SpatialDemography: a spatially explicit,stage‐structured,metacommunity model

The responses of species and populations to changes in the environment (e.g. changes in climate and land use) are often complex and difficult to predict. We have created the SpatialDemography model (R package: spatialdemography). The model is a spatially explicit, stage‐structured, matrix‐based metacommunity model, with the potential for modeling species’ and populations’ potential responses to environmental heterogeneity and change. The SpatialDemography model assumes a cellular landscape populated by organisms with four life stages: a mobile dispersing stage, two sessile non‐reproductive stages, and a reproductive adult stage. Individuals are assumed to originate at the center of a given cell and disperse according to a specified dispersal kernel (e.g. log‐normal). All adult individuals are capable of producing offspring. The model approach and framework are described in the context of a hypothetical example with multiple competing species in a four cell landscape. In this example simulation, both spatial location and species interactions were important for understanding population dynamics. SpatialDemography can be applied to questions where an understanding of transient and long‐term demographic responses to spatiotemporal changes is desired. It is primarily applicable to metapopulations and metacommunities of organisms with early dispersal and sessile adults (i.e. modular organisms such as plants and some marine organisms). SpatialDemography differs from other population models in that it is spatially explicit, can incorporate biotic interactions, and is implemented in R.     

Species-area relationships from a spatially explicit neutral model in an infinite landscape

We use recently developed technical methods to study species–area relationships from a spatially explicit extension of Hubbell's neutral model on an infinite landscape. Our model includes variable dispersal distances and exhibits qualitatively different behaviour from the cases of nearest-neighbour dispersal and finite periodic landscapes that have previously been studied. We show that different dispersal distances and even different dispersal kernels produce identical species–area curves up to rescaling of the two axes. This scaling property provides a straightforward method for fitting the model to empirical data. The species–area curves display all three phases observed empirically and enable the exponent describing the power law relationship for species–area curves to be identified as the gradient at the central phase. This exponent can take all values between 0 and 1 and is given by a simple function of the speciation rate, independent of all other model variables.     

空间直观景观模型的验证方法

空间直观景观模型已是当前景观生态学研究的一大热点。空间景观模型模拟空间格局变化。其模拟结果包含非空间数据和空间数据。空间直观景观模型的验证除进行非空间数据的验证外,还需要进行空间数据的验证。本文回顾了空间直观模型发展历程,总结现有的空间直观模型验证方法。包括主观评价、图形比较、偏差分析、回归分析、假设检验、多尺度拟合度分析和景观指数分析,同时提出今后空间直观景观模型验证方法研究的重点方向。     

Overgrowth competition, fragmentation and sex-ratio dynamics: a spatially explicit, sub-individual-based model

Sessile organisms that compete for access to resources by overgrowing each other may risk the local elimination of one sex or the other, as frequently happens within clumps of the dioecious liverwort Marchantia inflexa. A multi-stage, spatially implicit differential-equation model of M. inflexa growing in an isolated patch, analysed in a previous study, indicated that long-term coexistence of the sexes within such patches may be only temporary. Here we derive a spatially explicit, sub-individual-based model to reconsider this interpretation when much more ecological realism is taken into account, including the process of fragmentation. The model tracks temporally discrete growth increments in continuous space, representing growth architecture and the overgrowth process in significant geometric detail. Results remain generally consistent with the absence of long-term coexistence of the sexes in individual patches of Marchantia. Dynamics of sex-specific growth qualitatively resemble those generated by differential-equation models, suggesting that this much simpler framework may be adequate for multi-patch metapopulation models. Direct competition between fragmenting and non-fragmenting clones demonstrates the importance of fragmentation in overgrowth competition. The results emphasize the need for empirical work on mechanisms of overgrowth and for modeling and empirical studies of life history tradeoffs and sex-ratio dynamics in multi-patch systems.     

Coevolution across landscapes: a spatially explicit model of parasitoid-host coevolution

The geographic mosaic theory of coevolution suggests that population spatial structure may have a strong impact on coevolutionary dynamics. Therefore, coevolution must be studied across geographic scales, not just in single populations. To examine the impact of movement rate on coevolutionary dynamics, we developed a spatially explicit model of host–parasitoid coevolution. We described space as a coupled-map lattice and assumed that resistance (defined as the ability of a host to encapsulate a parasitoid egg) and virulence (defined as the successful parasitization of a host) traits were graded and costly. The model explicitly detailed population and evolutionary dynamics. When holding all parameters constant and varying only the movement rate of the host and parasitoid, profoundly different dynamics were observed. We found that fluctuations in the mean levels of resistance and virulence in the global population were greatest when the movement rate of the host and parasitoid was high. In addition, we found that the variation in resistance and virulence levels among neighboring patches was greatest when the movement rates of the host and parasitoid was low. However, as the distance among patches increased, so did the variation in resistance and virulence levels regardless of movement rate. These generalizations did not hold when spatial patterns in the distribution of resistance and virulence traits, such as spirals, were observed. Finally, we found that the evolution of resistance and virulence caused the abundance of hosts to increase and the abundance of parasitoids to decrease. As a result, the spatial distribution of hosts and parasitoids was influenced.     

Long-term control of species abundances in a dry grassland: a spatially explicit model

Abstract. The long-term spatio-temporal dynamics of a sparse dry-grassland community (Thymo-Festucetum) is investigated by a spatially explicit individual-based simulation model and by analytical model equations. The community (investigated over 15 yr in permanent plots) is characterized by a permanently low cover (30–50 %), mainly of the perennial tuft grass Festuca cinerea. Seedling establishment and the fate of juveniles are strongly dependent on weather conditions. The simulation programme focuses on the mechanism of clonal growth of grasses and the reproduction of tufts by fragmentation. Questions answered by the modelling approach were (1) which life-history features of the species are responsible for their persistence and for the low vegetation cover of the community and (2) what are the main mechanisms of species interactions. Different sets of simulation runs, together with the evaluation of the analytical models, show: (1) long-term persistence of the main species is possible only by a combination of sexual and clonal reproduction; the low cover is due to low germination rate, low mortality and limited growth of tufts; (2) the intra and interspecific control of the community is performed mainly via a reduction by already established individuals; (3) persistence of uncommon species relies on a diaspore buffer in, or around, the community (‘spatial mass effect’).     

Roots in space: a spatially explicit model for below-ground competition in plants

Game theory provides an untapped framework for predicting how below-ground competition will influence root proliferation in a spatially explicit environment. We model root competition for space as an evolutionary game. In response to nutrient competition between plants, an individual's optimal strategy (the spatial distribution of root proliferation) depends on the rooting strategies of neighbouring plants. The model defines and predicts the fundamental (in the absence of competition) and realized (in the presence of competition) root space of an individual plant. Overlapping fundamental root spaces guarantee smaller, yet still overlapping, realized root spaces as individuals concede some but not all space to a neighbour's roots. Root overlap becomes an intentional consequence of the neighbouring plants playing a nutrient foraging game. Root proliferation and regions of root overlap should increase with soil fertility, decline with the distance cost of root production (e.g. soil compactness) and shift with competitive asymmetries. Seemingly erratic patterns of root proliferation and root overlap become the expected outcome of nutrient foraging games played in soils with small-scale heterogeneities in nutrient availability.     

Mate finding, dispersal distances and population growth in invading species: a spatially explicit model

The expansion of populations into new areas is dependent upon dispersal distances and the ability of colonists to find mates. These factors interact through the spatial distribution of individuals. We develop a mechanistic, spatially explicit model to investigate the interaction between dispersal distances and mate finding in expanding populations. At high dispersal distances and low mate finding abilities, population growth was constrained by the inverse density dependent inability of adults to find mates (an Allee effect). In contrast, at low dispersal distances and high mate finding abilities, growth was constrained by the density dependent inability of dispersers to find vacant territories. Population growth was highest in between these extremes. We suggest that these spatial interactions play an important role in the expansion of populations into new areas and that this methodology provides a useful tool for investigating them.     

A spatially explicit neutral model of beta-diversity in tropical forests

To represent species turnover in tropical rain forest, we use a neutral model where a tree's fate is not affected by what species it belongs to, seeds disperse a limited distance from their parents, and speciation is in equilibrium with random extinction. We calculate the similarity function, the probability F(r) that two trees separated by a distance r belong to the same species, assuming that the dispersal kernel P(r), the distribution of seeds about their parents and the prospects of mortality and reproduction, are the same for all trees regardless of their species. If P(r) is radially symmetric Gaussian with mean-square dispersal distance sigma, F(r) can be expressed in closed form. If P(r) is a radially symmetric Cauchy distribution, then, in two-dimensional space, F(r) is proportional to 1/r for large r. Analytical results are compared with individual-based simulations, and the relevance to field observations is discussed.     

Field theory for biogeography: a spatially explicit model for predicting patterns of biodiversity

Predicting the variation of biodiversity across the surface of the Earth is a fundamental issue in ecology, and in this article we focus on one of the most widely studied spatial biodiversity patterns: the species–area relationship (SAR). The SAR is a central tool in conservation, being used to predict species loss following global climate change, and is striking in its universality throughout different geographical regions and across the tree of life. In this article we draw upon the methods of quantum field theory and the foundation of neutral community ecology to derive the first spatially explicit neutral prediction for the SAR. We find that the SAR has three phases, with a power law increase at intermediate scales, consistent with decades of documented empirical patterns. Our model also provides a building block for incorporating non-neutral biological variation, with the potential to bridge the gap between neutral and niche-based approaches to community assembly.
Ecology Letters (2010) 13: 87–95     

A spatially explicit individual-based model of reinforcement in hybrid zones

Abstract An individual-based model consisting of two dioecious populations in a two-dimensional environmental grid was constructed. Each population began with, and never exceeded, 1000 individuals; extinction was allowed. Genomes consisting of 30 biallelic loci for male sexual advertisement call, female mate preference, and population origin were constructed, and lineages of each individual in the starting populations were followed for 2000 generations. Type and level of hybrid disadvantage, initial population distribution, patchiness of environmental resources, and level of mate choice were varied. Persistence of bimodal hybrid zones was nonexistent at low levels of hybrid disadvantage and universal at high levels of hybrid disadvantage, with a narrow threshold in which persistence was unpredictable. Persistence occurred at lower levels of hybrid disadvantage when populations were initially parapatric rather than sympatric, and environments were patchy rather than homogeneous. Increased divergence in mating systems occurred when hybrid disadvantage was high, hybrids were infertile, populations were initially parapatric, and increased female choice was allowed. Mating system divergence was much higher in interacting populations compared with noninteracting populations, indicating that reinforcement caused most of the observed divergence. When hybrids were infertile, reinforcement contributed to speciation, because under hybrid infertility the probability of persistence at low levels of hybrid disadvantage was positively related to mate choice. The results agree with previous one-dimensional spatial models in finding that population persistence is more likely in parapatric and patchy population distributions. In addition, the results show that hybrid infertility may facilitate the process of reinforcement and speciation.     

ALADYN – a spatially explicit,allelic model for simulating adaptive dynamics

ALADYN is a freely available cross‐platform C++ modeling framework for stochastic simulation of joint allelic and demographic dynamics of spatially‐structured populations. Juvenile survival is linked to the degree of match between an individual's phenotype and the local phenotypic optimum. There is considerable flexibility provided for the demography of the considered species and the genetic architecture of the traits under selection. ALADYN facilitates the investigation of adaptive processes to spatially and/or temporally changing conditions and the resulting niche and range dynamics. To our knowledge ALADYN is so far the only model that allows a continuous resolution of individuals’ locations in a spatially explicit landscape together with the associated patterns of selection.     

Metapopulation dynamics and biological invasions: a spatially explicit model applied to a freshwater snail

The spatial spread of invading organisms is a major contemporary concern. We focus here on invasions in inherently fragmented habitats, such as freshwater systems, and explore the usefulness of metapopulation models in this context. Maximum-likelihood methods allow the estimation of colonization and extinction rates, as functions of habitat patch sizes and positions, from time series of presence/absence data. This framework also provides confidence intervals of these estimates and hypotheses tests. We analyze a previously unpublished 12-year survey of the spread of the introduced snail Tarebia granifera in 47 Martinican rivers. Simple metapopulation models reproduce with reasonable accuracy several quantitative aspects of the invasion, including regional abundance, spatiotemporal structure, and site-by-site colonization dates. Sensitivity analysis reveals that the invasion sequence depended strongly on metapopulation size (number of sites) and spatial structure (distances among sites). The invasion history has also been accelerated by stochastic events, as illustrated by a large, central river that happened to be colonized very early and served as an invasion pool. Finally, we discuss the benefits of this approach for the understanding of invasions in fragmented landscapes.     

kernelpop,a spatially explicit population genetic simulation engine

Individual‐based, spatially explicit models provide a mechanism to understand distributions of individuals on the landscape; however, few models have been coupled with population genetics. The primary benefits of such a combination is to assess performance of population‐genetic estimators in realistic situations. kernelpop represents a flexible framework to implement almost any arbitrary population‐genetic and demographic model in a spatially explicit context using a variety of dispersal kernels. Estimates of type I error associated with genome scans in metapopulations are provided as an illustration of this software's utility.     

Development and validation of a spatially explicit individual-based mixed crop growth model

Spatial disposition of plants in intercrops, and differences in sowing time between species, can strongly affect their ecological interactions and, in consequence, the system’s viability and performance. Empirical exploration of a wide range of spatial and temporal plant arrangements is costly and time-consuming. Modelling the growth of mixed crops is a tool which, combined with empirical tests, can greatly reduce the time and investment required for this task. Spatially explicit, individual-based dynamic models seem well suited for this purpose; their exploration and experimental validation for the case of simple, two-species, artificial plant communities, can also provide further insight as to how the spatial and temporal scales of a plant’s multispecific neighbourhood affect its growth and performance. The aim of this investigation was to further develop a published spatially explicit individual-based mixed crop growth model [Vandermeer, J. H. (1989). The Ecology of Intercropping, Cambridge, U.K.: Cambridge University Press, p. 237], and to validate it experimentally. With this purpose in mind: (1) computer programs to simulate individual plant growth and to perform statistical analysis of both deterministic and stochastic versions of the model were developed; (2) the model was parametrized using a complex experimental diculture with several cohorts and spatial arrangements; (3) the predictive capacity of the model was tested using independent spatio-temporal experimental arrangements; (4) a modified version of the model was written, which abandons the assumption of linearity of the neighbourhood index at the cost of increasing the number of parameters; (5) The performance of stochastic versions of both Vandermeer’s and our modified model were compared, employing a non-parametric measure of goodness of fit. We conclude that this approach to modelling plant growth subject to intra and interspecific competition is a remarkably efficient, general, conceptually elegant, heuristic tool whose predictive power can be further improved when nonlinear terms are introduced into the neighbourhood competition index, as done in our modified version of Vandermeer’s model.     

Spatial and temporal heterogeneity explain disease dynamics in a spatially explicit network model

There is an increasing recognition that individual-level spatial and temporal heterogeneity may play an important role in metapopulation dynamics and persistence. In particular, the patterns of contact within and between aggregates (e.g., demes) at different spatial and temporal scales may reveal important mechanisms governing metapopulation dynamics. Using 7 years of data on the interaction between the anther smut fungus (Microbotryum violaceum) and fire pink (Silene virginica), we show how the application of spatially explicit and implicit network models can be used to make accurate predictions of infection dynamics in spatially structured populations. Explicit consideration of both spatial and temporal organization reveals the role of each in spreading risk for both the host and the pathogen. This work suggests that the application of spatially explicit network models can yield important insights into how heterogeneous structure can promote the persistence of species in natural landscapes.     

Relative role of deterministic and stochastic determinants of soil animal community: a spatially explicit analysis of oribatid mites

1. Ecologists are debating the relative role of deterministic and stochastic determinants of community structure. Although the high diversity and strong spatial structure of soil animal assemblages could provide ecologists with an ideal ecological scenario, surprisingly little information is available on these assemblages. 2. We studied species-rich soil oribatid mite assemblages from a Mediterranean beech forest and a grassland. We applied multivariate regression approaches and analysed spatial autocorrelation at multiple spatial scales using Moran's eigenvectors. Results were used to partition community variance in terms of the amount of variation uniquely accounted for by environmental correlates (e.g. organic matter) and geographical position. Estimated neutral diversity and immigration parameters were also applied to a soil animal group for the first time to simulate patterns of community dissimilarity expected under neutrality, thereby testing neutral predictions. 3. After accounting for spatial autocorrelation, the correlation between community structure and key environmental parameters disappeared: about 40% of community variation consisted of spatial patterns independent of measured environmental variables such as organic matter. Environmentally independent spatial patterns encompassed the entire range of scales accounted for by the sampling design (from tens of cm to 100 m). This spatial variation could be due to either unmeasured but spatially structured variables or stochastic drift mediated by dispersal. Observed levels of community dissimilarity were significantly different from those predicted by neutral models. 4. Oribatid mite assemblages are dominated by processes involving both deterministic and stochastic components and operating at multiple scales. Spatial patterns independent of the measured environmental variables are a prominent feature of the targeted assemblages, but patterns of community dissimilarity do not match neutral predictions. This suggests that either niche-mediated competition or environmental filtering or both are contributing to the core structure of the community. This study indicates new lines of investigation for understanding the mechanisms that determine the signature of the deterministic component of animal community assembly.