Extinction times and phase transitions for spatially structured closed epidemics

This paper considers the time to extinction for a stochastic epidemic model of SEIR form without replacement of susceptibles. It first shows how previous rigorous results can be heuristically explained in terms of the more transparent dynamics of an approximating deterministic system. The model is then extended to include a host population structured into patches, with weak nearest-neighbour mixing of infection. It is shown, by considering the approximating deterministic system, that the expected time to extinction in a population of n + 1 patches each of size N is of the form a log N + bn, provided that N > N _c where N _c is a critical patch size below which transits are unlikely to occur. This corresponds to the simple decomposition of the time of an epidemic into the time it takes to spread through one patch plus the time it takes to transit to each of n successive patches. Expressions for this threshold and the coefficients of the time to extinction are given in terms of the transmission parameters of infection and the coupling strength between patches. These expressions are compared with numerical results using parameters relevant to a study of phocine distemper virus in North Sea seals, and the agreement is found to be good for large and small N. In the region when N ≈ N _c , where transits may or may not occur, interesting transitional behaviour is seen, leading to a non-monotonicity of the extinction time as a function of N.     

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.     

Regional and local scale metapopulation dynamics in the interaction between Callosobruchus maculatus and Anisopteromalus calandrae

Habitat structure increases the persistence of many extinction‐prone resource–consumer interactions. Metapopulation theory is one of the leading approaches currently used to explain why local, ephemeral populations persist at a regional scale. Central to the metapopulation concept is the amount of dispersal occurring between patches, too much or too little can result in regional extinction. In this study, the role of dispersal on the metapopulation dynamics of an over‐exploitative host–parasitoid interaction is assessed. In the absence of the parasitoid the highly vagile bruchid, Callosobruchus maculatus, can maintain a similar population size regardless of the permeability of the inter‐patch matrix and exhibits strong negative density‐dependence. After the introduction of the parasitoid the size of the bruchid population decreases with a corresponding increase in the occurrence of empty patches. In this case, limiting the dispersal of both species decouples the interaction to a greater extent and results in larger regional bruchid populations. Given the disparity between the dispersal rates of the two species, it is proposed that the more dispersive host benefits from the reduction in landscape permeability by increasing the opportunity to colonise empty patches and rescue extinction prone populations. Associated with the introduction of the parasitoid is a shift in the strength of density‐dependence as the population moves from bottom–up towards top–down regulation. The importance of local and regional scale measurements is apparent when the role of individual patches on regional dynamics is considered. By only taking regional dynamics into account the importance of dispersal regime on local dynamics is overlooked. Similarly, when local dynamics were examined, patches were found to have different influences on regional dynamics depending on dispersal regime and patch location.     

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.     

Approximate Bayesian estimation of extinction rate in the Finnish Daphnia magna metapopulation

Approximate Bayesian computation (ABC) is useful for parameterizing complex models in population genetics. In this study, ABC was applied to simultaneously estimate parameter values for a model of metapopulation coalescence and test two alternatives to a strict metapopulation model in the well‐studied network of Daphnia magna populations in Finland. The models shared four free parameters: the subpopulation genetic diversity (θ_S), the rate of gene flow among patches (4Nm), the founding population size (N₀) and the metapopulation extinction rate (e) but differed in the distribution of extinction rates across habitat patches in the system. The three models had either a constant extinction rate in all populations (strict metapopulation), one population that was protected from local extinction (i.e. a persistent source), or habitat‐specific extinction rates drawn from a distribution with specified mean and variance. Our model selection analysis favoured the model including a persistent source population over the two alternative models. Of the closest 750 000 data sets in Euclidean space, 78% were simulated under the persistent source model (estimated posterior probability = 0.769). This fraction increased to more than 85% when only the closest 150 000 data sets were considered (estimated posterior probability = 0.774). Approximate Bayesian computation was then used to estimate parameter values that might produce the observed set of summary statistics. Our analysis provided posterior distributions for e that included the point estimate obtained from previous data from the Finnish D. magna metapopulation. Our results support the use of ABC and population genetic data for testing the strict metapopulation model and parameterizing complex models of demography.     

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.     

A Stochastic Metapopulation Model with Variability in Patch Size and Position

Analytically tractable metapopulation models usually assume that every patch is identical, which limits their application to real metapopulations. We describe a new single species model of metapopulation dynamics that allows variation in patch size and position. The state of the metapopulation is defined by the presence or absence of the species in each patch. For a system of n patches, this gives 2ⁿ possible states. We show how to construct and analyse a matrix describing transitions between all possible states by first constructing separate extinction and colonisation matrices. We illustrate the model′s application to metapopulations by considering an example of malleefowl, Leipoa ocellata, in southern Australia, and calculate extinction probabilities and quasi-stationary distributions. We investigate the relative importance of modelling the particular arrangement of patches and the variation in patch sizes for this metapopulation and we use the model to examine the effects of further habitat loss on extinction probabilities.     

Extinction dynamics in mainland-island metapopulations: an N-patch stochastic model

A generalization of the well-known Levins’ model of metapopulations is studied. The generalization consists of (i) the introduction of immigration from a mainland, and (ii) assuming the dynamics is stochastic, rather than deterministic. A master equation, for the probability that n of the patches are occupied, is derived and the stationary probability P _s (n), together with the mean and higher moments in the stationary state, determined. The time-dependence of the probability distribution is also studied: through a Gaussian approximation for general n when the boundary at n = 0 has little effect, and by calculating P(0, t), the probability that no patches are occupied at time t, by using a linearization procedure. These analytic calculations are supplemented by carrying out numerical solutions of the master equation and simulations of the stochastic process. The various approaches are in very good agreement with each other. This allows us to use the forms for P _s 0) and P(0, t) in the linearization approximation as a basis for calculating the mean time for a metapopulation to become extinct. We give an analytical expression for the mean time to extinction derived within a mean field approach. We devise a simple method to apply our mean field approach even to complex patch networks in realistic model metapopulations. After studying two spatially extended versions of this nonspatial metapopulation model—a lattice metapopulation model and a spatially realistic model—we conclude that our analytical formula for the mean extinction time is generally applicable to those metapopulations which are really endangered, where extinction dynamics dominates over local colonization processes. The time evolution and, in particular, the scope of our analytical results, are studied by comparing these different models with the analytical approach for various values of the parameters: the rates of immigration from the mainland, the rates of colonization and extinction, and the number of patches making up the metapopulation.     

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.     

Host-parasitoid extinction and colonization in a fragmented prairie landscape

Few field studies of natural populations have examined the factors influencing local extinctions and colonization of empty habitat patches for a prey species and its predator. In this study, I carried out a census of planthopper (Prokelisia crocea; Hemiptera: Delphacidae) and egg parasitoid (Anagrus columbi; Hymenoptera: Mymaridae) incidence and densities in 147 host-plant patches (Spartina pectinata; Poaceae) over seven planthopper generations in a tall-grass prairie landscape. For both species, the likelihood of going extinct in a patch was related to a number of patch-specific variables: density, temporal variability in density, proportion of hosts parasitized (planthopper only), host-plant density, patch size, patch isolation, and composition of the surrounding matrix. Colonization likelihood was related only to the physical attributes of the patch. There was high patch turnover in this prairie landscape. On average, planthoppers went extinct in 23% of the patches and A. columbi went extinct in 51% of the patches in each generation. For the planthopper, extinction likelihood increased with a decrease in patch size and the proportion of the matrix composed of mudflat. Parasitism of eggs had no effect on the extinction likelihood of local P. crocea populations, suggesting that A. columbi may not play a major role in the patch dynamics of its host. The likelihood of extinction for A. columbi was dependent on factors that spanned three trophic levels. An increase in plant density, decrease in host density and decrease in parasitoid density all increased the likelihood of A. columbi extinction within a patch. The dependency on multiple trophic levels may explain the higher extinction risk for the parasitoid than its host. A. columbi extinction was also affected by the matrix habitat surrounding the patch—the effect was the opposite of that for P. crocea. Finally, vacant patches were colonized at rates of 53% and 34% per generation for the planthopper and parasitoid, respectively. For both species, colonization probabilities decreased with an increase in patch isolation. High host densities in a patch also favored high rates of colonization by A. columbi. I discuss how anthropogenic changes to the prairie landscape can affect the metapopulation dynamics and persistence time of this host-parasitoid interaction.     

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.     

The mathematical theory of group selection. I. Full solution of a nonlinear Levins E = E(x) model

The first complete overtime solution is obtained for a group selection model of Levins E = E(x) type with recolonization but no other gene flow between islands. Assuming a subdivided population at carrying capacity, the model describes selection at a biallelic locus (A, a) where a is opposed by Mendelian selection but is favored by a lower rate of extinction of demes having high a frequency. By contrast to the linear diffusion equations encountered in classical mathematical genetics, the PDE governing the dynamics is now nonlinear in the metapopulation gene frequency distribution φ(x, t); furthermore, the initial conditions now heavily influence the equilibrium distribution φ_∞(x). A fully explicit formula (20) expressing this dependence is derived. The results indicate that a fixation is never reached, but (A, a) polymorphism in the metapopulation will result if , where s 1 parametrizes the strength of Mendelian selection, E(x) is the Levins extinction operator, h (typically in the open interval (0, 1)) is the dominance of a, and B is a parameter measuring the flatness of the initial distribution f(x) in the x → 1 limit.     

Relative importance of host plant patch geometry and habitat quality on the patterns of occupancy,extinction and density of the monophagous butterfly <Emphasis Type="Italic">Iolana iolas</Emphasis>

Habitat fragmentation is a major cause of species rarity and decline because it increases local population extinctions and reduces recolonisation rates of remnant patches. Although two major patch characteristics (area and connectivity) have been used to predict distribution patterns in fragmented landscapes, other factors can affect the occurrence of a species as well as the probability of it becoming extinct. In this paper, we study the spatial structure and dynamics of the butterfly Iolana iolas in a 75-patch network of its host plant (Colutea hispanica) to determine the relative importance of patch area, connectivity and habitat quality characteristics on occupancy, extinction and density over the period 2003–2006. Occupancy in 2003, incidence (proportion of years occupied) and probability of extinction were mostly affected by patch area. Smaller patches were less likely to be occupied because they had a higher probability of extinction, partly due to environmental stochasticity. The density of I. iolas was negatively related to patch area in all study years. Only in 2004 was the density of I. iolas positively influenced by fruit production per plant. Our results suggest that for I. iolas, and probably for other specialist butterflies with clearly delimited resource requirements, metapopulation dynamics can be satisfactorily predicted using only geometric variables because most habitat characteristics are subsumed in patch area. However, this hypothesis should be subject to further testing under diverse environmental conditions to evaluate the extent of its generalisation.     

Patch occupancy of two hemipterans sharing a common host plant

Aim Two hemipteran species were chosen as a study system for the comparative analysis of patch occupancy and spatial population structure of insects sharing a common host plant. This study tested whether (1) the incidence in the host plant patches differed between the two species, and (2) the two species exhibited a different spatial population structure, i.e. were they affected differentially by isolation and area of the host plant patches. Location The porphyry landscape north of Halle (Saale) in Germany comprising 506 patches of the host plant Brachypodium pinnatum. Methods The host plant patches were surveyed for the two hemipterans. To assess the influence of patch quality on species occurrence the patches were characterized by mean cover abundance of B. pinnatum, type of subsoil, slope, exposure, and shading. The spatial configuration of the patches was considered by patch area and isolation. The influence of the habitat factors and the spatial configuration on the occupancy of the two species was analysed by logistic regression. Results Adarrus multinotatus was found in 441 patches, while Neophilaenus albipennis was found in only 90 patches. While A. multinotatus showed virtually no relationship to the habitat factors, the occupancy of N. albipennis was influenced by subsoil type, cover abundance, and shading. The effects of area and isolation on occupancy of the patches also differed between the two species. The occupancy of N. albipennis was determined largely by area and isolation, whereas in A. multinotatus no considerable effect of spatial configuration was found. Main conclusions The study revealed a marked difference between the two hemipteran species in respect of spatial population structure. Adarrus multinotatus built up a ‘patchy population’, whereas N. albipennis showed a ‘metapopulation’ structure within the same set of patches in the same landscape. Spatial population structure was found to be not only a function of spatial configuration of habitat patches, but population structure differed between the habitat generalist A. multinotatus and the habitat specialist N. albipennis.     

Spatially-correlated extinction in a metapopulation model of Leadbeater's Possum

The importance of considering spatially-correlated extinction in metapopulation viability analyses was investigated using a model of the population dynamics of Gymnobelideus leadbeateri McCoy (Leadbeater's Possum). Fire caused local extinction of G. leadbeateri and induced changes in the suitability of the habitat over a period of decades and centuries. Spatially-correlated fires, in which the correlation between the incidence of fire declines with distance, and uniformly-correlated fires were simulated. The predicted risk of metapopulation extinction increased: (i) as the variance in the number of fires each year increased, (ii) as the mean fire interval decreased, and (iii) as the mean dispersal distance decreased. Incorporating spatial correlation in the incidence of fires between patches had little effect on the results, provided the variance in the number of fires per year remained the same and fires modified habitat quality. The predicted risk of metapopulation extinction was greater for spatially-correlated fires than for uniformly-correlated fires when fires only caused local extinction but did not change habitat suitability. Incorporating spatial correlation in the incidence of fire within patches, which allowed partial burning of patches, reduced the predicted risk of extinction. This effect was only slight when patches were smaller than about 50 ha. The results of our simulations demonstrate the importance of considering correlations in disturbance regimes in metapopulation models, especially if these models are used to assist the design of nature reserves.     

Effect of habitat fragmentation on dispersal in the butterfly Proclossiana eunomia

Comparison of dispersal rates of the bog fritillary butterfly between continuous and fragmented landscapes indicates that between patch dispersal is significantly lower in the fragmented landscape, while population densities are of the same order of magnitude. Analyses of the dynamics of the suitable habitat for the butterfly in the fragmented landscape reveal a severe, non linear increase in spatial isolation of patches over a time period of 30 years (i.e. 30 butterfly generations), but simulations of the butterfly metapopulation dynamics using a structured population model show that the lower dispersal rates in the fragmented landscape are far above the critical threshold leading to metapopulation extinction. These results indicate that changes in individual behaviour leading to the decrease of dispersal rates in the fragmented landscape were rapidly selected for when patch spatial isolation increased. The evidence of such an adaptive answer to habitat fragmentation suggests that dispersal mortality is a key factor for metapopulation persistence in fragmented landscapes. We emphasise that landscape spatial configuration and patch isolation have to be taken into account in the debate about large-scale conservation strategies.     

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.     

Effects of patch characteristics and isolation on relative abundance of the scarce heath butterfly <Emphasis Type="Italic">Coenonympha hero</Emphasis> (Nymphalidae)

The scarce heath (Coenonympha hero) is an internationally threatened butterfly in Western Europe, where it occurs primarily on hay fields and abandoned arable land in a small-scale agricultural landscape of south-central Scandinavia. Due to afforestation, this habitat is becoming increasingly fragmented in Sweden, and it can be expected that the scarce heath will decline abruptly when threshold conditions for metapopulation persistence are no longer met. We used stepwise polychotomous logistic regression to compare habitat characteristics and isolation measures for patches that harbour large, small or no populations, respectively, in an area of south-western Sweden. We found that patch area, distance to the nearest large population and amount of Galium spp. explained a significant part of the variation in relative abundance among patches. Distance to nearest large population resulted in a better model to predict occupancy than both distance to the nearest inhabited patch and connectivity, which suggests that primarily large populations act as sources for small satellite populations. Today, sites of three of the eight larger populations in the study area have been planted with spruce or pine and will disappear within 20 years. We argue that the disappearance of these patches may very well lead to rapid extinction of the whole metapopulation system.     

Disobedient epiphytes: colonization and extinction rates in a metapopulation of Lepanthes rupestris (Orchidaceae) contradict theoretical predictions based on patch connectivity

The metapopulation concept is widely established in population biology. It predicts that the likelihood of colonization of an empty patch is positively correlated with its connectivity, because colonizers from occupied patches will be more likely to reach an empty patch if they are closer to it. Another prediction is that the likelihood of extinction of an occupied patch will be negatively correlated with its connectivity to other patches, as the occupied patch can be ‘reinforced’ by immigrants from patches that are close by. We tested these predictions using an extensive data set for an epiphytic orchid, Lepanthes rupestris from Puerto Rico. Our data did not support the first prediction, but we found that the likelihood of extinction is negatively correlated with patch connectivity. We hypothesize that this might be because most orchid seeds are wind dispersed and seeds that do not fall immediately below the mother plant are uniformly distributed after a steep leptokurtic distribution. We predict that taxa with similar seed and gene flow characteristics should show similar patterns in the association between colonization/extinction rates and patch connectivity. © 2014 The Linnean Society of London, Botanical Journal of the Linnean Society, 2014, 175 , 598–606.     

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.