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.     

Allee threshold and extinction threshold for spatially explicit metapopulation dynamics with Allee effects

In this paper, we investigate a spatially explicit metapopulation model with Allee effects. We refer to the patch occupancy model introduced by Levins (Bull Entomol Soc Am 15:237–240, 1969) as a spatially implicit metapopulation model, i.e., each local patch is either occupied or vacant and a vacant patch can be recolonized by a randomly chosen occupied patch from anywhere in the metapopulation. When we transform the model into a spatially explicit one by using a lattice model, the obtained model becomes theoretically equivalent to a “lattice logistic model” or a “basic contact process”. One of the most popular or standard metapopulation models with Allee effects, developed by Amarasekare (Am Nat 152:298–302, 1998), supposes that those effects are introduced formally by means of a logistic equation. However, it is easier to understand the ecological meaning of associating Allee effects with this model if we suppose that only the logistic colonization term directly suffers from Allee effects. The resulting model is also well defined, and therefore we can naturally examine it by Monte Carlo simulation and by doublet and triplet decoupling approximation. We then obtain the following specific features of one-dimensional lattice space: (1) the metapopulation as a whole does not have an Allee threshold for initial population size even when each local population follows the Allee effects; and (2) a metapopulation goes extinct when the extinction rate of a local population is lower than that in the spatially implicit model. The real ecological metapopulation lies between two extremes: completely mixing interactions between patches on the one hand and, on the other, nearest neighboring interactions with only two nearest neighbors. Thus, it is important to identify the metapopulation structure when we consider the problems of invasion species such as establishment or the speed of expansion.     

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.     

Metapopulation theory for fragmented landscapes

We review recent developments in spatially realistic metapopulation theory, which leads to quantitative models of the dynamics of species inhabiting highly fragmented landscapes. Our emphasis is in stochastic patch occupancy models, which describe the presence or absence of the focal species in habitat patches. We discuss a number of ecologically important quantities that can be derived from the full stochastic models and their deterministic approximations, with a particular aim of characterizing the respective roles of the structure of the landscape and the properties of the species. These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.     

Is metapopulation patch occupancy in nature well predicted by the Levins model?

Although the Levins model has made important theoretical contributions to ecology, its empirical support has not been conclusively established yet. We used published colonization and extinction data from 55 metapopulations to calculate their Levins equilibrium patch occupancy. Over all species, there were not significant differences between the observed patch occupancies and the Levins model's estimates. However, invertebrates and vertebrate species with some degree of threat had patch occupancies larger than the model's expectancies. A temporal sampling effect was found for invertebrate species, with departure from the Levins model decreasing as the length of the study period increased. There was a negative relationship between patch occupancy and extinction probability, as expected under the “rescue effect”. The high rates at which invertebrates produce propagules could lead the Levins model to underestimate patch occupancy, whereas the observed patch occupancy of threatened species may be a transient phenomenon that results from extinction probabilities that increase over time. Therefore, the Levins model captures the metapopulation dynamics of a wide range of species in a simple formula whereas its equilibrium point can be used as evidence of metapopulation stability. Although mechanistic models provide more precise and accurate metapopulation predictions, they also can sacrifice the generality and simplicity of the Levins model.     

Long-term demographic surveys reveal a consistent relationship between average occupancy and abundance within local populations of a butterfly metapopulation

Species distribution models are the tool of choice for large-scale population monitoring, environmental association studies and predictions of range shifts under future environmental conditions. Available data and familiarity of the tools rather than the underlying population dynamics often dictate the choice of specific method – especially for the case of presence–absence data. Yet, for predictive purposes, the relationship between occupancy and abundance embodied in the models should reflect the actual population dynamics of the modelled species. To understand the relationship of occupancy and abundance in a heterogeneous landscape at the scale of local populations, we built a spatio-temporal regression model of populations of the Glanville fritillary butterfly Melitaea cinxia in a Baltic Sea archipelago. Our data comprised nineteen years of habitat surveys and snapshot data of land use in the region. We used variance partitioning to quantify relative contributions of land use, habitat quality and metapopulation covariates. The model revealed a consistent and positive, but noisy relationship between average occupancy and mean abundance in local populations. Patterns of abundance were highly variable across years, with large uncorrelated random variation and strong local population stochasticity. In contrast, the spatio-temporal random effect, habitat quality, population connectivity and patch size explained variation in occupancy, vindicating metapopulation theory as the basis for modelling occupancy patterns in fragmented landscapes. Previous abundance was an important predictor in the occupancy model, which points to a spillover of abundance into occupancy dynamics. While occupancy models can successfully model large-scale population structure and average occupancy, extinction probability estimates for local populations derived from occupancy-only models are overconfident, as extinction risk is dependent on actual, not average, abundance.     

Do invasive species undergo metapopulation dynamics? A case study of the invasive Caspian gull,Larus cachinnans,in Poland

Aim The mechanisms of initial dispersal and habitat occupancy by invasive alien species are fundamental ecological problems. Most tests of metapopulation theory are performed on local population systems that are stable or in decline. In the current study we were interested in the usefulness of metapopulation theory to study patch occupancy, local colonization, extinction and the abundance of the invasive Caspian gull (Larus cachinnans) in its initial invasion stages. Location Waterbodies in Poland. Methods Characteristics of the habitat patches (waterbodies, 35 in total) occupied by breeding pairs of Caspian gulls and an equal sample of randomly selected unoccupied patches were compared with t‐tests. Based on presence–absence data from 1989 to 2006 we analysed factors affecting the probability of local colonization, extinction and the size of local populations using generalized linear models. Results Occupied habitat patches were significantly larger and less isolated (from other habitat patches and other local populations) and were located closer to rivers than empty patches. The proximity of local food resources (fish ponds, refuse dumps) positively affected the occurrence of breeding pairs. The probability of colonization was positively affected by patch area, and negatively by distances to fish ponds, nearest habitat patch, nearest breeding colony and to a river, and by higher forest cover around the patch boundaries. The probability of extinction was lower in patches with a higher number of breeding pairs and with a greater area of islets. The extinction probability increased with distances to other local populations, other habitat patches, fish ponds and to refuse dumps and with a higher cover of forest around the patch boundaries. The size of the local population decreased with distances to the nearest habitat patch, local population, river, fish pond and refuse dump. Local abundance was also positively affected by the area of islets in the patch. Main conclusions During the initial stages of the invasion of Caspian gulls in Poland the species underwent metapopulation‐like dynamics with frequent extinctions from colonized habitat patches. The results prove that metapopulation theory may be a useful conceptual framework for predicting which habitats are more vulnerable to invasion.     

Pattern does not equal process: what does patch occupancy really tell us about metapopulation dynamics?

Patch occupancy surveys are commonly used to parameterize metapopulation models. If isolation predicts patch occupancy, this is generally attributed to a balance between distance-dependent recolonization and spatially independent extinctions. We investigated whether similar patterns could also be generated by a process of spatially correlated extinctions following a unique colonization event (analogous to nonequilibrium processes in island biogeography). We simulated effects of spatially correlated extinctions on patterns of patch occupancy among pikas (Ochotona princeps) at Bodie, California, using randomly located extinction disks to represent the likely effects of predation. Our simulations produced similar patterns to those cited as evidence of balanced metapopulation dynamics. Simulations using a variety of disk sizes and patch configurations confirmed that our results are potentially applicable to a broad range of species and sites. Analyses of the observed patterns of patch occupancy at Bodie revealed little evidence of rescue effects and strong evidence that most recolonizations are ephemeral in nature. Persistence will be overestimated if static or declining patterns of patch occupancy are mistakenly attributed to dynamically stable metapopulation processes. Consequently, simple patch occupancy surveys should not be considered as substitutes for detailed experimental tests of hypothesized population processes, particularly when conservation concerns are involved.     

用空间直观模型是否足以从斑块占据性资料中推断集合种群的动态过程?

在集合种群的研究中,经常要根据空间占据性数据应用斑块模型来推断种群的动态过程,在保护生物学应用中,斑块占据性模型的参数估测对于阐释集合种群动态和预测种群对生境破坏的反应极为重要。我们探讨了一种广泛应用的空间直观模型——率函数模型(Incidence function model)中参数估测的不确定性问题,通过构建由50个斑块组成的网络和两个假想的已知参数的集合种群,应用模拟模型产生集合种群随时间变化的斑块占据性数据系列：即快照(snapshot)。然后,根据这些快照,应用率函数模型和最大似然法估测种群动态参数。此外,我们还给出了传统的率函数模型的一个变形,这个变形包含了目标区效应(Target area effect)：即一个斑块的占据概率不但取决于空间隔离度,也取决于斑块本身面积的大小。结果表明：根据同一个集合种群不同的快照所估测的参数可以有很大差异,一个快照得出的参数提示的是占据性强但存活率低的集合种群,而另一个快照可能反映的是一个占据性弱但存活率高的集合种群。应用传统的率函数模型于一个包含了目标区效应的集合种群,导致斑块大小相关的灭绝率参数估测的正偏差。因此,仅根据一个快照的空间占据性数据来推测集合种群的过程有很大的不确定性[动物学报49(6)：787～794,2003]。     

Contributions of high- and low-quality patches to a metapopulation with stochastic disturbance

Studies of time-invariant matrix metapopulation models indicate that metapopulation growth rate is usually more sensitive to the vital rates of individuals in high-quality (i.e., good) patches than in low-quality (i.e., bad) patches. This suggests that, given a choice, management efforts should focus on good rather than bad patches. Here, we examine the sensitivity of metapopulation growth rate for a two-patch matrix metapopulation model with and without stochastic disturbance and found cases where managers can more efficiently increase metapopulation growth rate by focusing efforts on the bad patch. In our model, net reproductive rate differs between the two patches so that in the absence of dispersal, one patch is high quality and the other low quality. Disturbance, when present, reduces net reproductive rate with equal frequency and intensity in both patches. The stochastic disturbance model gives qualitatively similar results to the deterministic model. In most cases, metapopulation growth rate was elastic to changes in net reproductive rate of individuals in the good patch than the bad patch. However, when the majority of individuals are located in the bad patch, metapopulation growth rate can be most elastic to net reproductive rate in the bad patch. We expand the model to include two stages and parameterize the patches using data for the softshell clam, Mya arenaria. With a two-stage demographic model, the elasticities of metapopulation growth rate to parameters in the bad patch increase, while elasticities to the same parameters in the good patch decrease. Metapopulation growth rate is most elastic to adult survival in the population of the good patch for all scenarios we examine. If the majority of the metapopulation is located in the bad patch, the elasticity to parameters of that population increase but do not surpass elasticity to parameters in the good patch. This model can be expanded to include additional patches, multiple stages, stochastic dispersal, and complex demography.     

Threshold parameters and metapopulation persistence

A method is presented to estimate the minimum viable metapopulation size based on the basic reproductive number R ₀ and the expected time to extinction τ _E for epidemiological models. We exemplify our approach with two simple deterministic metapopulation models of the patch occupancy type and then proceed to stochastic versions that permit the estimation of the minimum viable metapopulation size.     

Patch occupancy and abundance of local populations in landscapes differing in degree of habitat fragmentation: a case study of the colonial black‐headed gull,Chroicocephalus ridibundus

Aim This study investigated whether habitat fragmentation at the landscape level influences patch occupancy and abundance of the black‐headed gull, Chroicocephalus ridibundus, and whether the response of the species to environmental factors is consistent across replicated landscape plots. Location Water bodies (habitat patches) in southern Poland. Methods Surveys were conducted in two landscape types (four plots in each): (1) more‐fragmented landscape, in which habitat patches were small (mean size 2.2–6.2 ha) and far apart (mean distance 2.5–3.1 km); and (2) less‐fragmented landscape, in which habitat patches were large (mean size 9.2–16.5 ha) and separated by short distances (mean 0.9–1.4 km). Observations were performed twice in 284 potential habitat patches during the 2007 breeding season. Results Colonies were significantly more frequent and larger in the less‐fragmented landscapes than in the more‐fragmented ones. Probability of patch occupancy and number of breeding birds were positively related with patch size and these relationships were especially strong in the more‐fragmented landscapes. In the less‐fragmented landscapes, the occurrence of black‐headed gulls was negatively related to the distance to the nearest local population, but in the more‐fragmented landscapes such a relationship was not detected. As distance to the nearest habitat patch increased, the probability of the patch occupancy decreased in the more‐fragmented landscapes. Moreover, abundance was negatively influenced by distance to the nearest habitat patch, especially strongly in more‐fragmented landscapes. Proximity of corridors (rivers) positively influenced the occupation of patches regardless of landscape type. The number of islets positively influenced occupancy and abundance of local populations, and this relationship was stronger in the more‐fragmented landscapes. Main conclusions Our results are in agreement with predictions from metapopulation theory and are the first evidence that populations of black‐headed gulls may have a metapopulation structure. However, patch occupancy and abundance were differentially affected by explanatory variables in the more‐fragmented landscapes than in the less‐fragmented ones. This implies that it is impossible to derive, a priori, predictions about presence/abundance patterns based on only a single landscape.     

Stochastic models for mainland-island metapopulations in static and dynamic landscapes

This paper has three primary aims: to establish an effective means for modelling mainland-island metapopulations inhabiting a dynamic landscape; to investigate the effect of immigration and dynamic changes in habitat on metapopulation patch occupancy dynamics; and to illustrate the implications of our results for decision-making and population management. We first extend the mainland-island metapopulation model of Alonso and McKane [Bull. Math. Biol. 64:913–958, 2002] to incorporate a dynamic landscape. It is shown, for both the static and the dynamic landscape models, that a suitably scaled version of the process converges to a unique deterministic model as the size of the system becomes large. We also establish that, under quite general conditions, the density of occupied patches, and the densities of suitable and occupied patches, for the respective models, have approximate normal distributions. Our results not only provide us with estimates for the means and variances that are valid at all stages in the evolution of the population, but also provide a tool for fitting the models to real metapopulations. We discuss the effect of immigration and habitat dynamics on metapopulations, showing thatmainland-like patches heavily influence metapopulation persistence, and we argue for adopting measures to increase connectivity between this large patch and the other island-like patches. We illustrate our results with specific reference to examples of populations of butterfly and the grasshopperBryodema tuberculata.     

Neighbourhood size,dispersal distance and the complex dynamics of the spatial Ricker model

Amongst the most frequently made assumptions in simple population models are that individuals interact equally with every other individual and that dispersal occurs with equal likelihood to any location. This is especially true for models of a single population (as opposed to a patchy population or metapopulation). For many species of animals and probably for all plant species these assumptions are unlikely to hold true. Here one much-studied population model—the Ricker model—is reformulated such that interactions occur only between individuals located within a certain distance of each other and dispersal distance is finite. Two alternative reformulations are presented. Results demonstrate that both limiting the interaction neighbourhood and reducing dispersal distance tend to stabilise the global population dynamics, although the extent to which this occurs depends upon the reformulation used. Spatial pattern formation is a feature of the simulated population. At lower intrinsic rates of growth (r) these patterns tend to be static, while for higher r, they are dynamic. Both the stabilisation of global dynamics and spatial pattern formation are well-described features of metapopulation models. Here, similar effects are shown to occur on a single contiguous patch of habitat.     

Habitat quality of source patches and connectivity in fragmented landscapes

Because spatial connectivity is critical to dispersal success and persistence of species in highly fragmented landscapes, the way that we envision and measure connectivity is consequential for biodiversity conservation. Connectivity metrics used for predictive modeling of spatial turnover and patch occupancy for metapopulations, such as with Incidence Function Models (IFM), incorporate distances to and sizes of possible source populations. Here, our focus is on whether habitat quality of source patches also is considered in these connectivity metrics. We propose that effective areas (weighted by habitat quality) of source patches should be better surrogates for population size and dispersal potential compared to unadjusted patch areas. Our review of a representative sample of the literature revealed that only 12.5% of studies incorporated habitat quality of source patches into IFM-type connectivity metrics. Quality of source patches generally was not taken into account in studies even if habitat quality of focal patches was included in analyses. We provide an empirical example for a metapopulation of a rare wetland species, the round-tailed muskrat (Neofiber alleni), demonstrating that a connectivity metric based on effective areas of source patches better predicts patch colonization and occupancy than a metric that used simple patch areas. The ongoing integration of landscape ecology and metapopulation dynamics could be hastened by incorporating habitat quality of source patches into spatial connectivity metrics applied to species conservation in fragmented landscapes.     

Aggregate statistical measures and metapopulation dynamics

There are two main types of metapopulation models. Spatially implicit models are analytically tractable but neglect spatial heterogeneities. Spatially explicit models are more realistic but too complex. In this paper, I build a bridge between both approximations. I derive a new metapopulation model using a well-known technique in population genetics. Spatial heterogeneities are captured by an aggregate statistical measure of spatial correlation. When this correlation is zero, i.e., space is homogeneous, the model becomes the well-known Levins' model. As spatial correlation increases, equilibrium patch occupancy decreases from what would be expected under the spatially homogeneous assumption. I proceed by testing how well spatial complexities from a spatially explicit simulation can be encapsulated by such an aggregate statistical measure.     

Asynchronization of local population dynamics and persistence of a metapopulation: a lesson from an endangered composite plant, Aster kantoensis

Fragmentation of a large habitat makes local populations less linked to others, and a whole population structure changes to a metapopulation. The smaller a local population is, the more strengthened extinction factors become. Then, frequent extinctions of local populations threaten persistence of the metapopulation unless recolonizations occur rapidly enough after local extinctions. Spatially structured models have been more widely used for predicting future population dynamics and for assessing the extinction risk of a metapopulation. In this article, we first review such spatially structured models that have been applied to conservation biology, focusing on effects of asynchronization among local population dynamics on persistence of the whole metapopulation. Second, we introduce our ongoing project on extinction risk assessment of an endangered composite biennial plant, Aster kantoensis, in the riverside habitat, based on a lattice model for describing its spatiotemporal population dynamics. The model predicted that the extinction risk of A. kantoensis depends on both the frequency of flood occurrence and the time to coverage of a local habitat by other competitively stronger perennials. Finally, we present a measure (Hassell and Pacala's CV ²) for quantifying the effect of asynchronization among local population dynamics on the persistence of a whole metapopulation in conservation ecology. Received: January 12, 2000 / Accepted: February 8, 2000     

Can occupancy patterns be used to predict distributions in widely separated geographic regions?

Occupancy models, that describe the presence and absence patterns of a species in a given area, are increasingly being used to predict the occurrence of the species in unsurveyed sites, as an aid to conservation planning. In this paper, we consider whether conclusions about local distributions derived from one landscape can be extrapolated to others. We found that habitat patchiness influenced the distribution and abundance of the host-specific moth Wheeleria spilodactylus in a similar way in two landscapes widely separated geographically. In both geographic regions, the spatial location (positive effect of connectivity), and quantity of resource (positive effect of host plant density) increased the likelihood that the moth would be present, consistent with the expectations of metapopulation dynamics. Though some biological attributes of the species appeared to be slightly different, including population density and the timing of the life cycle (phenology), occupancy patterns in one landscape accurately predict occupancy in the other landscape. Our results suggest that it maybe possible to make predictions from one landscape to another, even when the landscapes are widely separated.