Space as the final frontier in stochastic simulations of biological systems

Recent technological and theoretical advances are only now allowing the simulation of detailed kinetic models of biological systems that reflect the stochastic movement and reactivity of individual molecules within cellular compartments. The behavior of many systems could not be properly understood without this level of resolution, opening up new perspectives of using computer simulations to accelerate biological research. We review the modeling methodology applied to stochastic spatial models, also to the attention of non-expert potential users. Modeling choices, current limitations and perspectives of improvement of current general-purpose modeling/simulation platforms for biological systems are discussed.     

Impacts of global change on plant diversity and vice versa: Old and new challenges for vegetation scientists

Abstract. The desire to stop the current dramatic loss of biodiversity has been a major stimulus for many vegetation ecologists to unravel the mechanisms responsible for the coexistence of species. After the Rio Janeiro Convention many ecologists were convinced that nature conservation would gain strong societal support if they could prove that the loss of species would have important negative effects on the ecosystem functions that are relevant to society. I conclude that in order to understand such possible effects, it is necessary to analyse the effects of individual species on those ecosystem processes that we consider to be relevant in the context of specific questions. The great challenge for the near future is to scale the effects of plant species on their local environment up to the level of the whole planet, so that we learn about possible feedbacks that might regulate or destabilize those characteristics of the globe that are essential to our society.     

Assessing variation in life‐history tactics within a population using mixture regression models: a practical guide for evolutionary ecologists

Mixed models are now well‐established methods in ecology and evolution because they allow accounting for and quantifying within‐ and between‐individual variation. However, the required normal distribution of the random effects can often be violated by the presence of clusters among subjects, which leads to multi‐modal distributions. In such cases, using what is known as mixture regression models might offer a more appropriate approach. These models are widely used in psychology, sociology, and medicine to describe the diversity of trajectories occurring within a population over time (e.g. psychological development, growth). In ecology and evolution, however, these models are seldom used even though understanding changes in individual trajectories is an active area of research in life‐history studies. Our aim is to demonstrate the value of using mixture models to describe variation in individual life‐history tactics within a population, and hence to promote the use of these models by ecologists and evolutionary ecologists. We first ran a set of simulations to determine whether and when a mixture model allows teasing apart latent clustering, and to contrast the precision and accuracy of estimates obtained from mixture models versus mixed models under a wide range of ecological contexts. We then used empirical data from long‐term studies of large mammals to illustrate the potential of using mixture models for assessing within‐population variation in life‐history tactics. Mixture models performed well in most cases, except for variables following a Bernoulli distribution and when sample size was small. The four selection criteria we evaluated [Akaike information criterion (AIC), Bayesian information criterion (BIC), and two bootstrap methods] performed similarly well, selecting the right number of clusters in most ecological situations. We then showed that the normality of random effects implicitly assumed by evolutionary ecologists when using mixed models was often violated in life‐history data. Mixed models were quite robust to this violation in the sense that fixed effects were unbiased at the population level. However, fixed effects at the cluster level and random effects were better estimated using mixture models. Our empirical analyses demonstrated that using mixture models facilitates the identification of the diversity of growth and reproductive tactics occurring within a population. Therefore, using this modelling framework allows testing for the presence of clusters and, when clusters occur, provides reliable estimates of fixed and random effects for each cluster of the population. In the presence or expectation of clusters, using mixture models offers a suitable extension of mixed models, particularly when evolutionary ecologists aim at identifying how ecological and evolutionary processes change within a population. Mixture regression models therefore provide a valuable addition to the statistical toolbox of evolutionary ecologists. As these models are complex and have their own limitations, we provide recommendations to guide future users.     

Predicting resource utilization: the utility of optimal foraging models

Predicting how predation changes communities is an important challenge for ecologists. One view assumes that predictions can be made in terms of behavioural phenomena. Static optimality methods have been used to devise models of prey choice and are thought to have performed well. Two examples from the literature show that models of diet choice have either been applied without first testing them at the individual level, or have been tested in a way that does not fulfil all their assumptions. A discussion of the nature of mathematical models shows why it is dangerous to translate theories into natural language and how important it is to appreciate the limitations on the mathematical functions describing behaviour. A final section discusses behavioural phenomena such as satiation and learning, which are likely to limit the predictive capacities of static optimization models. It is likely that dynamic models are the way forward although they may be harder to apply at the ecological level.     

Viola: A New Visual Programming Language Designed for the Rapid Development of Interacting Agent Systems

The construction of complex simulation models and the application of new computer hardware to ecological problems has resulted in the need for many ecologists to rely on computer programmers to develop their modelling software. However, this can lead to a lack of flexibility and understanding in model implementation and in resource problems for researchers. This paper presents a new programming language, Viola, based on a simple organisational concept which can be used by most researchers to develop complex simulations much more easily than could be achieved with standard programming languages such as C++. The language is object oriented and implemented through a visual interface. It is specifically designed to cope with complicated individual based behavioural simulations and comes with embedded concurrency handling abilities.     

Functional responses and predator–prey models: a critique of ratio dependence

Arditi and Ginzburg (2012) propose ordinary differential equations (ODEs) with ratio-dependent functional responses as the new null model for predation, based on their earlier work on ratio-dependent food chains and a number of functional response measurements. Here, I discuss some of their claims, arguing for a flexible and problem-driven approach to predator–prey modeling. Models to understand population cycles and models to predict the effect of basal enrichment on food chains need not be the same. While ratio-dependent functional responses in ODE models might sometimes be useful as limit cases for food chains, they are not intrinsically more useful than prey-dependent models to understand the effect of a given predator on prey population dynamics—and sometimes less useful, given the small temporal scales considered in many models. “Instantism” is showed to be an invalid criticism when ODEs are interpreted as describing average trajectories of stochastic birth–death processes. Moreover, other modeling frameworks with strong ties to time series statistics, such as stochastic difference equations, should be promoted to improve the feedback loop between field and theoretical research. The main problems of current trophic ecology do not lie in a wrong null model, as ecologists have already several at their disposal. The loose connection of ODE models with empirical data and spatial/temporal scaling up of empirical measurements constitute more serious challenges to our understanding of trophic interactions and their consequences on ecosystem functioning.     

Quantifying ecological memory in plant and ecosystem processes

The role of time in ecology has a long history of investigation, but ecologists have largely restricted their attention to the influence of concurrent abiotic conditions on rates and magnitudes of important ecological processes. Recently, however, ecologists have improved their understanding of ecological processes by explicitly considering the effects of antecedent conditions. To broadly help in studying the role of time, we evaluate the length, temporal pattern, and strength of memory with respect to the influence of antecedent conditions on current ecological dynamics. We developed the stochastic antecedent modelling (SAM) framework as a flexible analytic approach for evaluating exogenous and endogenous process components of memory in a system of interest. We designed SAM to be useful in revealing novel insights promoting further study, illustrated in four examples with different degrees of complexity and varying time scales: stomatal conductance, soil respiration, ecosystem productivity, and tree growth. Models with antecedent effects explained an additional 18–28% of response variation compared to models without antecedent effects. Moreover, SAM also enabled identification of potential mechanisms that underlie components of memory, thus revealing temporal properties that are not apparent from traditional treatments of ecological time‐series data and facilitating new hypothesis generation and additional research.     

On the role of spatial stochastic models in understanding landscape indices in ecology

Spatial stochastic models play an important role in understanding and predicting the behaviour of complex systems. Such models may be implemented with explicit knowledge of only a limited number of parameters relating to spatial relationships among locations. Consequently, they are often used instead of deterministic‐mechanistic models, which may potentially require an unrealistically large number of parameters. Currently, in contrast to spatial stochastic models, the parameterization of the joint spatial distribution of objects in landscape models is more often implicit than explicit. Here, we investigate the similarities and differences between bona fide spatial stochastic models and landscape models by focusing mostly on the relationships between processes, their realizations (patterns), representation and measurement, and their use in exploratory as well as confirmatory data analysis. One of the most important outcomes of recognizing the importance of stochastic processes is the acknowledgement that the spatial pattern observed in a landscape is only one realization of that process. Hence, while ecologists have been using landscape pattern indices (LPIs) to characterize landscape heterogeneity and/or make inferences about processes shaping the landscape, no stochastic modelling framework has been developed for their proper statistical elucidation. Consequently, several (mis)uses of LPIs draw conclusions about landscapes which are suspect. We show that several reports about sensitivities of LPIs to measurements have common roots that can be made explicitly manageable by adopting stochastic models of spatial structure. The key parameters of these stochastic models are composition and configuration, which, in general, cannot be estimated independently from each other. We outline how to develop the stochastic framework to interpret observations and make some recommendations to practitioners about everyday usage. The conceptual linkages between patterns and processes are particularly important in light of recent efforts to bridge the static‐structural and the dynamic‐analytic traditions of ecology.     

种群生存力分析研究进展和趋势

种群生存力分析（PVA）是正在迅速发展的新方法,已成为保护生物学研究的热点。它主要研究随机干扰对小种群绝灭的影响,其目的是制定最小可存活种群（MVP）,把绝灭减少到可接受的水平。随机干扰可分四类;统计随机性,环境随机性,自然灾害和遗传随机性。确定MVP的方法有三种：理论模型,模拟模型,模拟模型和岛屿生物地理学方法。理论模型主要研究理想或特定条件下随机因素对种群的影响;模拟模型是利用计算机模拟种群绝灭过程;岛屿生物地理学方法主要分析岛屿物种的分布和存活,证实分析模型和模拟模型。已有大量的文献研究统计随机性,环境随机性和自然灾害的行为特征,但遗传因素与种群生存力之间的关系还不清楚。建立包括四种随机性的综合性模型,广泛地检验PVA模型,系统地研制目标种的遗传和生态特性以及MVP的实际应用是PVA的发展趋势。     

A joint individual‐based model coupling growth and mortality reveals that tree vigor is a key component of tropical forest dynamics

Tree vigor is often used as a covariate when tree mortality is predicted from tree growth in tropical forest dynamic models, but it is rarely explicitly accounted for in a coherent modeling framework. We quantify tree vigor at the individual tree level, based on the difference between expected and observed growth. The available methods to join nonlinear tree growth and mortality processes are not commonly used by forest ecologists so that we develop an inference methodology based on an MCMC approach, allowing us to sample the parameters of the growth and mortality model according to their posterior distribution using the joint model likelihood. We apply our framework to a set of data on the 20‐year dynamics of a forest in Paracou, French Guiana, taking advantage of functional trait‐based growth and mortality models already developed independently. Our results showed that growth and mortality are intimately linked and that the vigor estimator is an essential predictor of mortality, highlighting that trees growing more than expected have a far lower probability of dying. Our joint model methodology is sufficiently generic to be used to join two longitudinal and punctual linked processes and thus may be applied to a wide range of growth and mortality models. In the context of global changes, such joint models are urgently needed in tropical forests to analyze, and then predict, the effects of the ongoing changes on the tree dynamics in hyperdiverse tropical forests.     

The contributions of mycorrhizal fungi to the determination of plant community structure

While it is now widely accepted, even by ecologists, that most plants in the majority of ecosystems are infected by mycorrhizal fungi, few experiments have been designed to investigate the function of the mutualism at the community level. Those involved with mycorrhizal research have been largely preoccupied with questions of the mineral, particularly phosphorus, nutrition of individual plants, while plant community ecologists have too often found it convenient, even when acknowledging the presence of infection, to ignore its possible function in the ecosystem. This presentation examines a selected number of seminal papers written by plant community ecologists and highlights some of ‘the most striking mysteries’ which they reveal. It describes experiments designed to determine whether knowledge of the presence and activity of the mycorrhizal mycelium can help us to unravel the ‘mysteries’ which they define. It is revealed that by having direct adverse effects upon seedlings of many ‘r’ selected species, while at the same time being beneficial, if not essential, to those that are ‘K’ selected, the activities of the mycelium of VA fungi have a direct bearing upon community composition. The extent to which ‘turf compatibility’ is actually a reflection of the compatibility of plant species with the VA mycorrhizal mycelium is discussed and the possible role of the mycelium in consigning some species to the ruderal habit is considered. It is concluded that those attempting scientifically to understand, or managerially to manipulate, plant communities, without recognizing the role of the mycorrhizal mycelium, do so at their peril, and it is recommended that scientists involved in research on mycorrhiza extend their vision beyond the limited horizons which are currently so often defined by considerations of the phosphorus nutrition of individual host plants.     

Caloric requirements of human populations: A model

Currently available models used for predicting human caloric requirements do not reflect the great variability in activity patterns observed among populations, and are insensitive to important anthropometric, demographic, and environmental variables. They are thus inadequate for application to many populations and problems of anthropological interest. We present a model for determining caloric requirements which more accurately accommodates the effects of variation in activity and in anthropometries on individual needs, and which predicts population requirements based on individual needs and demographic parameters. The model is tested on four populations (the Andean community of Nuñoa, Peru, the Dobe !Kung of Botswana, and two New Guinean villages) and is found to provide consistently better estimates of caloric requirements than are generated by the Food and Agriculture/World Health Organization's model. This model should be useful to anthropologists and human ecologists concerned with problems involving human energy consumption, such as the efficiency of subsistence strategies, optimum family composition, or certain consequences of increased labor migration or technological change.This research was supported by a grant from the Research Foundation of the State University of New York. Funds for computer time and materials were provided by the State University of New York at Binghamton and The Pennsylvania State University.     

Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets

In order to improve our understanding of directly transmitted pathogens within host populations, epidemic models should take into account individual heterogeneities as well as stochastic fluctuations in individual parameters. The associated cost results in an increasing level of complexity of the mathematical models which generally lack consistent formalisms. In this paper, we demonstrate that complex epidemic models could be expressed as colored stochastic Petri nets (CSPN). CSPN is a mathematical tool developed in computer science. The concept is based on the Markov Chain theory and on a standard well codified graphical formalism. This approach presents an alternative to other computer simulation methods since it offers both a theoretical formalism and a graphical representation that facilitate the implementation, the understanding and thus the replication or modification of the model. We explain how common concepts of epidemic models--such as the incidence function--can be easily translated into an individual based point of view in the CSPN formalism. We then illustrate this approach by using the well documented susceptible-infected model with recruitment and death.     

The interpretation of stem diameter–height allometry in trees: biomechanical constraints,neighbour effects,or biased regressions?

Static diameter–height allometry data have been used by many ecologists to demonstrate that diameter should increase at a faster rate than height during tree growth, as predicted by biomechanical models. We review the available evidence and examine the potential problems that arise in the interpretation of this relationship. In particular, we reveal how few studies investigating patterns of diameter–height allometry in trees have adequately controlled for neighbour effects. We also demonstrate how the interpretation of diameter–height allometry has suffered from a lack of uniformity in the selection of regression models, and how the use of least squares regression to estimate allometric scaling exponents can be biased. We conclude that most of the published data on static diameter–height relationships in trees tell us virtually nothing about either age (developmental) effects or neighbour effects; they are completely confounded. Further studies are required to analyse the long-term dynamic growth trajectories of individual trees in relation to local neighbour effects, and greater effort must be made to establish the consistent use of unbiased statistical methods between studies.     

Allee effects, aggregation, and invasion success

Understanding the factors that influence successful colonization can help inform ecological theory and aid in the management of invasive species. When founder populations are small, individual fitness may be negatively impacted by component Allee effects through positive density dependence (e.g., mate limitation). Reproductive and survival mechanisms that suffer due to a shortage of conspecifics may scale up to be manifest in a decreased per-capita population growth rate (i.e., a demographic Allee effect). Mean-field population level models are limited in representing how component Allee effects scale up to demographic Allee effects when heterogeneous spatial structure influences conspecific availability. Thus, such models may not adequately characterize the probability of establishment. In order to better assess how individual level processes influence population establishment and spread, we developed a spatially explicit individual-based stochastic simulation of a small founder population. We found that increased aggregation can affect individual fitness and subsequently impact population growth; however, relatively slow dispersal—in addition to initial spatial structure—is required for establishment, ultimately creating a tradeoff between probability of initial establishment and rate of subsequent spread. Since this result is sensitive to the scaling up of component Allee effects, details of individual dispersal and interaction kernels are key factors influencing population level processes. Overall, we demonstrate the importance of considering both spatial structure and individual level traits in assessing the consequences of Allee effects in biological invasions.     

Potential applications of mussel modelling

Mussels are extensively cultivated worldwide and are of growing economic importance. However, constraints on the exploitation of wild mussel resources have necessitated the need for tools to improve the management of mussel cultivation towards increased production. Ecological models are increasingly being used as a management tool, and therefore the existing approaches to modelling mussels have been reviewed with respect to their possible application to the improvement of shellfish management strategies. We suggest that dynamic energy budget (DEB) models have the greatest potential in this area, and discuss the mussel DEB models that have been developed to date in terms of their physiological complexity, accuracy of prediction of individual mussel growth and ability to predict mussel population production. Individual mussel production has been predicted; however, the focus of many of the models has been on the growth and reproduction of a single mussel and therefore population effects generally have not been included. Other models at the population level have included only limited population effects, and this has reduced the capacity of many of the models to accurately predict mussel production at the population level. Interactions at the population level (self-thinning and predation) are discussed and the models that describe the consequences of these processes are examined. In future DEB models will need to include the ability to parameterise population level processes if we are to have greater confidence in their application to shellfish management. Electronic Publication     

Strong neutral spatial effects shape tree species distributions across life stages at multiple scales

Traditionally, ecologists use lattice (regional summary) count data to simulate tree species distributions to explore species coexistence. However, no previous study has explicitly compared the difference between using lattice count and basal area data and analyzed species distributions at both individual species and community levels while simultaneously considering the combined scenarios of life stage and scale. In this study, we hypothesized that basal area data are more closely related to environmental variables than are count data because of strong environmental filtering effects. We also address the contribution of niche and the neutral (i.e., solely dependent on distance) factors to species distributions. Specifically, we separately modeled count data and basal area data while considering life stage and scale effects at the two levels with simultaneous autoregressive models and variation partitioning. A principal coordinates of neighbor matrix (PCNM) was used to model neutral spatial effects at the community level. The explained variations of species distribution data did not differ significantly between the two types of data at either the individual species level or the community level, indicating that the two types of data can be used nearly identically to model species distributions. Neutral spatial effects represented by spatial autoregressive parameters and the PCNM eigenfunctions drove species distributions on multiple scales, different life stages and individual species and community levels in this plot. We concluded that strong neutral spatial effects are the principal mechanisms underlying the species distributions and thus shape biodiversity spatial patterns.