Spatiotemporal dynamics of the spread of African tilapias (Pisces: Oreochromis spp.) into rivers of northeastern Mesoamerica

African tilapias (Oreochromis spp.) occur in more than 100 countries outside of their native ranges and research on their invasions is largely lacking. We investigated spatiotemporal patterns of tilapia spread into 29 drainage basins in Belize and parts of Guatemala and Mexico, drawing on field data and interviews with fishermen. Habitat-suitability models for tilapias were created from geospatial and species occurrence data, and fishermen interviews were used to reconstruct the chronology of tilapia spread into predicted suitable habitats. Tilapia (predominantly Nile tilapia, O. niloticus) presence was confirmed at 78 sites in 9 of 29 drainage basins. Our habitat-suitability model predicted that 7,510 linear km of river habitat in the study area were vulnerable to colonization by tilapias, predominately in mid- to low elevation main stem rivers, from sea level to 277 m above sea level. The reconstructed spatial chronology of spread showed that the invasion started in 1990 and progressed slowly (2 km yr^?1) through an establishment phase before rapid expansion (~30 km yr^?1) between 1996 and 2002, after which new detections slowed. Human movement of fish for aquaculture was identified as a primary cause of dispersal that interacted with flooding as an important secondary cause. The shortest paths across low elevation drainage divides between major basins revealed several potential corridors for future tilapia spread during flooding. Research into tilapia spatial metapopulation structure and economic fisheries status, more stringent regulation of aquaculture activities, pro-active fisheries management, and development of policies to screen potentially invasive species before importation are recommended to avoid additional releases of tilapia and further spread in the region.     

Theoretical models of species' borders: single species approaches

The range of potential mechanisms limiting species' distributions in space is nearly as varied and complex as the diversity of life itself. Yet viewed abstractly, a species' border is a geographic manifestation of a species' demographic responses to a spatially and temporally varying world. Population dynamic models provide insight into the different routes by which range limits can arise owing to gradients in demographic rates. In a metapopulation context, for example, range limits may be caused by gradients in extinction rates, colonization rates or habitat availability. We have consider invasion models in uniform and heterogeneous environments as a framework for understanding non-equilibrium range limits, and explore conditions under which invasions may cease to spread leaving behind a stationary range limit. We conclude that non-equilibrial range dynamics need further theoretical and empirical attention.     

Spatially structured metapopulation models: global and local assessment of metapopulation capacity

We model metapopulation dynamics in finite networks of discrete habitat patches with given areas and spatial locations. We define and analyze two simple and ecologically intuitive measures of the capacity of the habitat patch network to support a viable metapopulation. Metapopulation persistence capacity lambda(M) defines the threshold condition for long-term metapopulation persistence as lambda(M)>delta, where delta is defined by the extinction and colonization rate parameters of the focal species. Metapopulation invasion capacity lambda(I) sets the condition for successful invasion of an empty network from one small local population as lambda(I)>delta. The metapopulation capacities lambda(M) and lambda(I) are defined as the leading eigenvalue or a comparable quantity of an appropriate "landscape" matrix. Based on these definitions, we present a classification of a very general class of deterministic, continuous-time and discrete-time metapopulation models. Two specific models are analyzed in greater detail: a spatially realistic version of the continuous-time Levins model and the discrete-time incidence function model with propagule size-dependent colonization rate and a rescue effect. In both models we assume that the extinction rate increases with decreasing patch area and that the colonization rate increases with patch connectivity. In the spatially realistic Levins model, the two types of metapopulation capacities coincide, whereas the incidence function model possesses a strong Allee effect characterized by lambda(I)=0. For these two models, we show that the metapopulation capacities can be considered as simple sums of contributions from individual habitat patches, given by the elements of the leading eigenvector or comparable quantities. We may therefore assess the significance of particular habitat patches, including new patches that might be added to the network, for the metapopulation capacities of the network as a whole. We derive useful approximations for both the threshold conditions and the equilibrium states in the two models. The metapopulation capacities and the measures of the dynamic significance of particular patches can be calculated for real patch networks for applications in metapopulation ecology, landscape ecology, and conservation biology.     

A spatially structured metapopulation model with patch dynamics

Metapopulation models that incorporate both spatial and temporal structure are studied in this paper. The existence and stability of equilibria are provided, and an extinction threshold condition is derived which depends on patch dynamics (patch destruction and creation) and metapopulation dynamics (patch colonization and extinction). These results refine threshold conditions given by previous metapopulation models. By comparing landscapes with different spatial heterogeneities with respect to weighted long-term patch occupancies, we conclude that the pattern of a landscape is of overwhelming importance in determining metapopulation persistence and patch occupancy. We show that the same conclusion holds when a rescue effect is considered. We also derive a stochastic differential equations (SDE) model of the It? type based on our deterministic model. Our simulations reveal good agreement between the deterministic model and the SDE model.     

Colonization and extinction dynamics of an annual plant metapopulation in an urban environment

The metapopulation framework considers that the spatiotemporal distribution of organisms results from a balance between the colonization and extinction of populations in a suitable and discrete habitat network. Recent spatially realistic metapopulation models have allowed patch dynamics to be investigated in natural populations but such models have rarely been applied to plants. Using a simple urban fragmented population system in which favourable habitat can be easily mapped, we studied patch dynamics in the annual plant Crepis sancta (Asteraceae). Using stochastic patch occupancy models (SPOMs) and multi‐year occupancy data we dissected extinction and colonization patterns in our system. Overall, our data were consistent with two distinct metapopulation scenarios. A metapopulation (sensu stricto) dynamic in which colonization occurs over a short distance and extinction is lowered by nearby occupied patches (rescue effect) was found in a set of patches close to the city centre, while a propagule rain model in which colonization occurs from a large external population was most consistent with data from other networks. Overall, the study highlights the importance of external seed sources in urban patch dynamics. Our analysis emphasizes the fact that plant distributions are governed not only by habitat properties but also by the intrinsic properties of colonization and dispersal of species. The metapopulation approach provides a valuable tool for understanding how colonization and extinction shape occupancy patterns in highly fragmented plant populations. Finally, this study points to the potential utility of more complex plant metapopulation models than traditionally used for analysing ecological and evolutionary processes in natural metapopulations.     

Colonization–extinction dynamics of epixylic lichens along a decay gradient in a dynamic landscape

Metapopulation models are often used for understanding and predicting species dynamics in fragmented landscapes. Several models have been proposed depending on e.g. the relative importance of patch dynamics on the metapopulation dynamics. Dead wood is a dynamic substrate patch, and species that are confined to such patches have experienced a high degree of habitat loss in managed forests. Little is, however, known about how the population dynamics of epixylic species are affected by the fast dynamics of their substrate patches. We quantified the effect of local patch conditions and metapopulation processes on colonizations and extinctions of epixylic lichen species in a managed boreal forest landscape. This was done by twice surveying seven lichen metapopulations on 293 stumps in 30 stands of ages covering the duration of the dynamic patches (stumps). We also investigated the relative importance of local stochastic extinctions from stumps that remained available, and deterministic extinctions due to stump surface disappearance. We found importance of a decay gradient, surrounding metapopulation size, and local population sizes, in driving the colonization–extinction dynamics of epixylic lichens. The species were sorted along the stump decay gradient. Increasing surrounding metapopulation size was associated with increased colonization rates, and increasing local population size decreased lichen extinction rates. Finally, both local stochastic extinctions and deterministic extinctions due to patch disappearance occur, confirming that the long‐term persistence of epixylic lichens depends on colonization rates that compensate for stochastic population extinctions as well as deterministic extinctions.     

Spatial genetic structure in a metapopulation of the land snail Cepaea nemoralis (Gastropoda: Helicidae)

Habitat fragmentation is a major force affecting demography and genetic structure of wild populations, especially in agricultural landscapes. The land snail Cepaea nemoralis (L.) was selected to investigate the impact of habitat fragmentation on the spatial genetic structure of an organism with limited dispersal ability. Genetic and morphological patterns were investigated at a local scale of a 500 m transect and a mesoscale of 4 x 4 km in a fragmented agricultural landscape while accounting for variation in the landscape using least-cost models. Analysis of microsatellite loci using expected heterozygosity (HE), pairwise genetic distance (FST/1-FST) and spatial autocorrelograms (Moran's I) as well as shell characteristics revealed spatial structuring at both scales and provided evidence for a metapopulation structure. Genetic diversity was related to morphological diversity regardless of landscape properties. This pointed to bottlenecks caused by founder effects after (re)colonization. Our study suggests that metapopulation structure depended on both landscape features and the shape of the dispersal function. A range of genetic spatial autocorrelation up to 80 m at the local scale and up to 800 m at the mesoscale indicated leptokurtic dispersal patterns. The metapopulation dynamics of C. nemoralis resulted in a patchwork of interconnected, spatially structured subpopulations. They were shaped by gene flow which was affected by landscape features, the dispersal function and an increasing role of genetic drift with distance.     

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of “clusters” of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.     

Strong genetic differentiation due to multiple founder events during a recent range expansion of an introduced wall lizard population

Biological invasions represent ideal systems for the study of evolutionary processes associated with colonization events. It has been hypothesized that the genetic diversity is generally decreasing from the centre of the range to the margins due to multiple founder events. Invasive populations offer the opportunity to test this hypothesis at a fine spatial and temporal scale. We analysed the genetic structure of a large expanding non-native population of the Common Wall Lizard (Podarcis muralis) in Passau (Germany) using thirteen microsatellite loci. We analyzed the genetic structure and levels of admixture across a transect reflecting the expansion process and tested for a loss of genetic diversity and an increase of genetic differentiation from the centre to the invasion front. Our results demonstrate that significant genetic population structure can emerge rapidly at a small spatial scale. We found a trend for an increase in genetic differentiation and a decrease in genetic diversity from the invasion centre to the expanding range margin, suggesting that genetic drift is the major factor causing this pattern. The correlation between genetic diversity and average genetic differentiation was significant among sites. We hypothesize that the territoriality of P. muralis generates sufficient rates of noncontiguous and stratified dispersal from longer established sites to maintain significant genetic diversity at the invasion front. Simultaneously, territoriality might restrict the colonization success of migrants at established sites, so that in combination with founder events a strong differentiation arises.     

异质种群动态模型:破碎化景观动态模拟的新途径

景观破碎化导致物种以异质种群方式存活,使得基于异质种群动态模拟破碎化景观动态成为可能。异质种群动态模型的发展为景观动态模拟奠定了良好基础。根据空间处理方式的不同,异质种群模型可分为三大类,可不同程度地用于描述破碎化景观动态。(1)空间不确定异质种群模型,假定所有局域种群间均等互联,模型中不包含空间信息,仅能用于景观斑块动态描述;(2)空间确定异质种群模型,假设局域种群在二维空间上以规则格子形式排列,是一种准现实的空间处理方式,可用于景观动态的简单描述;(3)空间现实异质种群模型,包含了破碎化景观中局域种群的几何特征,可直接用于真实景观动态的模拟研究。空间现实的和基于个体的异质种群模型不但是未来异质种群模型发展的主流,也将成为未来破碎化景观动态研究的重要工具。为了更加准确完整地描述破碎化景观动态,不但应该综合运用已有的各种异质种群模型方法,更要引进新模型来刎画多物种、多变量、高维度、复杂连接的破碎化景观格局与过程。     

Plant Invasion Patches – Reconstructing Pattern and Process by Means of Herb-chronology

An understanding of the patterns of spread of invasive plant species requires analysis of the major dispersal mechanisms and of the patch structure of suitable habitats, both of which may be scale-dependent. On a larger scale, information from herbarium or literature records has proved useful for the reconstruction of past spread of invasive plants. The objective of this study is to investigate population development of invasive forbs at the scale of a site or stand (the population scale) by using herb-chronology. The feasibility of this approach has been largely disregarded until now because of the perceived difficulties in determining the age of perennial herbs. However, recent findings suggest that most of the dicotyledonous perennial herbs in the seasonal climates develop annual rings in the roots or subterraneous stems and thus demonstrate a high potential of the method in studies on plant invasions that went almost unnoticed. The spatial position and age (by means of analysis of annual rings) of individual plants were determined in invasion patches of five species of perennial forbs in Germany and in the USA. The data thus obtained revealed different spatio-temporal patterns of population development that are consistent with distinct models of (local) plant spread, including diffuse invasion and front-like invasion patterns, and thus suggest different processes at work in the course of invasion. The results suggest that analysis of spatial age structures is useful (i) to estimate rates of patch expansion, (ii) to distinguish between dispersal- and microsite-limited population development, (iii) to evaluate how different site conditions affect population development, and (iv) to help understand metapopulation dynamics.     

Its all about connections: hubs and invasion in habitat networks

During the early stages of invasion, the interaction between the features of the invaded landscape, notably its spatial structure, and the internal dynamics of an introduced population has a crucial impact on establishment and spread. By approximating introduction areas as networks of patches linked by dispersal, we characterised their spatial structure with specific metrics and tested their impact on two essential steps of the invasion process: establishment and spread. By combining simulations with experimental introductions of Trichogramma chilonis (Hymenoptera: Trichogrammatidae) in artificial laboratory microcosms, we demonstrated that spread was hindered by clusters and accelerated by hubs but was also affected by small‐population mechanisms prevalent for invasions, such as Allee effects. Establishment was also affected by demographic mechanisms, in interaction with network metrics. These results highlight the importance of considering the demography of invaders as well as the structure of the invaded area to predict the outcome of invasions.     

Initial conditions and their effect on invasion velocity across heterogeneous landscapes

Accurate, time dependent control options are required to halt biological invasions prior to equilibrium establishment, beyond which control efforts are often impractical. Although invasions have been successfully modeled using diffusion theory, diffusion models are typically confined to providing simple range expansion estimates. In this work, we use a Susceptible/Infected cellular automaton (CA) to simulate diffusion. The CA model is coupled with a network model to track the speed and direction of simulated invasions across heterogeneous landscapes, allowing for identification of locations for targeted control in both time and space. We evaluated the role of the location of initial establishment insofar as it affected the pattern and rate of spread and how these are influenced by patch attributes such as size. Our results show that the location of initial establishment can significantly affect the temporal dynamics of an invasion. Traditional network metrics such as degree and measures of topological distance were insufficient for predicting the direction and speed of the invasion. Our coupled models allow the dynamic tracking of invasions across fragmented landscapes for both theoretical and practical applications.     

Invasibility as an emergent property of native metapopulation structure

Biological invasions constitute major threats to global biodiversity. Eco‐evolutionary considerations highlight the importance of contemporary evolution in community responses to bioinvasions. However, effects of metapopulation structure on invasion success have been mostly overlooked even though metapopulation structure determines gene flow and is likely to affect evolutionary processes. Here, we investigate a stepping‐stone model with evolving alien native interaction strengths. We demonstrate analytically that the site of invasion can determine the success of an invading consumer because gene flow and demography of a local resource species interact to obstruct local resource adaptation. Our main results are 1) that invasion success is more likely in genetic sink populations of the native species and 2) that invasion is more likely to occur against the migrational flow of native species. These findings suggest that invasibility is best regarded as an emergent property not only of communities but of entire metapopulations. Since migration networks of aliens and natives are often mismatched due to anthropogenic interference, our results indicate how population structure eases the spread of invasives against the migrational flow of natives.     

Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integrodifference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile–adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, Calathea ovandensis. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates “remember” the past.     

Offense and defense in landscape-level invasion control

Biological invasions are multi-stage processes comprising chance demographic events, species interactions, and dispersal. Despite this complexity, simple models can increase understanding of the invasion process. We model the spread of aquatic invasive species through a network of lakes to evaluate the effectiveness of two intervention strategies. The first, which we call offense, contains the invader at sources; the second, which we call defense, protects uninvaded destinations. Deterministic models reveal the effects of these intervention strategies on spread rates. Practical applications involve finite collections of uninvaded lakes, however, and we therefore also present a stochastic model to describe how these strategies affect expected times to important invasion milestones. When the goal is to reduce overall spread rates, both approaches agree that offense is better early in invasions, but that defense is better after 1/2 the lakes are invaded. When the goal is to protect areas of high conservation value, however, defensive site protection always provides lower per site introduction rates. Although we focus on lakes, our results are quite general, and could be applied to any discrete habitat patches including, for example, fragmented terrestrial habitats.     

Accounting for multi‐scale spatial autocorrelation improves performance of invasive species distribution modelling (iSDM)

Aim Analyses of species distributions are complicated by various origins of spatial autocorrelation (SAC) in biogeographical data. SAC may be particularly important for invasive species distribution models (iSDMs) because biological invasions are strongly influenced by dispersal and colonization processes that typically create highly structured distribution patterns. We examined the efficacy of using a multi‐scale framework to account for different origins of SAC, and compared non‐spatial models with models that accounted for SAC at multiple levels. Location We modelled the spatial distribution of an invasive forest pathogen, Phytophthora ramorum, in western USA. Methods We applied one conventional statistical method (generalized linear model, GLM) and one nonparametric technique (maximum entropy, Maxent) to a large dataset on P. ramorum occurrence (n = 3787) to develop four types of model that included environmental variables and that either ignored spatial context or incorporated it at a broad scale using trend surface analysis, a local scale using autocovariates, or multiple scales using spatial eigenvector mapping. We evaluated model accuracies and amounts of explained spatial structure, and examined the changes in predictive power of the environmental and spatial variables. Results Accounting for different scales of SAC significantly enhanced the predictive capability of iSDMs. Dramatic improvements were observed when fine‐scale SAC was included, suggesting that local range‐confining processes are important in P. ramorum spread. The importance of environmental variables was relatively consistent across all models, but the explanatory power decreased in spatial models for factors with strong spatial structure. While accounting for SAC reduced the amount of residual autocorrelation for GLM but not for Maxent, it still improved the performance of both approaches, supporting our hypothesis that dispersal and colonization processes are important factors to consider in distribution models of biological invasions. Main conclusions Spatial autocorrelation has become a paradigm in biogeography and ecological modelling. In addition to avoiding the violation of statistical assumptions, accounting for spatial patterns at multiple scales can enhance our understanding of dynamic processes that explain ecological mechanisms of invasion and improve the predictive performance of static iSDMs.     

Digest: Propagule pressure might not matter in the establishment of invasive prokaryotes*

Lavigne et al. developed models to investigate the adaptive colonization of sink environments by asexual organisms. Their results have clear relevance to the spread of infectious disease, but they may also provide insights into prokaryotic invasions into natural communities. Their results show that propagule pressure might not be a good predictor of invasion success in prokaryotes, suggesting that more work is needed to understand how microbial invasions differ from those of plants and animals.     

Equilibrium or not? Modelling potential distribution of invasive species in different stages of invasion

Aim The assumption of equilibrium between organisms and their environment is a standard working postulate in species distribution models (SDMs). However, this assumption is typically violated in models of biological invasions where range expansions are highly constrained by dispersal and colonization processes. Here, we examined how stage of invasion affects the extent to which occurrence data represent the ecological niche of organisms and, in turn, influences spatial prediction of species’ potential distributions. Location Six ecoregions in western Oregon, USA. Methods We compiled occurrence data from 697 field plots collected over a 9‐year period (2001–09) of monitoring the spread of invasive forest pathogen Phytophthora ramorum. Using these data, we applied ecological‐niche factor analysis to calibrate models of potential distribution across different years of colonization. We accounted for natural variation and uncertainties in model evaluation by further investigating three hypothetical scenarios of varying equilibrium in a simulated virtual species, for which the ‘true’ potential distribution was known. Results We confirm our hypothesis that SDMs calibrated in early stages of invasion are less accurate than models calibrated under scenarios closer to equilibrium. SDMs that are developed in early stages of invasion tend to underpredict the potential range compared to models that are built in later stages of invasion. Main conclusions A full environmental niche of invasive species cannot be effectively captured with data from a realized distribution that is restricted by processes preventing full occupancy of suitable habitats. If SDMs are to be used effectively in conservation and management, stage of invasion needs to be considered to avoid underestimation of habitats at risk of invasion.     

Metapopulation Persistence in Random Fragmented Landscapes

Habitat destruction and land use change are making the world in which natural populations live increasingly fragmented, often leading to local extinctions. Although local populations might undergo extinction, a metapopulation may still be viable as long as patches of suitable habitat are connected by dispersal, so that empty patches can be recolonized. Thus far, metapopulations models have either taken a mean-field approach, or have modeled empirically-based, realistic landscapes. Here we show that an intermediate level of complexity between these two extremes is to consider random landscapes, in which the patches of suitable habitat are randomly arranged in an area (or volume). Using methods borrowed from the mathematics of Random Geometric Graphs and Euclidean Random Matrices, we derive a simple, analytic criterion for the persistence of the metapopulation in random fragmented landscapes. Our results show how the density of patches, the variability in their value, the shape of the dispersal kernel, and the dimensionality of the landscape all contribute to determining the fate of the metapopulation. Using this framework, we derive sufficient conditions for the population to be spatially localized, such that spatially confined clusters of patches act as a source of dispersal for the whole landscape. Finally, we show that a regular arrangement of the patches is always detrimental for persistence, compared to the random arrangement of the patches. Given the strong parallel between metapopulation models and contact processes, our results are also applicable to models of disease spread on spatial networks.