Optimal escapement levels in stochastic and deterministic harvesting models

A constant-escapement feedback policy is shown to be optimal in maximizing expected discounted net revenue from an animal resource whose dynamics are described by a stochastic stock-recruitment model, provided that unit harvesting costs satisfy certain conditions. The optimal escapement in this model is compared with that in the corresponding deterministic model and it is shown how the way in which unit harvesting costs vary with population abundance can be important in determining the relative sizes of the optimal escapements. In most cases, the optimal stochastic escapement is no less than the optimal deterministic escapement.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Some stochastic differential equation models of an aquatic ecosystem

A set of stochastic differential equations has been used to model an aquatic ecosystem. The randomness in the system has been introduced through initial conditions of the state variables, parameters, and input variables (light and temperature). These models were analysed using Monte Carlo simulation procedures and the results were similar to those observed in the experimental and field data. They were different, however, from the results of a deterministic simulation. This approach allows us to incorporate the maximum degree of information in the model and to study the behavior of the system without arbitrarily manipulating the values of the parameters. Some possible refinements and generalizations of this approach are also discussed.     

A note on density dependence in population models

One of the most studied phenomena in ecology is density dependent regulation. The model most frequently used to study this behaviour is the theta-logistic model. However, disagreement has developed within the ecology community pertaining to the interpretation of this model’s parameters, and thus as to appropriate values for the parameters to assume. In particular, the parameter θ$\theta$ has been allowed to take negative values, resulting in the ‘growth rate parameter’ estimated to be negative for species which are extant and exhibit no signs of becoming extinct in the short-term. Here we explain this phenomenon by formulating the theta-logistic model in the manner in which the original logistic model was formulated by Verhulst (1838), in doing so providing a simple interpretation of model parameters and thus restrictions on values the parameters may assume. We conclude that θ$\theta$ should (almost always) be restricted to values greater than −1$-1$. This has implications for studies assessing the form of density dependence from data. Additionally, another model appearing in the literature is presented which provides a more flexible model of density dependence at the expense of only one additional parameter.     

Increasing accuracy of dispersal kernels in grid-based population models

Dispersal kernels in grid-based population models specify the proportion, distance and direction of movements within the model landscape. Spatial errors in dispersal kernels can have large compounding effects on model accuracy. Circular Gaussian and Laplacian dispersal kernels at a range of spatial resolutions were investigated, and methods for minimizing errors caused by the discretizing process were explored. Kernels of progressively smaller sizes relative to the landscape grid size were calculated using cell-integration and cell-center methods. These kernels were convolved repeatedly, and the final distribution was compared with a reference analytical solution. For large Gaussian kernels (σ > 10 cells), the total kernel error was <10⁻¹¹ compared to analytical results. Using an invasion model that tracked the time a population took to reach a defined goal, the discrete model results were comparable to the analytical reference. With Gaussian kernels that had σ ≤ 0.12 using the cell integration method, or σ ≤ 0.22 using the cell center method, the kernel error was greater than 10%, which resulted in invasion times that were orders of magnitude different than theoretical results. A goal-seeking routine was developed to adjust the kernels to minimize overall error. With this, corrections for small kernels were found that decreased overall kernel error to <10⁻¹¹ and invasion time error to <5%.     

Using stochastic volatility models to analyse weekly ozone averages in Mexico City

In this paper we make use of some stochastic volatility models to analyse the behaviour of a weekly ozone average measurements series. The models considered here have been used previously in problems related to financial time series. Two models are considered and their parameters are estimated using a Bayesian approach based on Markov chain Monte Carlo (MCMC) methods. Both models are applied to the data provided by the monitoring network of the Metropolitan Area of Mexico City. The selection of the best model for that specific data set is performed using the Deviance Information Criterion and the Conditional Predictive Ordinate method.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is presented.     

A comparison of models for predicting population persistence

We consider a range of models that may be used to predict the future persistence of populations, particularly those based on discrete-state Markov processes. While the mathematical theory of such processes is very well-developed, they may be difficult to work with when attempting to estimate parameters or expected times to extinction. Hence, we focus on diffusion and other approximations to these models, presenting new and recent developments in parameter estimation for density dependent processes, and the calculation of extinction times for processes subject to catastrophes. We illustrate these and other methods using data from simulated and real time series. We give particular attention to a procedure, due to Ross et al. [Ross, J.V., Taimre, T., Pollett, P.K. On parameter estimation in population models, Theor. Popul. Biol., in press], for estimating the parameters of the stochastic SIS logistic model, and demonstrate ways in which these parameters may be used to estimate expected extinction times. Although the stochastic SIS logistic model is strictly density dependent and allows only for birth and death events, it nonetheless may be used to predict extinction times with some accuracy even for populations that are only weakly density dependent, or that are subject to catastrophes.     

On inferring population trends of mobile waterbirds from aerial transect surveys in variable environments

Environmental and Ecological Statistics - Monitoring waterbird populations in Australia is challenging for reasons of counting logistics, and because population aggregation and dispersion can shift...     

Identifying key species in ecosystems with stochastic sensitivity analysis

The development of approaches to estimate the vulnerability of biological communities and ecosystems to extirpations and reductions of species is a central challenge of conservation biology. One key aim of this challenge is to develop quantitative approaches to estimate and rank interaction strengths and keystoneness of species and functional groups, i.e. to quantify the relative importance of species. Network analysis can be a powerful tool for this because certain structural aspects of ecological networks are good indicators of the mechanisms that maintain co-evolved, biotic interactions. A static view of ecological networks would lead us to focus research on highly-central species in food webs (topological key players in ecosystems). There are a variety of centrality indices, developed for several types of ecological networks (e.g. for weighted and un-weighted webs). However, truly understanding extinction and its community-wide effects requires the use of dynamic models. Deterministic dynamic models are feasible when population sizes are sufficiently large to minimize noise in the overall system. In models with small population sizes, stochasticity can be modelled explicitly. We present a stochastic simulation-based ecosystem model for identification of “dynamic key species” in situations where stochastic models are appropriate. To demonstrate this approach, we simulated ecosystem dynamics and performed sensitivity analysis using data from the Prince William Sound, Alaska ecosystem model. We then compare these results to those of purely topological analyses and deterministic dynamic (Ecosim) studies. We present the relationships between various topological and dynamic indices and discuss their biological relevance. The trophic group with the largest effect on others is nearshore demersals, the species mostly sensitive to others is halibut, and the group of both considerable effect on and sensitivity to others is juvenile herring. The most important trophic groups in our dynamical simulations appear to have intermediate trophic levels.     

Closed population estimation models and their extensions in Program MARK

Program MARK provides > 65 data types in a common configuration for the estimation of population parameters from mark-encounter data. Encounter information from live captures, live resightings, and dead recoveries can be incorporated to estimate demographic parameters. Available estimates include survival (S or ϕ), rate of population change (λ), transition rates between strata (Ψ), emigration and immigration rates, and population size (N). Although N is the parameter most often desired by biologists, N is one of the most difficult parameters to estimate precisely without bias for a geographically and demographically closed population. The set of closed population estimation models available in Program MARK incorporate time (t) and behavioral (b) variation, and individual heterogeneity (h) in the estimation of capture and recapture probabilities in a likelihood framework. The full range of models from M ₀ (null model with all capture and recapture probabilities equal) to M _tbh are possible, including the ability to include temporal, group, and individual covariates to model capture and recapture probabilities. Both the full likelihood formulation of Otis et al. (1978) and the conditional model formulation of Huggins (1989, 1991) and Alho (1990) are provided in Program MARK, and all of these models are incorporated into the robust design (Kendall et al. 1995, 1997; Kendall and Nichols 1995) and robust-design multistrata (Hestbeck et al. 1991, Brownie et al. 1993) data types. Model selection is performed with AICc (Burnham and Anderson 2002) and model averaging (Burnham and Anderson 2002) is available in Program MARK to provide estimates of N with standard error that reflect model selection uncertainty.     

Extinction-effective population index: incorporating life-history variations in population viability analysis

Viability status of populations is a commonly used measure for decision-making in the management of populations. One of the challenges faced by managers is the need to consistently allocate management effort among populations. This allocation should in part be based on comparison of extinction risks among populations. Unfortunately, common criteria that use minimum viable population size or count-based population viability analysis (PVA) often do not provide results that are comparable among populations, primarily because they lack consistency in determining population size measures and threshold levels of population size (e.g., minimum viable population size and quasi-extinction threshold). Here I introduce a new index called the "extinction-effective population index," which accounts for differential effects of demographic stochasticity among organisms with different life-history strategies and among individuals in different life stages. This index is expected to become a new way of determining minimum viable population size criteria and also complement the count-based PVA. The index accounts for the difference in life-history strategies of organisms, which are modeled using matrix population models. The extinction-effective population index, sensitivity, and elasticity are demonstrated in three species of Pacific salmonids. The interpretation of the index is also provided by comparing them with existing demographic indices. Finally, a measure of life-history-specific effect of demographic stochasticity is derived.     

Stability and exploitation in two-species discrete time population models with delay

A two species model is developed which incorporates interactions at both the adult stage and the juvenile stage, as well as delays between birth and sexual maturity.The local stability of the model is examined. In particular, four necessary conditions are given and a simple sufficiency condition derived, which may avoid the need to calculate eigenvalues.The optimal steady state escapement levels are then derived under the assumption that neither species is completely removed. The optimal levels are those which maximize the discounted present value of the net economic yield.Finally, the results are applied to two models; one a familiar interspecific competition model and the other a two sex whaling model proposed by the author.     

A multivariate analysis of beta diversity across organisms and environments

We examined variability in hierarchical beta diversity across ecosystems, geographical gradients, and organism groups using multivariate spatial mixed modeling analysis of two independent data sets. The larger data set comprised reported ratios of regional species richness (RSR) to local species richness (LSR) and the second data set consisted of RSR:LSR ratios derived from nested species-area relationships. There was a negative, albeit relatively weak, relationship between beta diversity and latitude. We found only relatively subtle differences in beta diversity among the realms, yet beta diversity was lower in marine systems than in terrestrial or freshwater realms. Beta diversity varied significantly among organisms' major characteristics such as body mass, trophic position, and dispersal type in the larger data set. Organisms that disperse via seeds had highest beta diversity, and passively dispersed organisms showed the lowest beta diversity. Furthermore, autotrophs had lower beta diversity than organisms higher up the food web; omnivores and carnivores had consistently higher beta diversity. This is evidence that beta diversity is simultaneously controlled by extrinsic factors related to geography and environment, and by intrinsic factors related to organism characteristics.     

Qualitative analysis of generalized volterra models

Generalized Volterra models are analyzed qualitatively to provide some information concerning their applicability as ecological-model estimators. For the general two-population system (including prey-predator, competitive, and other cases), the stability of the equilibrium points and other properties of the phase representation are investigated. For n-population systems, stability analysis is carried out mainly by means of several Liapunov functions. The persistence (or global stability of nontrivial equilibrium) of n-population systems is investigated, leading to an interaction-exclusion principle which implies restrictions on the interaction structure of the system, especially in the case of trophic systems.     

Bayesian analysis of Jolly-Seber type models

We propose the use of finite mixtures of continuous distributions in modelling the process by which new individuals, that arrive in groups, become part of a wildlife population. We demonstrate this approach using a data set of migrating semipalmated sandpipers (Calidris pussila) for which we extend existing stopover models to allow for individuals to have different behaviour in terms of their stopover duration at the site. We demonstrate the use of reversible jump MCMC methods to derive posterior distributions for the model parameters and the models, simultaneously. The algorithm moves between models with different numbers of arrival groups as well as between models with different numbers of behavioural groups. The approach is shown to provide new ecological insights about the stopover behaviour of semipalmated sandpipers but is generally applicable to any population in which animals arrive in groups and potentially exhibit heterogeneity in terms of one or more other processes.     

重污染河道浮游动物种群的特点

苏州城市河道水情复杂,氮磷浓度较高,属于重污染的滞流水体.通过对试验区南园水系为期1a的调查研究表明:该河段共有浮游动物33种,其中原生动物4种,轮虫类24种,枝角类4种,桡足类1种.各河段浮游动物年平均密度为678 ind·L-1,生物量为56.028 mg·L-1.从种类数来看,轮虫类大于原生动物大于枝角类大于桡足类.从密度看,全年平均以轮虫最多,其次为原生动物,桡足类最少.从生物量看,以枝角类最高,桡足类次之,原生动物最少.从季节变化来看,春夏季较多,秋冬季较少.优势种为轮虫类和枝角类,这些种类极耐有机污染,耐低溶氧.在苏州古城区重污染河道中,浮游动物的总量与水体理化指标及浮游植物的数量等均没有线性相关性(差异显著,p<0.05),这可能与苏州城市河道污染较重有关.城市河道特殊的水域环境决定了浮游动物种群的形成、演变及其发展都有其特殊性.探讨了重污染的城市河道的浮游动物种类组成特点,提出了控制某些优势种群发展的设想,为改善河道水环境提供了理论依据.     

Unveiling human-assisted dispersal mechanisms in invasive alien insects: Integration of spatial stochastic simulation and phenology models

Capturing the spread of biological invasions in heterogeneous landscapes is a complex modelling task where information on both dispersal and population dynamics needs to be integrated. Spatial stochastic simulation and phenology models have rarely been combined to assist in the study of human-assisted long-distance dispersal events.Here we develop a process-based spatially explicit landscape-extent simulation model that considers the spread and detection of invasive insects. Natural and human-assisted dispersal mechanisms are modelled with an individual-based approach using negative exponential and negative power law dispersal kernels and gravity models. The model incorporates a phenology sub-model that uses daily temperature grids for the prediction and timing of the population dynamics in each habitat patch. The model was applied to the study of the invasion by the important maize pest western corn rootworm (WCR) Diabrotica virgifera ssp. virgifera in Europe. We parameterized and validated the model using maximum likelihood and simulation methods from the historical invasion of WCR in Austria.WCR was found to follow stratified dispersal where international transport networks in the Danube basin played a key role in the occurrence of long-distance dispersal events. Detection measures were found to be effective and altitude had a significant effect on limiting the spread of WCR. Spatial stochastic simulation combined with phenology models, maximum likelihood methods and predicted versus observed regression showed a high degree of flexibility that captured the salient features of WCR spread in Austria. This modelling approach is useful because it allows to fully exploit and the often limited and heterogeneous information available regarding the population dynamics and dispersal of alien invasive insects.