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.     

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.     

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.     

Metapopulation models for seasonally migratory animals

Metapopulation models are widely used to study species that occupy patchily distributed habitat, but are rarely applied to migratory species, because of the difficulty of identifying demographically independent subpopulations. Here, we extend metapopulation theory to describe the directed seasonal movement of migratory populations between two sets of habitat patches, breeding and non-breeding, with potentially different colonization and extinction rates between patch types. By extending the classic metapopulation model, we show that migratory metapopulations will persist if the product of the two colonization rates exceeds the product of extinction rates. Further, we develop a spatially realistic migratory metapopulation model and derive a landscape metric-the migratory metapopulation capacity-that determines persistence. This new extension to metapopulation theory introduces an important tool for the management and conservation of migratory species and may also be applicable to model the dynamics of two host-parasite systems.     

生境破坏的模式对集合种群动态和续存的影响

构建了空间关联的集合种群模型,该模型不但包含了种群的空间结构信息,而且引入了破坏生境的全局密度和局部密度两个指标,它们描述了破坏生境的模式.模型揭示了破坏生境的空间分布格局复杂地影响了集合种群的动态和续存,破坏和未破坏生境斑块的均匀混合不利于集合种群的增长和续存,而生境类型聚集分布可以促进集合种群的快速增长和长期续存;对于两种斑块类型相对均匀混合的生境来说,均匀场假设可能会高估集合种群的续存,对于相对斑块类型高度聚集的生境,均匀场假设可能会低估集合种群的续存;物种的迁移范围也会影响集合种群的续存,迁移范围越大的物种越容易抵御生境的破坏而免遭灭绝.这意味着在生物保护中不能仅仅考虑生境的恢复和斑块质量的改善,生境结构的构建也是很重要的,加强生境斑块之间的连通性也有利于物种的长期续存.     

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.     

Dances with fire: Tracking metapopulation dynamics of<Emphasis Type="Italic">polygonella basiramia</Emphasis> in Florida scrub (USA)

The regional persistence of species subject to local population colonization and extinction necessarily depends on how landscape features and disturbance affect metapopulation dynamics. Here, we characterize the metapopulation structure and short-term dynamics ofPolygonella basiramia. This rare, short-lived perennial herb is endemic to Florida scrublands and lacks a seed bank. Fires create the open sand gaps within a shrub matrix that support this species but also kill established plants. Thus, persistence depends on frequent colonization of unoccupied gaps. We are monitoring population dynamics within and among 1204 gaps distributed among 19 shrub patches. Considerable subpopulation turnover is evident at the gap level with rates of gap extinction exceeding rates of colonization in the first year. Whether declines in overall abundance continue is likely to depend on patterns of disturbance and regional stochasticity in this dynamic landscape.Polygonella is more likely to occupy larger and less isolated gaps, demonstrating that landscape features and disturbance strongly affect metapopulation dynamics. BecausePolygonella basiramia displays characteristics, occupancy patterns, and turnover dynamics consistent with metapopulation theory, it represents a model system for studying plant metapopulations.     

Modelling the spatial dynamics and persistence of the leaf beetle Gonioctena olivacea in dynamic habitats

In dynamic landscapes natural and anthropogenic disturbance as well as succession are responsible for the emergence and subsequent disappearance of suitable habitat patches. Species inhabiting such landscapes are faced with varying number and spatial configuration of patches. A stochastic, spatially explicit simulation model was developed in order to analyse the persistence of the leaf beetle Gonioctena olivacea in a system of dynamic patches of its host plant Cytisus scoparius . The model was parameterized with data from a three-year field study on the spatial configuration, distribution, and turnover of the host plant patches as well as the patch occupancy, extinction, and colonization rates of the beetle. The simulations showed large fluctuations in the occurrence of the beetle in the patches. High levels of occupancy were related to high aggregation of the patches within the landscape. The velocity of patch turnover was found to have a severe effect on the persistence of the beetle metapopulation. Enhancing the turnover rate by only a few patches, the mean time to extinction decreases rapidly. Moreover, the results revealed that not necessarily an effect of connectivity can be detected in the analysis of occupancy patterns in dynamic landscapes, although the colonization of patches is clearly connectivity-dependent. In general, this modelling study demonstrates the importance of detailed information on patch turnover. The amount and spatial distribution of suitable habitat is a major driver of metapopulation dynamics of species in dynamic landscapes.     

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.     

Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

How patch configuration affects the impact of disturbances on metapopulation persistence

Disturbances affect metapopulations directly through reductions in population size and indirectly through habitat modification. We consider how metapopulation persistence is affected by different disturbance regimes and the way in which disturbances spread, when metapopulations are compact or elongated, using a stochastic spatially explicit model which includes metapopulation and habitat dynamics. We discover that the risk of population extinction is larger for spatially aggregated disturbances than for spatially random disturbances. By changing the spatial configuration of the patches in the system--leading to different proportions of edge and interior patches--we demonstrate that the probability of metapopulation extinction is smaller when the metapopulation is more compact. Both of these results become more pronounced when colonization connectivity decreases. Our results have important management implication as edge patches, which are invariably considered to be less important, may play an important role as disturbance refugia.     

Local populations of different sizes, mechanistic rescue effect and patch preference in the Levins metapopulation model

In this paper three extensions of the Levins metapopulation model are discussed: (1) It is shown that the Levins model is still valid if patches contain local populations of different sizes with different colonization and extinction rates. (2) A more mechanistic formulation of the rescue effect is presented. (3) The addition of preference of dispersers for occupied or empty patches and its consequences for conservation strategies are studied.     

Implications of empirical data quality to metapopulation model parameter estimation and application

Parameter estimation is a critical step in the use of any metapopulation model for predictive purposes. Typically metapopulation studies assume that empirical data are of good quality and any errors are so insignificant that they can be ignored. However, three types of errors occur commonly in metapopulation data sets. First, patch areas can be mis-estimated. Second, unknown habitat patches may be located within or around the study area. Third, there may be false zeros in the data set, that is, some patches were observed to be empty while there truly was a population in the patch. This study investigates biases induced into metapopulation model parameter estimates by these three types of errors. It was found that mis-estimated areas influence the scaling of extinction risk with patch area; extinction probabilities for large patches become overestimated. Missing patches cause overestimation of migration distances and colonization ability of the species. False zeros can affect very strongly all model components, the extinction risk in large patches, intrinsic extinction rates in general, migration distances and colonization ability may become all overestimated. Biases in parameter estimates translate into corresponding biases in model predictions, which are serious particularly if metapopulation persistence becomes overestimated. This happens for example when the migration capability of the species is overestimated. Awareness of these biases helps in understanding seemingly anomalous parameter estimation results. There are also implications for field work: it may be reasonable to allocate effort so that serious errors in data are minimized. It is particularly important to avoid observing false zeros for large and/or isolated patches.     

Extinction, colonization, and species occupancy in tidepool fishes

Despite the increasing sophistication of ecological models with respect to the size and spatial arrangement of habitat, there is relatively little empirical documentation of how species dynamics change as a function of habitat size and the fraction of habitat occupied. In an assemblage of tidepool fishes, I used maximum-likelihood estimation to test whether models which included habitat size provided a better fit to empirical data on extinction and colonization probabilities than models that assumed constant probabilities over all habitats. I found species differences in how extinction and colonization probabilities scaled with habitat size (and hence local population size). However, there was little evidence for a relationship between extinction and colonization probabilities and the fraction of occupied tidepools, as assumed in simple metapopulation models. Instead, colonization and extinction were independent of the fraction of occupied tidepools, favoring a MacArthur-Wilson island-mainland model. When I incorporated declines in extinction probability with tidepool volume in a simple simulation model, I found that predicted occupancy could change greatly, especially when colonization was low. However, the predicted fraction of occupied patches in the simulation model changed little when I incorporated the range of values reported here for extinction and colonization and the rate at which they scale with habitat size. Quantifying extinction and colonization patterns of natural populations is fundamental to understanding how species are distributed spatially and whether metapopulation models of species occupancy provide explanatory power for field populations. Received: 14 March 1997 / Accepted: 21 September 1997     

Testing metapopulation concepts: effects of patch characteristics and neighborhood occupancy on the dynamics of an endangered lagomorph

Metapopulation ecology is a field that is richer in theory than in empirical results. Many existing empirical studies use an incidence function approach based on spatial patterns and key assumptions about extinction and colonization rates. Here we recast these assumptions as hypotheses to be tested using 18 years of historic detection survey data combined with four years of data from a new monitoring program for the Lower Keys marsh rabbit. We developed a new model to estimate probabilities of local extinction and colonization in the presence of nondetection, while accounting for estimated occupancy levels of neighboring patches. We used model selection to identify important drivers of population turnover and estimate the effective neighborhood size for this system. Several key relationships related to patch size and isolation that are often assumed in metapopulation models were supported: patch size was negatively related to the probability of extinction and positively related to colonization, and estimated occupancy of neighboring patches was positively related to colonization and negatively related to extinction probabilities. This latter relationship suggested the existence of rescue effects. In our study system, we inferred that coastal patches experienced higher probabilities of extinction and colonization than interior patches. Interior patches exhibited higher occupancy probabilities and may serve as refugia, permitting colonization of coastal patches following disturbances such as hurricanes and storm surges. Our modeling approach should be useful for incorporating neighbor occupancy into future metapopulation analyses and in dealing with other historic occupancy surveys that may not include the recommended levels of sampling replication.     

The influence of patch demographics on metapopulations, with particular reference to successional landscapes

The classical view of metapopulations relates the regional abundance of a species to the balance between the extinction and colonization dynamics of identical local populations. Species in successional landscapes may represent the most appropriate examples of classical metapopulations. However, Levins‐type metapopulation models do not explicitly separate population loss due to successional habitat change from other causes of extinction. A further complication is that the chance of population loss due to successional habitat change may be related to the age of a patch. I developed simple patch occupancy models to include succession and included consideration of patch age structure to address two related questions: what are the implications of changes in patch demographic rates and when is a move to a structured patch occupancy model justified? Age‐related variation in patch demography could increase or decrease the equilibrium fraction of the available habitat occupied by a species when compared to the predictions of an unstructured model. Metapopulation persistence was enhanced when the age class of patches with the highest species occupancy suffered relatively low losses to habitat succession. Conversely, when the age class of patches with the highest species occupancy also had relatively high successional loss rates, extinction thresholds were higher that would be predicted by a simple unstructured model. Hence age‐related variation in patch successional rate introduces biases into the predictions of simple unstructured models. Such biases can be detected from field surveys of the fraction of occupied and unoccupied patches in each age class. Where a bias is demonstrated, unstructured models will not be adequate for making predictions about the effects of changing parameters on metapopulation size. Thinking in successional terms emphasizes how landscapes might be managed to enhance or reduce the patch occupancy by any particular metapopulation     

Spatial and temporal variation in patch occupancy and population density in a model system of an arctic Collembola species assemblage

We employed an experimental model system to investigate the mechanisms underlying patterns of patch occupancy and population density in a high arctic assemblage of Collembola species inhabiting a sedge tussock landscape on Svalbard. The replicate model systems consisted of 5 cores of the tussocks (habitat patches) imbedded in a barren matrix. Four of the patches were open so that animals could migrate between them, while there was one closed patch per system to test the effect of migration on extinction rate. There were model systems of two types: one with long and one with short inter‐patch distances to test the effect of patch isolation on colonisation and extinction rates. Each of the four most common collembolan species at the field site were introduced to two open patches per system (source patches), with the other two functioning as colonisation patches for the species. The experiment was run in an ecotrone over three identical, simulated arctic summers separated by winters of 3 weeks. Six replicates of systems with short and long inter‐patch distances were sampled at the end of each summer. The species varied markedly in their performance in both open arenas and closed patches, indicating differential responses to patch humidity, consistent with their differential distribution along the moisture gradient in the field site. The extinction – colonisation dynamics differed markedly between species as predicted from our field studies. This could partly be ascribed to differential dispersal and colonisation ability, but also to different tolerance to spatially variable patch quality and/or tendency for aggregative behaviour. Three of the species exhibited dynamics that superficially resemble what could be expected from classical metapopulation dynamics. However, there was a striking discrepancy between what would be expected from the effect of migration on the extinction rate of isolated patches (in particular closed patches) and the observed rates. Thus, metapopulation processes, such as stochastic colonisation and extinction events due to demographic stochasticity, were relatively unimportant compared to other sources of spatial variability among which subtle differences in patch quality are probably most important. We discuss the value of combining field studies with model system experiments, in particular when habitat quality cannot easily be measured in the field. However, our field and laboratory studies also emphasise the need for a thorough knowledge of species‐specific life history traits for making biologically sound interpretations based on both observational and experimental data.     

The rescue effect and inference from isolation–extinction relationships

The rescue effect in metapopulations hypothesises that less isolated patches are unlikely to go extinct because recolonisation may occur between breeding seasons (‘recolonisation rescue’), or immigrants may sufficiently bolster population size to prevent extinction altogether (‘demographic rescue’). These mechanisms have rarely been demonstrated directly, and most evidence of the rescue effect is from relationships between isolation and extinction. We determined the frequency of recolonisation rescue for metapopulations of black rails (Laterallus jamaicensis) and Virginia rails (Rallus limicola) from occupancy surveys conducted during and between breeding seasons, and assessed the reliability of inferences about the occurrence of rescue drawn from isolation–extinction relationships, including autologistic isolation measures that corrected for unsurveyed patches and imperfect detection. Recolonisation rescue occurred at expected rates, but was elevated during periods of disturbance that resulted in non‐equilibrium metapopulation dynamics. Inferences from extinction–isolation relationships were unreliable, particularly for autologistic measures and for the more vagile Virginia rail.     

Metapopulation Dynamics of the Mistletoe and Its Host in Savanna Areas with Different Fire Occurrence

Mistletoes are aerial hemiparasitic plants which occupy patches of favorable habitat (host trees) surrounded by unfavorable habitat and may be possibly modeled as a metapopulation. A metapopulation is defined as a subdivided population that persists due to the balance between colonization and extinction in discrete habitat patches. Our aim was to evaluate the dynamics of the mistletoe Psittacanthus robustus and its host Vochysia thyrsoidea in three Brazilian savanna areas using a metapopulation approach. We also evaluated how the differences in terms of fire occurrence affected the dynamic of those populations (two areas burned during the study and one was fire protected). We monitored the populations at six-month intervals. P. robustus population structure and dynamics met the expected criteria for a metapopulation: i) the suitable habitats for the mistletoe occur in discrete patches; (ii) local populations went extinct during the study and (iii) colonization of previously non-occupied patches occurred. The ratio of occupied patches decreased in all areas with time. Local mistletoe populations went extinct due to two different causes: patch extinction in area with no fire and fire killing in the burned areas. In a burned area, the largest decrease of occupied patch ratios occurred due to a fire event that killed the parasites without, however, killing the host trees. The greatest mortality of V. thyrsoidea occurred in the area without fire. In this area, all the dead trees supported mistletoe individuals and no mortality was observed for parasite-free trees. Because P. robustus is a fire sensitive species and V. thyrsoidea is fire tolerant, P. robustus seems to increase host mortality, but its effect is lessened by periodic burning that reduces the parasite loads.