Which traits promote persistence of feral GM crops? Part 2: implications of metapopulation structure

Transgenes may spread from crops into the environment via the establishment of feral populations, often initiated by seed spill from transport lorries or farm machinery. Locally, such populations are often subject to large environmental variability and usually do not persist longer than a few years. Because secondary feral populations may arise from seed dispersal to adjacent sites, the dynamics of such populations should be studied in a metapopulation context. We study a structured metapopulation model with local dispersal, mimicking a string of roadside subpopulations of a feral crop. Population growth is assumed to be subject to local disturbances, introducing spatially random environmental stochasticity. Our aim is to understand the role of dispersal and environmental variability in the dynamics of such ephemeral populations. We determine the effect of dispersal on the extinction boundary and on the distribution of persistence times, and investigate the influence of spatially correlated disturbances as opposed to spatially random disturbances. We find that, given spatially random disturbances, dispersal slows down the decline of the metapopulation and results in the occurrence of long-lasting local populations which remain more or less static in space. We identify which life history traits, if changed by genetic modification, have the largest impact on the population growth rate and persistence times. For oilseed rape, these are seed bank survival and dormancy. Combining our findings with literature data on transgene-induced life history changes, we predict that persistence is promoted by transgenes for oil-modifications (high stearate or high laurate) and, possibly, for insect resistence (Bt). Transgenic tolerance to glufosinate herbicide is predicted to reduce persistence.     

Does colonization asymmetry matter in metapopulations?

Despite the considerable evidence showing that dispersal between habitat patches is often asymmetric, most of the metapopulation models assume symmetric dispersal. In this paper, we develop a Monte Carlo simulation model to quantify the effect of asymmetric dispersal on metapopulation persistence. Our results suggest that metapopulation extinctions are more likely when dispersal is asymmetric. Metapopulation viability in systems with symmetric dispersal mirrors results from a mean field approximation, where the system persists if the expected per patch colonization probability exceeds the expected per patch local extinction rate. For asymmetric cases, the mean field approximation underestimates the number of patches necessary for maintaining population persistence. If we use a model assuming symmetric dispersal when dispersal is actually asymmetric, the estimation of metapopulation persistence is wrong in more than 50% of the cases. Metapopulation viability depends on patch connectivity in symmetric systems, whereas in the asymmetric case the number of patches is more important. These results have important implications for managing spatially structured populations, when asymmetric dispersal may occur. Future metapopulation models should account for asymmetric dispersal, while empirical work is needed to quantify the patterns and the consequences of asymmetric dispersal in natural metapopulations.     

Linking dendritic network structures to population demogenetics: The downside of connectivity

Spatial structures strongly influence ecological processes. Connectivity is known to positively influence metapopulation demography and genetics by increasing the rescue effect and thus favoring individual and gene flow between populations. This result has not been tested in the special case of dendritic networks, which encompass stream and cave ecosystem for instance. We propose a first approach using an individual based model to explore the population demography and genetics in various dendritic networks. To do so, we first generate a large number of different networks, and we analyze the relationship between their hydrographical characteristics and connectivity. We show that connectivity mean and variance of connectivity are strongly correlated in dendritic networks. Connectivity segregates two types of networks: Hortonian and non‐Hortonian networks. We then simulate the population dynamics for a simple life cycle in each of the generated networks, and we analyze persistence time as well as populations structure at quasi‐stationary state. Our main results show that connectivity in dendritic networks can promote local extinction and genetic isolation by distance at low dispersal and diminish the size of the metapopulation at high dispersal. We discuss these unexpected findings in the light of connectivity spatial distribution in dendritic networks in the case of our model.     

Metapopulation persistence in dynamic landscapes: the role of dispersal distance

Species associated with transient habitats need efficient dispersal strategies to ensure their regional survival. Using a spatially explicit metapopulation model, we studied the effect of the dispersal range on the persistence of a metapopulation as a function of the local population and landscape dynamics (including habitat patch destruction and subsequent regeneration). Our results show that the impact of the dispersal range depends on both the local population and patch growth. This is due to interactions between dispersal and the dynamics of patches and populations via the number of potential dispersers. In general, long-range dispersal had a positive effect on persistence in a dynamic landscape compared to short-range dispersal. Long-range dispersal increases the number of couplings between the patches and thus the colonisation of regenerated patches. However, long-range dispersal lost its advantage for long-term persistence when the number of potential dispersers was low due to small population growth rates and/or small patch growth rates. Its advantage also disappeared with complex local population dynamics and in a landscape with clumped patch distribution.     

Exploring rarity using a general model for distribution and abundance

We describe a simple model for changes in the distribution and abundance of a metapopulation and use it to explore the conditions leading to different types of rarity. The model suggests that localized populations (those with low patch occupancy but high local abundance) arise from low dispersal, low heterogeneity in extant population size, and frequent local extinctions relative to the potential for recolonization. Scarce populations (with low distribution and abundance) arise when relative local extinction rate is low to moderate and heterogeneity is high or successful dispersal is relatively low. Sparse populations (widespread, but with low local abundance) arise when relative local extinction rate is very low and either spatial heterogeneity or mortality through unsuccessful dispersal is high. In sparse or common species, there may be unstable as well as stable equilibria, implying a threshold distribution and abundance for persistence. The model supports a general correlation between distribution and abundance and suggests that persistence may be threatened by dispersal rates being either too high or too low. The model provides a new perspective on rarity and suggests a simple theoretical foundation for understanding the population-dynamic mechanisms that determine distribution and abundance.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

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.     

Relative impacts of adult movement, larval dispersal and harvester movement on the effectiveness of reserve networks

Movement of individuals is a critical factor determining the effectiveness of reserve networks. Marine reserves have historically been used for the management of species that are sedentary as adults, and, therefore, larval dispersal has been a major focus of marine-reserve research. The push to use marine reserves for managing pelagic and demersal species poses significant questions regarding their utility for highly-mobile species. Here, a simple conceptual metapopulation model is developed to provide a rigorous comparison of the functioning of reserve networks for populations with different admixtures of larval dispersal and adult movement in a home range. We find that adult movement produces significantly lower persistence than larval dispersal, all other factors being equal. Furthermore, redistribution of harvest effort previously in reserves to remaining fished areas ('fishery squeeze') and fishing along reserve borders ('fishing-the-line') considerably reduce persistence and harvests for populations mobile as adults, while they only marginally changes results for populations with dispersing larvae. Our results also indicate that adult home-range movement and larval dispersal are not simply additive processes, but rather that populations possessing both modes of movement have lower persistence than equivalent populations having the same amount of 'total movement' (sum of larval and adult movement spatial scales) in either larval dispersal or adult movement alone.     

Habitat destruction in a simple predator-prey patch model: how predators enhance prey persistence and abundance

We model a metapopulation of predator-prey patches using both spatially implicit or mean-field (MF) and spatially explicit (SE) approaches. We show that in the MF model there are parameter regimes for which prey cannot persist in the absence of predators, but can in their presence. In addition, there are parameter regimes for which prey may persist in isolation, but the presence of predators will increase prey patch density. Predators may thus enhance prey persistence and overall abundance. The key mechanism responsible for this effect is the occurrence of prey dispersal from patches that are occupied by both prey and predators. In addition, these patches should be either long-lived, such as that occurs when predators keep prey from overexploiting its local resource, or the presence of a predator on a patch should significantly enhance the prey dispersal out of that patch. In the SE approach these positive effects of predators on prey persistence and abundance occur for even larger parameter ranges than in the MF model. Prey dispersal from predator-prey patches may thus be important for persistence of both species as a community, independent of the modeling framework studied. Comparison of the MF and SE approaches shows that local dispersal constraints can have the edge over global dispersal for the persistence of the metapopulation in regimes where the two species have a beneficial effect on each other. In general, our model provides an example of feedback in multiple-species metapopulations that can make the implementation of conservation schemes based on single-species arguments very risky.     

How does intraspecific density regulation influence metapopulation synchrony and persistence?

Intraspecific density regulation influences the synchronization of local population dynamics through dispersal. Spatial synchrony in turn may jeopardize metapopulation persistence. Joining results from previous studies suggests that spatial synchrony is highest at moderate over-compensation and is low at compensating and at very strong over-compensating density regulation. We scrutinize this supposition of a unimodal relationship using a process-based metapopulation model with explicit local population dynamics. We extend the usually studied range of density regulation to under-compensation and analyse resulting metapopulation persistence. We find peaks of spatial synchrony not only at over-compensatory but also under-compensatory density regulation and show that effects of local density compensation on synchrony follow a bimodal rather than unimodal relationship. Persistence of metapopulations however, shows a unimodal relationship with a broad plateau of high persistence from compensatory to over-compensatory density regulation. This range of high persistence comprises both levels of low and high spatial synchrony. Thus, not synchrony alone jeopardizes metapopulation persistence, but only in interplay with high local extinction risk. The functional forms of the relations of density compensation with spatial synchrony and persistence are robust to increases in dispersal mortality, landscape dynamics, or density dependence of dispersal. However, with each of these increases the maxima of spatial synchrony and persistence shift to higher over-compensation and levels of synchrony are reduced. Overall, for over-compensation high landscape connectivity has negative effects while for under-compensation connectivity affects persistence positively. This emphasizes the importance of species life-history traits for management decisions with regard to landscape connectivity: while dispersal corridors are essential for species with under-compensatory density regulation, they may have detrimental effects for endangered species with over-compensation.     

The effects of density-dependence and local dispersal in individual-based stochastic metapopulations

We describe simulation models for metapopulations of individual‐based random walk populations with local dispersal on a coupled map lattice. The models were used to assess the factors determining persistence time, in particular the incidence of density‐dependence required for long‐term persistence of a temporally and spatially stochastic metapopulation, the extent of persistence possible in the absence of density‐dependence, and the factors that affect this.
Metapopulation persistence depended on the overall rate of increase of the metapopulation mean. This was maximised by (in order of importance) high mean and variance in the local rate of increase, high dispersal rates (20% or more of individuals dispersing each generation), large lattice size, and large dispersal range (to at least 24 neighbouring subpopulations).
With density‐dependence, the emergent dynamics of the metapopulation mean following global perturbation (reduction in density) resembled those of the logistic growth model. However, the overall metapopulation rate of increase and equilibrium level bore no resemblance to those of the subpopulations: rate of increase was higher (negative mean local rates of increase may give positive overall growth), and equilibrium mean metapopulation density was well below the local carrying capacity. This highlights the need to sample populations at an appropriate scale when seeking to understand regulatory mechanisms.
Metapopulations with the strongest tendency to grow gave the highest equilibrium mean density, the highest incidence of density‐dependence, and the longest persistence time. However, long‐term persistence with low average density and very low incidence of density‐dependence was possible on a sufficiently large lattice. For example, with 40×40 subpopulations, mean metapopulation persistence time was around 10⁴ generations, with mean subpopulation size of 2% of the carrying capacity, and local density‐dependence acting just once every 2500 generations on average. Metapopulation processes may explain our inability to detect density‐dependence in many real populations, and may also play an important part in the persistence of rare species.     

Spatial population structure of a specialist leaf-mining moth

1. The spatial structure of natural populations may profoundly influence their dynamics. Depending on the frequency of movements among local populations and the consequent balance between local and regional population processes, earlier work has attempted to classify metapopulations into clear-cut categories, ranging from patchy populations to sets of remnant populations. In an alternative, dichotomous scheme, local populations have been classified as self-sustaining populations generating a surplus of individuals (sources) and those depending on immigration for persistence (sinks). 2. In this paper, we describe the spatial population structure of the leaf-mining moth Tischeria ekebladella, a specialist herbivore of the pedunculate oak Quercus robur. We relate moth dispersal to the distribution of oaks on Wattkast, a small island (5 km(2)) off the south-western coast of Finland. 3. We build a spatially realistic metapopulation model derived from assumptions concerning the behaviour of individual moths, and show that the model is able to explain part of the variation in observed patterns of occurrence and colonization. 4. While the species was always present on large trees, a considerable proportion of the local populations associated with small oaks showed extinction-recolonization dynamics. The vast majority of moth individuals occur on large trees. 5. According to model predictions, the dominance of local vs. regional processes in tree-specific moth dynamics varies drastically across the landscape. Most local populations may be defined broadly as 'sinks', as model simulations suggest that in the absence of immigration, only the largest oaks will sustain viable moth populations. Large trees in areas of high oak density will contribute most to the overall persistence of the metapopulation by acting as sources of moths colonizing other trees. 6. No single 'metapopulation type' will suffice to describe the oak-moth system. Instead, our study supports the notion that real populations are often a mix of earlier identified categories. The level to which local populations may persist after landscape modification will vary across the landscape, and sweeping classifications of metapopulations into single categories will contribute little to understanding how individual local populations contribute to the overall persistence of the system.     

Maintenance of the sexes and persistence of a clonal organism in spatially complex metapopulations

Clonal organisms persist at a range of population sex ratios, from equal numbers of males and females to single-sex systems. When intersexual competition is strong enough to drive one sex locally extinct, the maintenance of the sexes is facilitated by the semi-independent dynamics of populations within a metapopulation. These semi-independent dynamics are influenced by dispersal and recolonization rates, which are affected by the spatial arrangement of populations. To establish the quantitative relationship between spatially complex metapopulations and the maintenance of the sexes, we used a mathematical model of the liverwort Marchantia inflexa. This clonal organism is found in discrete patches on rocks and along the banks of streams, which form single-sex and two-sex metapopulations. In this system, asexual propagules mainly disperse short distances. Long-distance between-patch dispersal and recolonization mainly occurs via sexual propagules, which require both sexes to be present. Dispersal of these two types of propagules could interact with the spatial arrangement of populations to affect the maintenance of the sexes. With our mathematical model, we found that at intermediate distances between populations, metapopulations maintained both sexes, and the spatial arrangement of populations changed the threshold at which one sex was lost. On the other hand, when populations were close to one another, one sex was lost and the single-sex metapopulation persisted through dispersal of asexual propagules. When populations were far apart, one sex was lost, and the metapopulation either went extinct due to lack of recolonization by asexual propagules or persisted because clumped populations facilitated recolonization. These idealized spatial arrangements help clarify the effects of the spatial arrangement on the maintenance of the sexes and the persistence of metapopulations of clonal organisms, which can help explain geographic parthenogenesis and the distribution of asexual populations, the persistence of asexual species, and inform the conservation of clonal organisms.     

The effects of connectivity on metapopulation persistence: network symmetry and degree correlations

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation''s dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in- and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in–out degree distribution, namely the ‘in–out degree correlation’ (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in–out degree distribution and particularly, the IODC are dominant factors controlling persistence.     

Spatial variation in branch size promotes metapopulation persistence in dendritic river networks

1. Despite years of attention, the dynamics of species constrained to disperse within riverine networks are not well captured by existing metapopulation models, which often ignore local dynamics within branches.
2. We develop a modelling framework, based on traditional metapopulation theory, for patch occupancy dynamics subject to local colonisation–extinction dynamics within branches and regional dispersal between branches in size-structured, bifurcating riverine networks. Using this framework, we investigate whether and how spatial variation in branch size affects species persistence for dendritic systems with directional dispersal, including one-way (up- or downstream only) and two-way (both up- and downstream) dispersal.
3. Variation in branch size generally promotes species persistence more obviously at higher relative extinction rate, suggesting that previous studies ignoring differences in branch size in real riverine systems might overestimate species extinction risk.
4. Two-way dispersal is not always superior to one-way dispersal as a strategy for metapopulation persistence especially at high relative extinction rate. The type of dispersal that maximises species persistence is determined by the hierarchical level of the largest, and hence most influential, branch within the network. When considering the interactive effects of up- and downstream dispersal, we find that moderate upstream-biased dispersal maximises metapopulation viability, mediated by spatial branch arrangement.
5. Overall, these results suggest that both branch-size variation and species traits interact to determine species persistence, theoretically demonstrating the ecological significance of their interplay.

     

The role of landscape-dependent disturbance and dispersal in metapopulation persistence

The fundamental processes that influence metapopulation dynamics (extinction and recolonization) will often depend on landscape structure. Disturbances that increase patch extinction rates will frequently be landscape dependent such that they are spatially aggregated and have an increased likelihood of occurring in some areas. Similarly, landscape structure can influence organism movement, producing asymmetric dispersal between patches. Using a stochastic, spatially explicit model, we examine how landscape-dependent correlations between dispersal and disturbance rates influence metapopulation dynamics. Habitat patches that are situated in areas where the likelihood of disturbance is low will experience lower extinction rates and will function as partial refuges. We discovered that the presence of partial refuges increases metapopulation viability and that the value of partial refuges was contingent on whether dispersal was also landscape dependent. Somewhat counterintuitively, metapopulation viability was reduced when individuals had a preponderance to disperse away from refuges and was highest when there was biased dispersal toward refuges. Our work demonstrates that landscape structure needs to be incorporated into metapopulation models when there is either empirical data or ecological rationale for extinction and/or dispersal rates being landscape dependent.     

Local retention,dispersal and fluctuating connectivity among populations of a coral reef fish

The persistence and resilience of marine populations in the face of disturbances is directly affected by connectivity among populations. Thus, understanding the magnitude and pattern of connections among populations and the temporal variation in these patterns is critical for the effective management and conservation of marine species. Despite recent advances in our understanding of marine connectivity, few empirical studies have directly measured the magnitude or pattern of connections among populations of marine fishes, and none have explicitly investigated temporal variation in demographic connectivity. We use genetic assignment tests to track the dispersal of 456 individual larval fishes to quantify the extent of connectivity, dispersal, self-recruitment and local retention within and among seven populations of a coral reef fish (Stegastes partitus) over a three-year period. We found that some larvae do disperse long distances (~200 km); however, self-recruitment was a regular phenomenon. Importantly, we found that dispersal distances, self-recruitment, local retention and the pattern of connectivity varied significantly among years. Our data highlight the unpredictable nature of connectivity, and underscore the need for more, temporally replicated, empirical measures of connectivity to inform management decisions.     

Optimal harvesting strategies for a metapopulation

We consider optimal strategies for harvesting a population that is composed of two local populations. The local populations are connected by the dispersal of juveniles, e.g. larvae, and together form a metapopulation. We model the metapopulation dynamics using coupled difference equations. Dynamic programming is used to determine policies for exploitation that are economically optimal. The metapopulation harvesting theory is applied to a hypothetical fishery and optimal strategies are compared to harvesting strategies that assume the metapopulation is composed either of single unconnected populations or of one well-mixed population. Local populations that have high per capita larval production should be more conservatively harvested than would be predicted using conventional theory. Recognizing the metapopulation structure of a stock and using the appropriate theory can significantly improve economic gains.     

Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.     

Identification of metapopulation dynamics among Northern Goshawks of the Alexander Archipelago, Alaska, and Coastal British Columbia

Northern Goshawks occupying the Alexander Archipelago, Alaska, and coastal British Columbia nest primarily in old-growth and mature forest, which results in spatial heterogeneity in the distribution of individuals across the landscape. We used microsatellite and mitochondrial data to infer genetic structure, gene flow, and fluctuations in population demography through evolutionary time. Patterns in the genetic signatures were used to assess predictions associated with the three population models: panmixia, metapopulation, and isolated populations. Population genetic structure was observed along with asymmetry in gene flow estimates that changed directionality at different temporal scales, consistent with metapopulation model predictions. Therefore, Northern Goshawk assemblages located in the Alexander Archipelago and coastal British Columbia interact through a metapopulation framework, though they may not fit the classic model of a metapopulation. Long-term population sources (coastal mainland British Columbia) and sinks (Revillagigedo and Vancouver islands) were identified. However, there was no trend through evolutionary time in the directionality of dispersal among the remaining assemblages, suggestive of a rescue–effect dynamic. Admiralty, Douglas, and Chichagof island complex appears to be an evolutionarily recent source population in the Alexander Archipelago. In addition, Kupreanof island complex and Kispiox Forest District populations have high dispersal rates to populations in close geographic proximity and potentially serve as local source populations. Metapopulation dynamics occurring in the Alexander Archipelago and coastal British Columbia by Northern Goshawks highlight the importance of both occupied and unoccupied habitats to long-term population persistence of goshawks in this region.