Using Scalar Models for Precautionary Assessments of Threatened Species

Abstract:  Scalar population models, commonly referred to as count-based models, are based on time-series data of population sizes and may be useful for screening-level ecological risk assessments when data for more complex models are not available. Appropriate use of such models for management purposes, however, requires understanding inherent biases that may exist in these models. Through a series of simulations, which compared predictions of risk of decline of scalar and matrix-based models, we examined whether discrepancies may arise from different dynamics displayed due to age structure and generation time. We also examined scalar and matrix-based population models of 18 real populations for potential patterns of bias in population viability estimates. In the simulation study, precautionary bias (i.e., overestimating risks of decline) of scalar models increased as a function of generation time. Models of real populations showed poor fit between scalar and matrix-based models, with scalar models predicting significantly higher risks of decline on average. The strength of this bias was not correlated with generation time, suggesting that additional sources of bias may be masking this relationship. Scalar models can be useful for screening-level assessments, which should in general be precautionary, but the potential shortfalls of these models should be considered before using them as a basis for management decisions.     

Imperfectly optimal animals

Summary We consider models of behavior that apply to two different problems: when a predator should leave a foraging site and how a female should choose the best available male. In each case we derive rules for an optimal solution to the problem. We also derive models based on very simple, plausible rules of behavior that we suspect animals may actually use. Although the expected payoffs from optimality models always exceed the expected payoffs from our simpler behavioral models, under certain conditions the difference is not large. When good foraging sites last but a short time and when females' mobility in their habitat is limited, the results of simple models and optimal models are very close indeed.Because of the difficulty of distinguishing between the results of each type of model and because natural selection will presumably provide a best mix of solutions to a range of problems rather than a best solution to any one problem, we suggest that behavioral ecologists expend more effort on simple, plausible models of animal behavior. Such models provide ready-made testable hypotheses about the animal's approximation to optimality and about the actual mechanisms of behavior.     

Age,stages, and the role of generation time in matrix models

The earliest matrix models, proposed in the 1940s, consider age classes, and were later proved to be equivalent to the discrete time version of the stable population theory. In this theory and models, besides the asymptotic growth rate, a very important characteristic is the turnover of individuals, measured in various ways by generation time. Models considering stages, on the contrary, do not take into account the age of individuals and seem largely preferable to age-structured models for many populations in which demographic characteristics are related to biological stages (such a seed, rosette, flowering plant, etc.) rather than to age per itself. These two kinds of models can be embedded as particular cases of stage by age models or multistate models. Theses general models can be used to develop a multistate stable population theory with many advantages. This general theory is reviewed with emphasis on general rules for sensitivity analyses in which generation time plays a central role.     

Optimal annual routines: new tools for conservation biology?

Many applied problems in ecology and conservation require prediction, and population models are important tools for that purpose. Formerly, the majority of predictive population models were based on matrix models. As the limitations of classical matrix models have become clearer, the use of individual-based models has increased. These models use behavioral rules imposed at the level of the individual to establish the emergent consequences of those rules at the population level. Individual behaviors in such models use an array of different rule types, from empirically derived probabilities to long-term fitness considerations. There has been surprisingly little discussion of the strengths and weaknesses of these different rule types. Here, we consider different strategies for modeling individual behaviors, together with some problems associated with individual-based models. We propose a novel approach based on modeling optimal annual routines. Annual routines allow individual behaviors to be predicted over a whole annual cycle within the context of long-term fitness considerations. Temporal trade-offs between different behaviors are automatically included in annual routine models, overcoming some of the primary limitations of other individual-based models. Furthermore, as well as population predictions, individual behaviors and indices of condition are emergent features of annual routine models. We show that these can be more sensitive to environmental change than population size, offering alternative, repeatable metrics for monitoring population status. Annual routine models provide no panacea for the problems of data limitations in predictive population modeling. However, as a result of their ability to deal with life-history trade-offs, as well as their potential for relatively rapid and accurate validation and parameterization, we suggest that annual routine models have strong potential for predictive population modeling in applied conservation settings.     

How complex do models need to be to predict dispersal of threatened species through matrix habitats?

Persistence of species in fragmented landscapes depends on dispersal among suitable breeding sites, and dispersal is often influenced by the "matrix" habitats that lie between breeding sites. However, measuring effects of different matrix habitats on movement and incorporating those differences into spatially explicit models to predict dispersal is costly in terms of time and financial resources. Hence a key question for conservation managers is: Do more costly, complex movement models yield more accurate dispersal predictions? We compared the abilities of a range of movement models, from simple to complex, to predict the dispersal of an endangered butterfly, the Saint Francis' satyr (Neonympha mitchellii francisci). The value of more complex models differed depending on how value was assessed. Although the most complex model, based on detailed movement behaviors, best predicted observed dispersal rates, it was only slightly better than the simplest model, which was based solely on distance between sites. Consequently, a parsimony approach using information criteria favors the simplest model we examined. However, when we applied the models to a larger landscape that included proposed habitat restoration sites, in which the composition of the matrix was different than the matrix surrounding extant breeding sites, the simplest model failed to identify a potentially important dispersal barrier, open habitat that butterflies rarely enter, which may completely isolate some of the proposed restoration sites from other breeding sites. Finally, we found that, although the gain in predicting dispersal with increasing model complexity was small, so was the increase in financial cost. Furthermore, a greater fit continued to accrue with greater financial cost, and more complex models made substantially different predictions than simple models when applied to a novel landscape in which butterflies are to be reintroduced to bolster their populations. This suggests that more complex models might be justifiable on financial grounds. Our results caution against a pure parsimony approach to deciding how complex movement models need to be to accurately predict dispersal through the matrix, especially if the models are to be applied to novel or modified landscapes.     

Spatial statistical models that use flow and stream distance

We develop spatial statistical models for stream networks that can estimate relationships between a response variable and other covariates, make predictions at unsampled locations, and predict an average or total for a stream or a stream segment. There have been very few attempts to develop valid spatial covariance models that incorporate flow, stream distance, or both. The application of typical spatial autocovariance functions based on Euclidean distance, such as the spherical covariance model, are not valid when using stream distance. In this paper we develop a large class of valid models that incorporate flow and stream distance by using spatial moving averages. These methods integrate a moving average function, or kernel, against a white noise process. By running the moving average function upstream from a location, we develop models that use flow, and by construction they are valid models based on stream distance. We show that with proper weighting, many of the usual spatial models based on Euclidean distance have a counterpart for stream networks. Using sulfate concentrations from an example data set, the Maryland Biological Stream Survey (MBSS), we show that models using flow may be more appropriate than models that only use stream distance. For the MBSS data set, we use restricted maximum likelihood to fit a valid covariance matrix that uses flow and stream distance, and then we use this covariance matrix to estimate fixed effects and make kriging and block kriging predictions. Received: July 2005 / Revised: March 2006     

On the consequences of aggregation and balancing of networks on system properties derived from ecological network analysis

In the ecological network analysis (ENA) of complex flow food webs the assumption is often made that the models characterizing the flows and stocks of ecosystems occur in a steady state where inflows equals outflows. An assessment of the system indices derived from ENA of six balanced and unbalanced system models, respectively, indicate to differences between indices. The aggregation of highly articulated flow models into models with fewer compartments also has drastic effects on the system metrics, particularly on the information indices.     

Does including physiology improve species distribution model predictions of responses to recent climate change?

Thermal constraints on development are often invoked to predict insect distributions. These constraints tend to be characterized in species distribution models (SDMs) by calculating development time based on a constant lower development temperature (LDT). Here, we assessed whether species-specific estimates of LDT based on laboratory experiments can improve the ability of SDMs to predict the distribution shifts of six U.K. butterflies in response to recent climate warming. We find that species-specific and constant (5 degrees C) LDT degree-day models perform similarly at predicting distributions during the period of 1970-1982. However, when the models for the 1970-1982 period are projected to predict distributions in 1995-1999 and 2000-2004, species-specific LDT degree-day models modestly outperform constant LDT degree-day models. Our results suggest that, while including species-specific physiology in correlative models may enhance predictions of species' distribution responses to climate change, more detailed models may be needed to adequately account for interspecific physiological differences.     

Population level risk assessment: practical considerations for evaluation of population models from a risk assessor's perspective

Population models are increasingly being considered as a tool for pesticide risk assessment in order to evaluate how potential effects act on the population level and population recovery. While the importance and difficulties of such models have been discussed by various authors during the past decade, mainly with a focus on how to describe or develop such models, several biological and methodological aspects have never been addressed so far, which are relevant for the application of models in risk assessment. These include a critical review of our knowledge of a species, the use of field data by taking methodological constraints into account, how to include uncertainty in model validation or how to measure effects. Although these aspects will be critical for the acceptance of population models by authorities, most of them apply not only to population models, but also to standard risk assessment. In the present article, we give practical recommendations for addressing these questions in population level risk assessments.     

土壤和地下水中污染物迁移模型研究进展

国内外学者已建立了多种模型来描述污染物在土壤和地下水中的环境行为。要选择一个合适的模型在实际中成功地应用,或建立一个新的模型,必须掌握和了解污染物迁移模型的研究现状。文章评述了现有的模型,并对模型的结构作了一定的阐述。     

Measuring impacts on species with models and metrics of varying ecological and computational complexity

Approaches to assess the impacts of landscape disturbance scenarios on species range from metrics based on patterns of occurrence or habitat to comprehensive models that explicitly include ecological processes. The choice of metrics and models affects how impacts are interpreted and conservation decisions. We explored the impacts of 3 realistic disturbance scenarios on 4 species with different ecological and taxonomic traits. We used progressively more complex models and metrics to evaluate relative impact and rank of scenarios on the species. Models ranged from species distribution models that relied on implicit assumptions about environmental factors and species presence to highly parameterized spatially explicit population models that explicitly included ecological processes and stochasticity. Metrics performed consistently in ranking different scenarios in order of severity primarily when variation in impact was driven by habitat amount. However, they differed in rank for cases where dispersal dynamics were critical in influencing metapopulation persistence. Impacts of scenarios on species with low dispersal ability were better characterized using models that explicitly captured these processes. Metapopulation capacity provided rank orders that most consistently correlated with those from highly parameterized and data-rich models and incorporated information about dispersal with little additional computational and data cost. Our results highlight the importance of explicitly considering species’ ecology, spatial configuration of habitat, and disturbance when choosing indicators of species persistence. We suggest using hybrid approaches that are a mixture of simple and complex models to improve multispecies assessments.     

区域及全球尺度的NPP过程模型和NPP对全球变化的响应

植被净第一性生产力（NPP）不仅是表征植被活动和生态过程的关键参数,而且是判定生态系统碳汇和反映生态系统对全球变化响应的主要因子。当前,模型模拟成为大尺度NPP研究的主要手段,而在众多NPP估算模型中,过程模型逐渐趋于主导地位。虽然目前有关NPP的研究有很多,但还没有关注于大尺度上应用的过程模型及其模拟的NPP对全球变化的响应。因此本文主要侧重于 NPP 过程模型在区域及全球尺度上的应用,具体包含以下内容,①进一步将区域及全球尺度的NPP过程模型分为静态植被模型和动态植被模型。②阐明这些模型间存在的区别与联系。③归纳出NPP过程模型在区域及全球尺度上应用的3大挑战：时空尺度转换、多源数据的获取与融合以及模型模拟结果的验证与评价,并根据其解决方案总结出通用的模型应用框架。④从气候变化、大气成分变化和土地利用/土地覆盖变化3个方面探讨NPP对全球变化的响应机制,以期找到NPP变化的规律与模式。最后根据NPP模型的发展对未来区域及全球尺度的NPP过程模型进行展望,认为未来模型的综合性将更高,机理性也将更强,同时与全球变化研究结合得更加紧密,且基于多个已有模型的混合模型也是未来NPP模型发展的一个重要方向。此外,本文认为对NPP模拟结果的尺度效应研究也是未来NPP研究的热点之一。     

Database-driven models of the world's Large Marine Ecosystems

We present a new methodology for database-driven ecosystem model generation and apply the methodology to the world's 66 currently defined Large Marine Ecosystems. The method relies on a large number of spatial and temporal databases, including FishBase, SeaLifeBase, as well as several other databases developed notably as part of the Sea Around Us project. The models are formulated using the freely available Ecopath with Ecosim (EwE) modeling approach and software. We tune the models by fitting to available time series data, but recognize that the models represent only a first-generation of database-driven ecosystem models. We use the models to obtain a first estimate of fish biomass in the world's LMEs. The biggest hurdles at present to further model development and validation are insufficient time series trend information, and data on spatial fishing effort.     

Scaling-up spatially-explicit ecological models using graphics processors

How the properties of ecosystems relate to spatial scale is a prominent topic in current ecosystem research. Despite this, spatially explicit models typically include only a limited range of spatial scales, mostly because of computing limitations. Here, we describe the use of graphics processors to efficiently solve spatially explicit ecological models at large spatial scale using the CUDA language extension. We explain this technique by implementing three classical models of spatial self-organization in ecology: a spiral-wave forming predator-prey model, a model of pattern formation in arid vegetation, and a model of disturbance in mussel beds on rocky shores. Using these models, we show that the solutions of models on large spatial grids can be obtained on graphics processors with up to two orders of magnitude reduction in simulation time relative to normal pc processors. This allows for efficient simulation of very large spatial grids, which is crucial for, for instance, the study of the effect of spatial heterogeneity on the formation of self-organized spatial patterns, thereby facilitating the comparison between theoretical results and empirical data. Finally, we show that large-scale spatial simulations are preferable over repetitions at smaller spatial scales in identifying the presence of scaling relations in spatially self-organized ecosystems. Hence, the study of scaling laws in ecology may benefit significantly from implementation of ecological models on graphics processors.     

Comparison of six correlative models in predictive vegetation mapping on a local scale

A variety of statistical techniques has been used in predictive vegetation modelling (PVM) that attempt to predict occurrence of a given community or species in respect to environmental conditions. We compared the performance of three profile models, BIOCLIM, GARP and MAXENT with three nonparametric models of group discrimination techniques, MARS, NPMR and LRT. The two latter models are relatively new statistical techniques that have just entered the field of PVM. We ran all models on a local scale for a given grassland community (Teucrio-Seslerietum) using the same input data to examine their performance. Model accuracy was evaluated both by Cohen’s kappa statistics (κ) and by area under receiver operating characteristics curve based both on resubstitution of training data and on an independent test data set. MAXENT of profile models and MARS of group discrimination techniques achieved the best prediction.     

Fitting animal survival models with temporal random effects

Estimating temporal variance in animal demographic parameters is of particular importance in population biology. We implement the Schall’s algorithm for incorporating temporal random effects in survival models using recovery data. Our frequentist approach is based on a formulation of band-recovery models with random effects as generalized linear mixed models and a linearization of the link function conditional on the random effects. A simulation study shows that our procedure provides unbiased and precise estimates. The method is then implemented on two case studies using recovery data on fish and birds.     

Prevalence-adjusted optimisation of fuzzy models for species distribution

Most performance criteria which have been applied to train ecological models focus on the accuracy of the model predictions. However, these criteria depend on the prevalence of the training set and often do not take into account ecological issues such as the distinction between omission and commission errors. Moreover, a previous study indicated that model training based on different performance criteria results in different optimised models. Therefore, model developers should train models based on different performance criteria and select the most appropriate model depending on the modelling objective. This paper presents a new approach to train fuzzy models based on an adjustable performance criterion, called the adjusted average deviation (aAD). This criterion was applied to develop a species distribution model for spawning grayling in the Aare River near Thun, Switzerland. To analyse the strengths and weaknesses of this approach, it was compared to model training based on other performance criteria. The results suggest that model training based on accuracy-based performance criteria may produce unrealistic models at extreme prevalences of the training set, whereas the aAD allows for the identification of more accurate and more reliable models. Moreover, the adjustable parameter in this criterion enables modellers to situate the optimised models in the search space and thus provides an indication of the ecological model relevance. Consequently, it may support modellers and river managers in the decision making process by improving model reliability and insight into the modelling process. Due to the universality and the flexibility of the approach, it could be applied to any other ecosystem or species, and may therefore be valuable to ecological modelling and ecosystem management in general.     

Metacommunity models predict the local-regional species richness relationship in a natural system

Many natural communities exhibit positive relationships between local and regional species richness (LSR-RSR relationships), which can be either linear or curvilinear. Previous models have shown that the form of this relationship depends on the relative rates of colonization and extinction and the sensitivity of these rates to competition. We use simple models to show that the LSR-RSR relationship also depends on the type of metacommunity structure (Levins-like or mainland-island), and our models generate a wider range of realistic forms than do most previous models. We parameterize and test our models with two independent data sets for Daphnia in rock pools on islands in Finland and Sweden. We find that the Levins-like model with competition correctly predicts the observed LSR-RSR relationship and provides the best fit to the average local species richness per island. Simulations show that our models are robust to relaxing our assumption of identical species properties. Our study is one of the first to make and successfully test quantitative predictions for how a widely studied community pattern, the LSR-RSR relationship, arises from metacommunity dynamics.     

Nonlinear relationships between vital rates and state variables in demographic models

To accurately estimate population dynamics and viability, structured population models account for among-individual differences in demographic parameters that are related to individual state. In the widely used matrix models, such differences are incorporated in terms of discrete state categories, whereas integral projection models (IPMs) use continuous state variables to avoid artificial classes. In IPMs, and sometimes also in matrix models, parameterization is based on regressions that do not always model nonlinear relationships between demographic parameters and state variables. We stress the importance of testing for nonlinearity and propose using restricted cubic splines in order to allow for a wide variety of relationships in regressions and demographic models. For the plant Borderea pyrenaica, we found that vital rate relationships with size and age were nonlinear and that the parameterization method had large effects on predicted population growth rates, X (linear IPM, 0.95; nonlinear IPMs, 1.00; matrix model, 0.96). Our results suggest that restricted cubic spline models are more reliable than linear or polynomial models. Because even weak nonlinearity in relationships between vital rates and state variables can have large effects on model predictions, we suggest that restricted cubic regression splines should be considered for parameterizing models of population dynamics whenever linearity cannot be assumed.     

Transferability of Species Distribution Models: a Functional Habitat Approach for Two Regionally Threatened Butterflies

Abstract:  Numerous models for predicting species distribution have been developed for conservation purposes. Most of them make use of environmental data (e.g., climate, topography, land use) at a coarse grid resolution (often kilometres). Such approaches are useful for conservation policy issues including reserve-network selection. The efficiency of predictive models for species distribution is usually tested on the area for which they were developed. Although highly interesting from the point of view of conservation efficiency, transferability of such models to independent areas is still under debate. We tested the transferability of habitat-based predictive distribution models for two regionally threatened butterflies, the green hairstreak ( Callophrys rubi ) and the grayling ( Hipparchia semele ), within and among three nature reserves in northeastern Belgium. We built predictive models based on spatially detailed maps of area-wide distribution and density of ecological resources. We used resources directly related to ecological functions (host plants, nectar sources, shelter, microclimate) rather than environmental surrogate variables. We obtained models that performed well with few resource variables. All models were transferable—although to different degrees—among the independent areas within the same broad geographical region. We argue that habitat models based on essential functional resources could transfer better in space than models that use indirect environmental variables. Because functional variables can easily be interpreted and even be directly affected by terrain managers, these models can be useful tools to guide species-adapted reserve management.