatment decisions.The existing literature on modeling of biological control of insect pests has generally focused on simulations of the population dynamics of pest and natural enemy species and the processes underlying pest control. But agriculture is a managed ecosystem where predator–prey relationships are heavily influenced by human managers. In modeling managerial choices, this study develops an intra-seasonal dynamic bioeconomic optimization model for insecticide-based pest management that explicitly takes into account both the biological control effect of natural enemies on pest density and the nontarget mortality effect of insecticides on the level of natural pest control supplied. The model captures predator–prey interactions, linking them to crop growth and yield damage functions, which in turn are evaluated in a dynamic optimization framework. We introduce a new decision rule for judicious insecticide decisions using a natural enemy-adjusted economic threshold. This threshold represents the pest population density at which insecticide control becomes optimal in spite of the opportunity cost of injury to natural enemies of the target pest. Using field data from Michigan, the model is applied to the case of soybean aphid (Aphis glycines, Matsumura), a recent invasive pest of soybean (Glycine max), whose management is of both economic and environmental importance to the North Central region of the United States. As illustrated by the numerical examples, such natural enemy-adjusted threshold is likely to lead to fewer recommendations for insecticide use than naïve models that ignore natural enemies, resulting in less insecticide use, while maintaining profitability for farmers that rely on chemical pest control methods.The bioeconomic model developed in this study can be used to conduct a wide variety of analyses such as identifying dynamically optimal spray strategies and estimating the implied economic value of natural control services. Furthermore, with the incorporation of inter-year carry-over factors, such as overwintering of pests and natural enemies, the current model can contribute to building multi-year models for studying long-term pest management.     

A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.     

A stochastic bioeconomic model for the management of clam farming

The Manila clam Tapes philippinarum is one of the most important commercial mollusc species in Europe. Intensive clam farming takes place in several coastal lagoons of the Northern Adriatic Sea, supporting local economy but raising the problem of the environmental sustainability of this activity. In this work, we propose a bioeconomic model that provides guidelines for an efficient management of intensive clam farming. Clam demography is described by a stochastic model of growth and survival, accounting for the effect of water temperature, seeding substratum and density dependence of vital rates. The model is calibrated on and applied to the case of Sacca di Goro, a lagoon located in the Po River Delta (Northern Italy). We consider two distinct management criteria: the optimisation of the marketable yield and the optimisation of monetary benefits, respectively. The use of a stochastic formulation allows us to reveal the existing trade-off between maximizing the median yield or profit and minimizing its variance. A Pareto analysis shows that seeding in spring or fall on sandy substrata and harvesting 18 months later provides the best compromise between these two contrasting objectives, maximizing profits while minimizing the associated uncertainty level. Finally, we show that seeding clams at high densities (more than 750 clams m⁻² on muddy substrata and more than 1500 elsewhere) can have not only a potentially negative impact on the ecological sustainability of clam farming, but also a negative economic effect.     

A simulation model for the management of low density recreational areas

In order to take account of the congestion externalities associated with increased use intensity during a given period at a low density recreational resource, it is necessary to determine the effects of alternative use levels on the expected quality of each individual's experience. This paper describes a simulation model for wilderness recreation designed to provide such measures. In order to illustrate the model it is applied to the Spanish Peaks Areas in Montana.     

Predicting the economic impact of an invasive species on an ecosystem service.

Quantifying the impact of alien invasive species on ecosystem services is an essential step in developing effective practices and policy for invasive species management. Here we develop a stochastic bioeconomic model that enables the economic impact of an invasive pest to be estimated before its arrival, based on relatively poorly specified ecological and economic parameters. We developed the model by using a hypothetical invasion of the varroa bee mite (Varroa destructor) into Australia and the negative flow-on effects that it would have on pollination by reducing honey bee populations, giving rise to a loss of pollination services, reduced crop yields, and additional production costs. If the mite were to continue to be prevented from entering the country over the next 30 years, we estimate that the economic costs avoided would be U.S. $16.4-38.8 million (Aus $21.3-50.5 million) per year. We suggest that current invasion response funding arrangements in Australia, which do not acknowledge these avoided damages, require amendment.     

A simulation model for the management of vicuña populations

The population dynamics of the vicuña was modelled based on field data from the Central Galeras Sector, Perú. Rains were simulated in order to obtain net primary productivity and grass availability which act upon density-dependent fecundity and mortality. The model produces a population growth curve that tends to stabilize at densities around 100 vicuñas per km². Harvest and shearing processes were simulated as part of the vicuña population management model. Harvest was based upon a fixed threshold density D_e below which no harvest occurs; for densities above D_e harvesting is applied at a rate proportional to the difference between D_e and the current population density (fixed escapement or ‘bang-bang’ harvest rule). Management optimization was analyzed by determining the optimal escapement density D_e, which maximized either net profits or the number of animals harvested. Analyzing the results as cumulative totals over 20 years of simulation, an optimum harvest production was obtained for a D_e of about 40 vicuñas per km², and maximum profit was obtained for a D_e around 70 vicuñas per km². Analyzing the results of 20 years of simulation as annual averages with an original population density of 40 vicuñas per km², the harvest production and profits were maximized for a D_e of 40 and 60 vicuñas per km², respectively.The model was validated using data from the Reserva Nacional San Guillermo, Argentina, where vicuña and guanaco populations coexist (although their interaction was not modelled). The sensitivity analysis was performed with three different techniques: (a) stepwise multiple linear regression, (b) visual graphic analysis based on a polar coordinates system, and (c) direct evaluation of the effect on management decisions. The curve shape parameters of the fecundity and mortality functions proved to be the most important ones in determining the outcome of the model.     

A metapopulation approach of the dynamics of arthropods from Mediterranean-type ecosystems

In this paper we developed a general stage-structured, Leslie-type model, suitable to simulate dynamics of soil arthropods under typical Mediterranean conditions. In order to explore arthropods’ life-history strategies in relation to enhanced spatial heterogeneity of the Mediterranean ecosystems, metapopulation characteristics were considered and different habitat quality regimes, in terms of dominant microclimatic conditions, were taken into account. Environmental stochasticity in temperature and humidity was incorporated into the model, and an elasticity analysis was conducted to quantify contribution of different life-history traits to metapopulation growth rate. The application of the model revealed well-known life-cycle characteristics of Mediterranean arthropods, such as seasonally fluctuating population sizes and skewing phenologies, a fact that confirms models’ reliability. Furthermore, the model seems able to elucidate controversial points of the animals’ life-cycle development, such as the long-term maintenance of populations in the field and the underlying mechanisms related to the adjustment to the specific features of the Mediterranean ecosystem. Subpopulations inhabiting various microsites display different dynamics and the interaction between these subpopulations, via dispersion, seems to be able to ensure stochastic equilibrium for the system. Dispersal appears to play a decisive role, allowing arthropods to conform to spatial severities and habitats fragmentation, rescuing individuals and recolonizing previously extinct habitats.     

Nitrogen inputs promote the spread of an invasive marsh grass.

Excess nutrient loading and large-scale invasion by nonnatives are two of the most pervasive and damaging threats to the biotic and economic integrity of our estuaries. Individually, these are potent forces, but it is important to consider their interactive impacts as well. In this study we investigated the potential limitation of a nonnative intertidal grass, Spartina alterniflora, by nitrogen (N) in estuaries of the western United States. Nitrogen fertilization experiments were conducted in three mud-flat habitats invaded by S. alterniflora in Willapa Bay, Washington, USA, that differed in sediment N. We carried out parallel experiments in San Francisco Bay, California, USA, in three habitats invaded by hybrid Spartina (S. alterniflora x S. foliosa), in previously unvegetated mud flat, and in native S. foliosa or Salicornia virginica marshes. We found similar aboveground biomass and growth rates between habitats and estuaries, but end-of-season belowground biomass was nearly five times greater in San Francisco Bay than in Willapa Bay. In Willapa Bay, aboveground biomass was significantly correlated with sediment N content. Addition of N significantly increased aboveground biomass, stem density, and the rate of spread into uninvaded habitat (as new stems per day) in virtually all habitats in both estuaries. Belowground biomass increased in Willapa Bay only, suggesting that belowground biomass is not N limited in San Francisco Bay due to species differences, N availability, or a latitudinal difference in the response of Spartina to N additions. The relative impact of added N was greater in Willapa Bay, the estuary with lower N inputs from the watershed, than in San Francisco Bay, a highly eutrophic estuary. Nitrogen fertilization also altered the competitive interaction between hybrid Spartina and Salicornia virginica in San Francisco Bay by increasing the density and biomass of the invader and decreasing the density of the native. There was no significant effect of N on the native, Spartina foliosa. Our results indicate that excess N loading to these ecosystems enhances the vulnerability of intertidal habitats to rapid invasion by nonnative Spartina sp.     

A model for ecological assessment to pesticide pollution management

Applying the relational analysis in the Grey System Theory and Method, the comprehensive evaluation on five pesticide pollution controlling techniques in the vegetable production has been made and a comprehensive profit (cp–comprehensive cost (cc) evaluation system (composed of 15 comprehensive cost indices and 14 comprehensive profit indices) has been established, with a index optimization matrix of comprehensive cost indices and comprehensive profit indices obtained and a ratio model of comprehensive cost to comprehensive profit (R_cc/cp) built. Results show that the R_cc/cp value of vegetables intercropping soybeans in insect-proof thin film greenhouses is the smallest and the R_cc/cp value of vegetables intercropping taros in insect-proof net greenhouses, pheromones in insect-proof thin film greenhouses, pheromones in insect-proof thin film greenhouses and ground planting (only using chemical pesticide for insect-proof without covering materials and synthetic sex pheromone) other four techniques are 0.6268, 0.6393, 0.6407, 0.9809 respectively. In accordance with the R_cc/cp value, vegetables intercropping soybeans in insect-proof thin film greenhouses can be the most optimized pesticide pollution controlling technique in the vegetable growing.     

Quantifying the importance of patch-specific changes in habitat to metapopulation viability of an endangered songbird

A growing number of programs seek to facilitate species conservation using incentive-based mechanisms. Recently, a market-based incentive program for the federally endangered Golden-cheeked Warbler (Dendroica chrysoparia) was implemented on a trial basis at Fort Hood, an Army training post in Texas, USA. Under this program, recovery credits accumulated by Fort Hood through contracts with private landowners are used to offset unintentional loss of breeding habitat of Golden-cheeked Warblers within the installation. Critical to successful implementation of such programs is the ability to value, in terms of changes to overall species viability, both habitat loss and habitat restoration or protection. In this study, we sought to answer two fundamental questions: Given the same amount of change in breeding habitat, does the change in some patches have a greater effect on metapopulation persistence than others? And if so, can characteristics of a patch (e.g., size or spatial location) be used to predict how the metapopulation will respond to these changes? To answer these questions, we describe an approach for using sensitivity analysis of a metapopulation projection model to predict how changes to specific habitat patches would affect species viability. We used a stochastic, discrete-time projection model based on stage-specific estimates of survival and fecundity, as well as various assumptions about dispersal among populations. To assess a particular patch's leverage, we quantified how much metapopulation viability was expected to change in response to changing the size of that patch. We then related original patch size and distance from the largest patch to each patch's leverage to determine if general patch characteristics could be used to develop guidelines for valuing changes to patches within a metapopulation. We found that both the characteristic that best predicted patch leverage and the magnitude of the relationship changed under different model scenarios. Thus, we were unable to find a consistent set of relationships, and therefore we emphasize the dangers in relying on general guidelines to assess patch value. Instead, we provide an approach that can be used to quantitatively evaluate patch value and identify critical needs for future research.     

A hierarchical Bayesian non-linear spatio-temporal model for the spread of invasive species with application to the Eurasian Collared-Dove

The spread of invasive species is a long studied subject that garners much interest in the ecological research community. Historically the phenomenon has been approached using a purely deterministic mathematical framework (usually involving differential equations of some form). These methods, while scientifically meaningful, are generally highly simplified and fail to account for uncertainty in the data and process, of which our knowledge could not possibly exist without error. We propose a hierarchical Bayesian model for population spread that accommodates data sources with errors, dependence structures between population dynamics parameters, and takes into account prior scientific understanding via non-linear relationships between model parameters and space-time response variables. We model the process (i.e., the bird population in this case) as a Poisson response with spatially varying diffusion coefficients as well as a logistic population growth term using a common reaction-diffusion equation that realistically mimics the ecological process. We focus the application on the ongoing invasion of the Eurasian Collared-Dove.     

Development of an integrated decision-support model for density management within jack pine stand-types

The objectives of this study were to (1) develop a modular-based structural stand density management model (SSDMM) and corresponding algorithmic analogue for natural (naturally regenerated stands without a history of density regulation) and managed (naturally or artificially regenerated stands with a history of density regulation) jack pine (Pinus banksiana Lamb.) stand-types, and (2) demonstrate the utility of the model in operational density management decision-making. Employing an Ontario-centric database consisting of 262 and 221 tree-list measurements obtained from 91 and 139 permanent and temporary sample plots situated within natural and managed stand-types, respectively, combined with data derived from density control experiments and sawmill simulation studies, six integrated estimation modules were constructed: Module A consisted of the parameterization of the core yield–density relationships which together drive the entire yield prediction system (e.g., size–density relationships for quadratic mean diameter, dominant height, mean volume, and mean live crown ratio, and site-specific height–age relationships); Module B consisted of the development of Weibull-based parameter prediction equation systems for recovering diameter distributions and composite height-diameter equations for height estimation; Module C consisted of the development of composite taper equations for predicting log products and stem volumes; Module D consisted of the development of allometric-based composite biomass equations for each above-ground component (bark, stem, branch and foliage) from which biomass estimates and associated carbon-based equivalents were derived; Module E consisted of the development of sawmill-specific composite equations for estimating chip and lumber volumes; and Module F consisted of the development of composite equations for estimating wood density and mean maximum branch diameter. The utility of the model was demonstrated by simultaneously contrasting a set of complex density management regimes (commercial thinning and variable planting densities) in terms of a broad array of stand-level yield outcomes and performance measures: overall productivity, log-product distributions, biomass production and carbon yields, recoverable products (chip and lumber volumes) and associated monetary values, economic efficiency, duration of optimal site occupancy, structural stability, and fibre attributes (wood density and mean maximum branch diameter). In summary, the modular-based SSDMM provides the analytical foundation for evaluating the likelihood of realizing a multitude of stand-level objectives when designing density control regimes for jack pine stand-types.     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

SPAnDX: a process-based population dynamics model to explore management and climate change impacts on an invasive alien plant,Acacia nilotica

This paper describes a process-based metapopulation dynamics and phenology model of prickly acacia, Acacia nilotica, an invasive alien species in Australia. The model, SPAnDX, describes the interactions between riparian and upland sub-populations of A. nilotica within livestock paddocks, including the effects of extrinsic factors such as temperature, soil moisture availability and atmospheric concentrations of carbon dioxide. The model includes the effects of management events such as changing the livestock species or stocking rate, applying fire, and herbicide application. The predicted population behaviour of A. nilotica was sensitive to climate. Using 35 years daily weather datasets for five representative sites spanning the range of conditions that A. nilotica is found in Australia, the model predicted biomass levels that closely accord with expected values at each site. SPAnDX can be used as a decision-support tool in integrated weed management, and to explore the sensitivity of cultural management practices to climate change throughout the range of A. nilotica. The cohort-based DYMEX modelling package used to build and run SPAnDX provided several advantages over more traditional population modelling approaches (e.g. an appropriate specific formalism (discrete time, cohort-based, process-oriented), user-friendly graphical environment, extensible library of reusable components, and useful and flexible input/output support framework).     

A model examining hierarchical wetland networks for watershed stormwater management

There is increasing awareness that solutions to degraded quality and excessive quantity of stormwater and resulting impacts on downstream water bodies may require a watershed approach to management rather that the incremental approach that is now common. Examination of low-relief watersheds characteristic of the southeastern coastal plain reveals common hierarchical patterns of surface water convergence that may be emulated in developed watersheds to enhance the efficacy of peak-flow attenuation and pollutant removal. A dynamic systems model was developed to compare stormwater management using a hierarchical network of treatment wetlands with the standard incremental approach wherein treatment systems are designed considering only site-level effluent criteria. The model simulates watershed hydrology, suspended sediment transport and phosphorus removal and transformation. Results indicate that watershed planning of stormwater collection and treatment systems using hierarchical networks can greatly enhance overall effectiveness (annual retention improvements of 31% for flow, 36% for sediment and 27% for phosphorus) with respect to an equal area of uniformly sized wetlands. Further, network proportions can be adjusted to specific runoff characteristics. Distinct roles were observed for each wetland size class: small headwater wetlands effectively removed sediment, medium-sized mid-reach wetlands retained phosphorus, while large wetlands primarily stored and attenuated long-period hydrologic flows.     

Sex ratio and optimal harvest of canvasback ducks,A model

The North American population of canvasback ducks (Aythya valisineria) exhibits extreme distortion of the sex ratio in favor of males. This paper describes a model which accounts for this pattern by relatively heavier female mortality in both the breeding and nonbreeding seasons. The density-dependence of winter mortality leads to the conclusion that the observed sex ratio depresses total population numbers. Variation in nesting success is shown to influence sex ratios and strongly depress population numbers. Because a standard harvest scheme can be demonstrated to severely depress the numbers of ducks, an alternative graduated or weighted harvest procedure is recommended.