Relationships between migration rates and landscape resistance assessed using individual-based simulations

Linking landscape effects on gene flow to processes such as dispersal and mating is essential to provide a conceptual foundation for landscape genetics. It is particularly important to determine how classical population genetic models relate to recent individual-based landscape genetic models when assessing individual movement and its influence on population genetic structure. We used classical Wright-Fisher models and spatially explicit, individual-based, landscape genetic models to simulate gene flow via dispersal and mating in a series of landscapes representing two patches of habitat separated by a barrier. We developed a mathematical formula that predicts the relationship between barrier strength (i.e., permeability) and the migration rate (m) across the barrier, thereby linking spatially explicit landscape genetics to classical population genetics theory. We then assessed the reliability of the function by obtaining population genetics parameters (m, F(ST) ) using simulations for both spatially explicit and Wright-Fisher simulation models for a range of gene flow rates. Next, we show that relaxing some of the assumptions of the Wright-Fisher model can substantially change population substructure (i.e., F(ST) ). For example, isolation by distance among individuals on each side of a barrier maintains an F(ST) of ～0.20 regardless of migration rate across the barrier, whereas panmixia on each side of the barrier results in an F(ST) that changes with m as predicted by classical population genetics theory. We suggest that individual-based, spatially explicit modelling provides a general framework to investigate how interactions between movement and landscape resistance drive population genetic patterns and connectivity across complex landscapes.     

Resolving discrepancies between deterministic population models and individual-based simulations

ABSTRACT This work ties together two distinct modeling frameworks for population dynamics: an individual-based simulation and a set of coupled integrodifferential equations involving population densities. The simulation model represents an idealized predator-prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual interactions, whereas the population-level framework is a generalized version of reaction-diffusion models that incorporate population densities coupled to one another by interaction rates. Here I use various combinations of long-range dispersal for both the offspring and adult stages of both prey and predator species, providing a broad range of spatial and temporal dynamics, to compare and contrast the two model frameworks. Taking the individual-based modeling results as given, two examinations of the reaction-dispersal model are made: linear stability analysis of the deterministic equations and direct numerical solution of the model equations. I also modify the numerical solution in two ways to account for the stochastic nature of individual-based processes, which include independent, local perturbations in population density and a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new parameters into the population-level model, which I adjust to reproduce the individual-based model results. The individual-based model is then modified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population-level model without stochasticity.     

Dose-structured population dynamics

Applied population dynamics modeling is relied upon with increasing frequency to quantify how human activities affect human and non-human populations. Current techniques include variously the population's spatial transport, age, size, and physiology, but typically not the life-histories of exposure to other important things occurring in the ambient environment, such as chemicals, heat, or radiation. Consequently, the effects of such 'abiotic' aspects of an ecosystem on populations are only currently addressed through individual-based modeling approaches that despite broad utility are limited in their applicability to realistic ecosystems [V. Grimm, Ten years of individual-based modeling in ecology: what have we learned and what could we learn in the future? Ecol. Model. 115 (1999) 129-148][1]. We describe a new category of population dynamics modeling, wherein population dynamical states of the biotic phases are structured on dose, and apply this framework to demonstrate how chemical species or other ambient aspects can be included in population dynamics in three separate examples involving growth suppression in fish, inactivation of microorganisms with ultraviolet irradiation, and metabolic lag in population growth. Dose-structuring is based on a kinematic approach that is a simple generalization of age-structuring, views the ecosystem as a multi-component mixture with reacting biotic/abiotic components. The resulting model framework accommodates (a) different memories of exposure as in recovery from toxic ambient conditions, (b) differentiation between exogenous and endogenous sources of variation in population response, and (c) quantification of acute or sub-acute effects on populations arising from life-history exposures to abiotic species. Classical models do not easily address the very important fact that organisms differ and have different experiences over their life cycle. The dose structuring is one approach to incorporate some of these elements into the existing structures of the classical models, while retaining many of the features (and other limitations) of classical models.     

Individual variability and population regulation: a model of the significance of within-generation density dependence

Most models of theoretical population ecology consider population density as a state variable and thus ignore the fact that populations are composed not of identical average individuals but of individuals which are usually different. However, this individual variability may be important for population regulation. We therefore analysed an individual-based population model which explicitly describes within-generation processes, i.e. individual growth, starvation, and resource dynamics. The results show that if population dynamics are dominated by slow changes in resource level, the population size in the model undergoes wide oscillation, often leading to extinction. If, on the other hand, fast within-generation processes predominate, such as starvation and sudden drops in resource levels, the population fluctuates to a limited extent around an average. Within-generation density dependence may thus be an important mechanism which is largely ignored in classic time-discrete state-variable models. We conclude that the individual-based approach provides important insights into the hierarchical organization of population dynamics, i.e. the relationship between fast processes at the individual level and slower processes at the population level.     

Competition among plants: Concepts, individual-based modelling approaches, and a proposal for a future research strategy

Competition is a key process in plant populations and communities. We thus need, if we are to predict the responses of ecological systems to environmental change, a comprehensive and mechanistic understanding of plant competition. Considering competition, however, only at the population level is not sufficient because plant individuals usually are different, interact locally, and can adapt their behaviour to the current state of themselves and of their biotic and abiotic environment. Therefore, simulation models that are individual-based and spatially explicit are increasingly used for studying competition in plant systems. Many different individual-based modelling approaches exist to represent competition, but it is not clear how good they are in reflecting essential aspects of plant competition. We therefore first summarize current concepts and theories addressing plant competition. Then, we review individual-based approaches for modelling competition among plants. We distinguish between approaches that are used for more than 10 years and more recent ones. We identify three major gaps that need to be addressed more in the future: the effects of plants on their local environment, adaptive behaviour, and below-ground competition. To fill these gaps, the representation of plants and their interactions have to be more mechanistic than most existing approaches. Developing such new approaches is a challenge because they are likely to be more complex and to require more detailed knowledge and data on individual-level processes underlying competition. We thus need a more integrated research strategy for the future, where empirical and theoretical ecologists as well as computer scientists work together on formulating, implementing, parameterization, testing, comparing, and selecting the new approaches.     

植物间正相互作用对种群动态和群落结构的影响:基于个体模型的研究进展

植物间的相互作用对种群动态和群落结构有着重要的影响。大量的野外实验已经揭示了正相互作用(互利)在群落中的普遍存在及其重要性。为了弥补野外实验方法的不足, 模型方法被越来越多地应用于正相互作用及其生态学效应的研究中。该文基于个体模型研究, 探讨了植物间正相互作用对种群动态和群落结构的影响。介绍了植物间正相互作用的定义和发生机制、植物间相互作用与环境梯度的关系。正相互作用是指发生在相邻的植物个体之间, 至少对其中一个个体有益的相互作用。植物通过直接(生境改善或资源富集)或间接(协同防御等)作用使局部环境有利于邻体而发生正相互作用。胁迫梯度假说认为互利的强度或重要性随着环境胁迫度的增加而增加, 但是越来越多的经验研究认为胁迫梯度假说需要改进。以网格模型和影响域模型为例, 介绍了基于个体的植物间相互作用模型方法。基于个体模型, 对近年来国内外正相互作用对种群时间动态(如生物量-密度关系)、空间分布格局和群落结构(如群落生物量-物种丰富度关系)影响的研究进行了总结。指出未来的研究应集中在对正相互作用概念和机制的理解, 新的模型, 新的种群、群落, 甚至生态系统问题, 以及在全球变化背景下进行相关的研究。     

Two complementary paradigms for analysing population dynamics

To understand why population growth rate is sometimes positive and sometimes negative, ecologists have adopted two main approaches. The most common approach is through the density paradigm by plotting population growth rate against population density. The second approach is through the mechanistic paradigm by plotting population growth rate against the relevant ecological processes affecting the population. The density paradigm is applied a posteriori, works sometimes but not always and is remarkably useless in solving management problems or in providing an understanding of why populations change in size. The mechanistic paradigm investigates the factors that supposedly drive density changes and is identical to Caughley's declining population paradigm of conservation biology. The assumption that we can uncover invariant relationships between population growth rate and some other variables is an article of faith. Numerous commercial fishery applications have failed to find the invariant relationships between stock and recruitment that are predicted by the density paradigm. Environmental variation is the rule, and non-equilibrial dynamics should force us to look for the mechanisms of population change. If multiple factors determine changes in population density, there can be no predictability in either of these paradigms and we will become environmental historians rather than scientists with useful generalizations for the population problems of this century. Defining our questions clearly and adopting an experimental approach with crisp alternative hypotheses and adequate controls will be essential to building useful generalizations for solving the practical problems of population management in fisheries, wildlife and conservation.     

Temporal self-similarity created by spatial individual-based population dynamics

We report an individual-based single-species model producing temporal scale-free, self-similar dynamics in time. Individuals in the population renew in an explicit space with a large number of loci. We show that reproduction, subsequent dispersal of the offspring, and mortality will organise population fluctuations such that the emerging dynamics represent power law and scale-free structures. Further, we show that spatially structured population dynamics may show red frequency spectra, a property that the simple nonlinear population models are generally lacking.     

Pitfalls and challenges of estimating population growth rate from empirical data: consequences for allometric scaling relations

The intrinsic rate of increase is a fundamental concept in population ecology, and a variety of problems require that estimates of population growth rate be obtained from empirical data. However, depending on the extent and type of data available (e.g. time series, life tables, life history traits), several alternative empirical estimators of population growth rate are possible. Because these estimators make different assumptions about the nature of age‐dependent mortality and density‐dependence of population dynamics, among other factors, these quantities capture fundamentally different aspects of population growth and are not interchangeable. Nevertheless, they have been routinely commingled in recent ecoinformatic analyses relating to allometry and conservation biology. Here we clarify some of the confusion regarding the empirical estimation of population growth rate and present separate analyses of the frequency distributions and allometric scaling of three alternative, non‐interchangeable measures of population growth. Studies of allometric scaling of population growth rate with body size are additionally sensitive to the statistical line fitting approach used, and we find that different approaches yield different allometric scaling slopes. Across the mix of population growth estimators and line fitting techniques, we find scattered and limited support for the key allometric prediction from the metabolic theory of ecology, namely that log₁₀(population growth rate) should scale as ?0.25 power of log₁₀(body mass). More importantly, we conclude that the question of allometric scaling of population growth rate with body size is highly sensitive to previously unexamined assumptions regarding both the appropriate population growth parameter to be compared and the line fitting approach used to examine the data. Finally, we suggest that the ultimate test of allometric scaling of maximum population growth rates with body size has not been done and, moreover, may require data that are not currently available.     

Individual variability and population regulation: an individual-based model

To study the influence of individual variability on population dynamics an individual-based model of the dynamics of a single population consisting of different individuals is constructed. The model is based on differences in individual assimilation rates due to intraspecific competition and variability of initial weights. The model exhibits "imperfect regulation", i.e., the number of individuals in the population oscillates and sooner or later the population becomes extinct. When individual variability is included, the model produces longer population extinction times than without individual variability. The average extinction time is not however a monotonic function of the degree of individual variability.     

Predicting shifts in dynamics of cannibalistic field populations using individual-based models

The occurrence of qualitative shifts in population dynamical regimes has long been the focus of population biologists. Nonlinear ecological models predict that these shifts in dynamical regimes may occur as a result of parameter shifts, but unambiguous empirical evidence is largely restricted to laboratory populations. We used an individual-based modelling approach to predict dynamical shifts in field fish populations where the capacity to cannibalize differed between species. Model-generated individual growth trajectories that reflect different population dynamics were confronted with empirically observed growth trajectories, showing that our ordering and quantitative estimates of the different cannibalistic species in terms of life-history characteristics led to correct qualitative predictions of their dynamics.     

Analysis of the effect of inoculum characteristics on the first stages of a growing yeast population in beer fermentations by means of an individual-based model

The yeast Saccharomyces cerevisiae has a limited replicative lifespan. The cell mass at division is partitioned unequally between a larger, old parent cell and a smaller, new daughter cell. Industrial beer fermentations maintain and reuse yeast. At the end of fermentation a portion of the yeast is ‘cropped’ from the vessel for ‘serial repitching’. Harvesting yeast may select a population with an imbalance of young and aged individuals, but the output of any bioprocess is dependent on the physiology of each single cell in the population. Unlike continuous models, individual-based modelling is an approach that considers each microbe as an individual, a unique and discrete entity, with characteristics that change throughout its life. The aim of this contribution is to explore, by means of individual-based simulations, the effects of inoculum size and cell genealogical age on the dynamics of virtual yeast fermentation, focussing on: (1) the first stages of population growth, (2) the mean biomass evolution of the population, (3) the rate of glucose uptake and ethanol production, and (4) the biomass and genealogical age distributions. The ultimate goal is to integrate these results in order to make progress in the understanding of the composition of yeast populations and their temporal evolution in beer fermentations. Simulation results show that there is a clear influence of these initial features of the inocula on the subsequent growth dynamics. By contrasting both the individual and global properties of yeast cells and populations, we gain insight into the interrelation between these two types of data, which helps us to deal with the macroscopic behaviour observed in experimental research.     

The disruption of dominance hierarchies by a non-native species: an individual-based analysis

We studied the effects of the exotic rainbow trout (Oncorhynchus mykiss) on the performance and the dominance hierarchy of native Atlantic salmon (Salmo salar) at the group and individual level using laboratory and semi-natural experiments. At the group level, we compared the effects of interspecific and intraspecific competition (substitutive and additive design) on behavioural responses and growth of young-of-the-year Atlantic salmon. At the individual level, the same design was used to evaluate: (1) the temporal consistency of behavioural responses, dominance hierarchy and growth rate of Atlantic salmon; (2) the pattern of correlations between behaviours; and (3) the relationship between individual growth rate and behaviour. In the laboratory, group-level analyses revealed a weak but similar effect of rainbow trout and intraspecific competition on the behaviour and growth of Atlantic salmon. In contrast, individual-based analyses demonstrated that rainbow trout (but not intraspecific competition) strongly affected behavioural strategy, dominance hierarchy and growth trajectory of individual Atlantic salmon. Specifically, behaviours, dominance status and growth rate of salmon were temporally consistent in the intraspecific environment, while these patterns were disrupted when rainbow trout were present. Similarly, we found that rainbow trout strongly affected behavioural correlations and the relationships between individual growth rate and behaviour. The semi-natural experiments confirmed these results as interspecific competition affected relationships between individual growth rate of salmon, initial weight and activity index. Overall, individual-based analyses highlighted important mechanisms that were concealed at the group level, and that may be crucial to understand ecological and evolutionary consequences of exotic species. Moreover, these results demonstrated that competition with an exotic species disrupts the hierarchical relationship among native individuals and may therefore represent a potential for a shift in selective pressure.     

Using an individual-based model for assessment of sea turtle population viability

Marine turtle species have a complex life history characterized by interannual variability in reproductive performance and a long life span. These ecological features in combination with the animals highly migratory nature create numerous difficulties when trying to assess population dynamics. This study attempts to couple existing information on species demographics and behavioral strategies with simple energetic rules in a theoretical framework. We study sea turtle population dynamics using an individual-based model that incorporates known behavioral-ecological characteristics of the species. Methodology used to design the model was based on the superindividual approach (Scheffer et al. Ecol Model 80:161–170, 1995). We constructed our simulation experiment on a virtual sea turtle population, which was parameterized by using recent literature reviews with emphasis on reproductive parameters of the Mediterranean loggerhead sea turtle population. Switching rules describing critical processes of reproductive performances were established as theoretical functions of efficiency of energy transfer. In order to explore the significance of variable reproductive patterns upon population dynamics and persistence, a series of simulations was performed. The model was also run under fluctuated demographic variables to perform a sensitivity analysis of critical parameters and life-history stages. Based on the specific model parameterization, simulation results show that population persistence was most sensitive to fecundity and to survival at the pelagic juvenile stage. Additionally a surprising finding is the relatively high importance of egg survival in terms of both hatching and hatchling success. We conclude that enhancing the population with new individuals by increasing survival in the early life stages could compensate for additional losses in other age classes. The need for further research regarding biological and behavioral features as well as basic demographic insights into the endangered loggerhead sea turtle is also highlighted.     

Incorporating territory compression into population models

The ideal despotic distribution, whereby the lifetime reproductive success a territory's owner achieves is unaffected by population density, is a mainstay of behaviour-based population models. We show that the population dynamics of an island population of Seychelles warblers ( Acrocephalus sechellensis ) cannot be modelled with an ideal despotic distribution, and suggest the effects of both territory shrinkage and territorial disputes on reproductive success must be included to adequately model the population dynamics of this species. To do this we introduce two different approaches. The first is reductionist, using data on how population density affects individuals' reproductive success to predict population growth rates. Because such a model is mechanistic, it can be used to predict population dynamics in novel environments, making it a desirable long-term solution. However, because territorial populations are typically tightly regulated, birth and death rate data at low population densities are often unavailable. Hence, our second approach statistically infers the relationship between population density and per territory reproductive success, and thus provides a stop-gap solution for the shorter term. Our analysis indicates that although the Cousin population of Seychelles warblers is highly resilient to environmental stochasticity, the degree of resilience is considerably underestimated by approaches that ignore intrinsic regulation through territory shrinkage and territorial disputes.     

Connecting geographical distributions with population processes

The geographical distribution of a species is determined by a large number of complex processes operating over spatial scales spanning 10 orders of magnitude. Patterns in population processes have been described at numerous scales. We show that two patterns, measured at different scales, jointly allow us to infer heretofore unknown patterns in the distribution of demographic patterns across the geographical range of a species. The resulting model describes three fundamentally different modes of geographical variation in vital rates of populations. One mode is characterized by a positive nonlinear relationship between the maximum rate of population growth and the intensity of intraspecific competition across a geographical range. That is, populations that grow rapidly are also those where individuals experience the greatest per capita negative effect of the presence of other individuals. The second mode of behaviour is described by a negative nonlinear relationship between maximum growth rate and density dependence. Under this scenario, populations with low capacity to grow rapidly have highest intensities of intraspecific competitive effects. A third mode of behaviour is characterized by a weak positive relationship between growth rate and intraspecific competition, with very little geographical variation in maximum growth rate. A survey of studies relating temporal means and variances in population abundance for a variety of species indicate that the second mode of geographical variation in population dynamics across species ranges is the most common, though a few species appear to be characterized by the third mode.     

Positive and negative feedbacks in human population dynamics: future equilibrium or collapse?

The future number of people inhabiting the planet will influence the impact over natural ecosystems. In consequence, the growth of the human population represents one of the most important challenges for the near future. In this paper we used population dynamic theory to analyze human population growth. The results suggest that human population growth exhibited important fluctuations during the last 2000 years. In particular two different phases during the last 400 years can be distinguished, a positive relationship with population size implying positive feedback processes, followed by a negative relationship with population size – suggesting that negative feedback processes have been operating during the last 45 years. Our results support the view that ecological concepts derived from population ecology can be useful for understanding human dynamics. While cooperation at low densities in animal populations reminds us the Boserupian view that population growth induces economic development and higher standards of living, competition at high densities reconciles ecological theory with the original Malthusian view. We conclude that the present reduction in human per capita growth rates appears to be consequence of different limiting factors operating in combination around the globe in a similar manner, except in Africa where the factors operating appears to be very different. Humans may achieve a stable equilibrium population in the next century but the possibility of a population collapse caused by second‐order oscillations should be considered.     

Trophic interactions and population growth rates: describing patterns and identifying mechanisms

While the concept of population growth rate has been of central importance in the development of the theory of population dynamics, few empirical studies consider the intrinsic growth rate in detail, let alone how it may vary within and between populations of the same species. In an attempt to link theory with data we take two approaches. First, we address the question ''what growth rate patterns does theory predict we should see in time-series?'' The models make a number of predictions, which in general are supported by a comparative study between time-series of harvesting data from 352 red grouse populations. Variations in growth rate between grouse populations were associated with factors that reflected the quality and availability of the main food plant of the grouse. However, while these results support predictions from theory, they provide no clear insight into the mechanisms influencing reductions in population growth rate and regulation. In the second part of the paper, we consider the results of experiments, first at the individual level and then at the population level, to identify the important mechanisms influencing changes in individual productivity and population growth rate. The parasitic nematode Trichostrongylus tenuis is found to have an important influence on productivity, and when incorporated into models with their patterns of distribution between individuals has a destabilizing effect and generates negative growth rates. The hypothesis that negative growth rates at the population level were caused by parasites was demonstrated by a replicated population level experiment. With a sound and tested model framework we then explore the interaction with other natural enemies and show that in general they tend to stabilize variations in growth rate. Interestingly, the models show selective predators that remove heavily infected individuals can release the grouse from parasite-induced regulation and allow equilibrium populations to rise. By contrast, a tick-borne virus that killed chicks simply leads to a reduction in the equilibrium. When humans take grouse they do not appear to stabilize populations and this may be because many of the infective stages are available for infection before harvesting commences. In our opinion, an understanding of growth rates and population dynamics is best achieved through a mechanistic approach that includes a sound experimental approach with the development of models. Models can be tested further to explore how the community of predators and others interact with their prey.     

Neighbour joining trees, dominant markers and population genetic structure

Population genetic theory for 'traditional' codominant loci showing low levels of allelic diversity (eg allozymes) has been well characterised and evaluated. In contrast, appropriate methods for the analysis of data from more recently developed marker systems are still being refined. For multilocus dominant markers such as amplified fragment length polymorphisms (AFLPs) and randomly amplified polymorphic DNA (RAPDs), the methods of data analysis can be split into two main categories. In population-based approaches, population allele frequencies are compared to obtain some measure of the partitioning of genetic diversity into within- and between-population components. In contrast, individual-based approaches use individual multilocus genotypes as the unit of analysis. Inferences on population processes such as gene flow are based on inter-relationships among individual samples as visualised on phenetic diagrams such as neighbour joining trees. Using a simulation approach coupled with neighbour joining analyses, we show that while the underlying population genetic structure is an important determinant of tree shape in the analysis of dominant data, the number of loci examined also affects the topology. At low levels of population differentiation (eg FST=0.07), mutually exclusive clustering of individuals into their respective populations can occur when sufficiently large numbers of loci are scored (eg 250 loci, typical of many AFLP studies). In contrast, unresolved star-shaped topologies can be recovered at higher levels of population differentiation (FST= >0.15) when lower numbers of loci are employed (eg 50 loci, typical of many RAPD studies). Thus, the relationship between tree topology and the extent of genetic structuring of populations is contingent upon the number of dominant loci scored. The consequences of these findings for the biological interpretation of individual-based analysis of dominant data sets are discussed.     

McComedy: A user-friendly tool for next-generation individual-based modeling of microbial consumer-resource systems

Individual-based modeling is widely applied to investigate the ecological mechanisms driving microbial community dynamics. In such models, the population or community dynamics emerge from the behavior and interplay of individual entities, which are simulated according to a predefined set of rules. If the rules that govern the behavior of individuals are based on generic and mechanistically sound principles, the models are referred to as next-generation individual-based models. These models perform particularly well in recapitulating actual ecological dynamics. However, implementation of such models is time-consuming and requires proficiency in programming or in using specific software, which likely hinders a broader application of this powerful method. Here we present McComedy, a modeling tool designed to facilitate the development of next-generation individual-based models of microbial consumer-resource systems. This tool allows flexibly combining pre-implemented building blocks that represent physical and biological processes. The ability of McComedy to capture the essential dynamics of microbial consumer-resource systems is demonstrated by reproducing and furthermore adding to the results of two distinct studies from the literature. With this article, we provide a versatile tool for developing next-generation individual-based models that can foster understanding of microbial ecology in both research and education.