Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics

Infectious diseases provide a particularly clear illustration of the spatiotemporal underpinnings of consumer-resource dynamics. The paradigm is provided by extremely contagious, acute, immunizing childhood infections. Partially synchronized, unstable oscillations are punctuated by local extinctions. This, in turn, can result in spatial differentiation in the timing of epidemics and, depending on the nature of spatial contagion, may result in traveling waves. Measles epidemics are one of a few systems documented well enough to reveal all of these properties and how they are affected by spatiotemporal variations in population structure and demography. On the basis of a gravity coupling model and a time series susceptible-infected-recovered (TSIR) model for local dynamics, we propose a metapopulation model for regional measles dynamics. The model can capture all the major spatiotemporal properties in prevaccination epidemics of measles in England and Wales.     

A unifying framework for metapopulation dynamics

Many biologically important processes, such as genetic differentiation, the spread of disease, and population stability, are affected by the (natural or enforced) subdivision of populations into networks of smaller, partly isolated, subunits. Such "metapopulations" can have extremely complex dynamics. We present a new general model that uses only two functions to capture, at the metapopulation scale, the main behavior of metapopulations. We show how complex, structured metapopulation models can be translated into our generalized framework. The metapopulation dynamics arising from some important biological processes are illustrated: the rescue effect, the Allee effect, and what we term the "antirescue effect." The antirescue effect captures instances where high migration rates are deleterious to population persistence, a phenomenon that has been largely ignored in metapopulation conservation theory. Management regimes that ignore a significant antirescue effect will be inadequate and may actually increase extinction risk. Further, consequences of territoriality and conspecific attraction on metapopulation-level dynamics are investigated. The new, simplified framework can incorporate knowledge from epidemiology, genetics, and population biology in a phenomenological way. It opens up new possibilities to identify and analyze the factors that are important for the evolution and persistence of the many spatially subdivided species.     

Cyanobacteria dynamics in a restored Finnish lake: a long term simulation study

Several explanations have been presented for the formation of lacustrine cyanobacteria blooms. These include elevated water temperature, nutrient enrichment, low N/P ratios, low light energy requirements, high pH and/or low carbon dioxide concentration, selective zooplankton grazing, excretion of compounds which suppress the growth of competing algae, and migration. The impact of the first four were studied in Lake Tuusulanjärvi, a eutrophic Finnish lake, using deterministic simulation. The study, which covered 15 years, included a sequence of cases on the recovery of the lake after the implementation of two restoration measures: aeration of the hypolimnion, and termination of municipal waste discharge, both of which were done during the study period. The focus was on Microcystis and Oscillatoria, and on the N-fixing cyanobacteria, Anabaena and Aphanizomenon. Eukaryotic phytoplankton were also included in the study. Monitoring data were used. The roles of the hypotheses were discussed, from the point of view of the utility of the information in water resources management.     

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.     

A pilot study of lake Ma'rib,Yemen

We provide information on the location, capacity, climate, land tenure and use, vegetation, conservation, economic, and social value of a large artificial lake in Yemen. We also list the extant freshwater macrofauna of Ma'rib lake, which comprises leeches, crustaceans, insects, molluscs, fishes, amphibians and birds.     

Long-term dynamics in a metapopulation of the American pika

A 20-yr study of a metapopulation of the American pika revealed a regional decline in occupancy in one part of a large network of habitat patches. We analyze the possible causes of this decline using a spatially realistic metapopulation model, the incidence function model. The pika metapopulation is the best-known mammalian example of a classical metapopulation with significant population turnover, and it satisfies closely the assumptions of the incidence function model, which was parameterized with data on patch occupancy. The model-predicted incidences of patch occupancy are consistent with observed incidences, and the model predicts well the observed turnover rate between four metapopulation censuses. According to model predictions, the part of the metapopulation where the decline has been observed is relatively unstable and prone to large oscillations in patch occupancy, whereas the other part of the metapopulation is predicted to be persistent. These results demonstrate how extinction-colonization dynamics may produce spatially correlated patterns of patch occupancy without any spatially correlated processes in local dynamics or extinction rate. The unstable part of the metapopulation gives an empirical example of multiple quasi equilibria in metapopulation dynamics. Phenomena similar to those observed here may cause fluctuations in species' range limits.     

Modelling epiphyte metapopulation dynamics in a dynamic forest landscape

We combine simulations with spatial statistics to estimate the parameters of a metapopulation model for the epiphytic lichen Lobaria pulmonaria specializing on aspen ( Populus tremula ) and goat willow ( Salix caprea ) in Fennoscandian boreal old-growth forests. We estimated the parameters of a forest landscape model (FIN-LANDIS) by repeatedly running simulations and selecting the set of parameters for tree ecology and fire regime that reproduced empirical host tree density and spatial patterns. Second, we tested which variables were important in epiphyte colonization and estimated the dispersal kernel. Third, we run a metapopulation model for the lichen across the estimated landscape scenarios and selected values for the remaining parameters that reproduced the empirical patterns of epiphyte occurrence. There was little variation in predicted dynamics, occupancy and spatial patterns between replicate metapopulation simulations. However, more data would be required for accurately estimating the parameters of FIN-LANDIS primarily because of the inherent stochasticity in large scale forest fires. Following the beginning of fire suppression in the study area 150 years ago, the model predicts that lichen occupancy first increases but subsequently declines. The lower occupancy in the past than at present is explained by high rate of tree destruction by fires, which increases local extinction rate in patch-tracking metapopulations. In the absence of fires, the occupancy increases because of lower extinction rate, but without forest fires or alternative means of host tree regeneration, the lichen is predicted to go ultimately extinct because of severely reduced density of aspen and goat willow.     

Population dynamics of epiphytic orchids in a metapopulation context

Background and Aims

Populations of many epiphytes show a patchy distribution where clusters of plants growing on individual trees are spatially separated and may thus function as metapopulations. Seed dispersal is necessary to (re)colonize unoccupied habitats, and to transfer seeds from high- to low-competition patches. Increasing dispersal distances, however, reduces local fecundity and the probability that seeds will find a safe site outside the original patch. Thus, there is a conflict between seed survival and colonization.

Methods

Populations of three epiphytic orchids were monitored over three years in a Mexican humid montane forest and analysed with spatially averaged and with spatially explicit matrix metapopulation models. In the latter, population dynamics at the scale of the subpopulations (epiphytes on individual host trees) are based on detailed stage-structured observations of transition probabilities and trees are connected by a dispersal function.

Key Results

Population growth rates differed among trees and years. While ignoring these differences, and averaging the population matrices over trees, yields negative population growth, metapopulation models predict stable or growing populations because the trees that support growing subpopulations determine the growth of the metapopulation. Stochastic models which account for the differences among years differed only marginally from deterministic models. Population growth rates were significantly lower, and extinctions of local patches more frequent in models where higher dispersal results in reduced local fecundity compared with hypothetical models where this is not the case. The difference between the two models increased with increasing mean dispersal distance. Though recolonization events increased with dispersal distance, this could not compensate the losses due to reduced local fecundity.

Conclusions

For epiphytes, metapopulation models are useful to capture processes beyond the level of the single host tree, but local processes are equally important to understand epiphyte population dynamics.     

From individual behavior to metapopulation dynamics: unifying the patchy population and classic metapopulation models

Spatially structured populations in patchy habitats show much variation in migration rate, from patchy populations in which individuals move repeatedly among habitat patches to classic metapopulations with infrequent migration among discrete populations. To establish a common framework for population dynamics in patchy habitats, we describe an individual-based model (IBM) involving a diffusion approximation of correlated random walk of individual movements. As an example, we apply the model to the Glanville fritillary butterfly (Melitaea cinxia) inhabiting a highly fragmented landscape. We derive stochastic patch occupancy model (SPOM) approximations for the IBMs assuming pure demographic stochasticity, uncorrelated environmental stochasticity, or completely correlated environmental stochasticity in local dynamics. Using realistic parameter values for the Glanville fritillary, we show that the SPOMs mimic the behavior of the IBMs well. The SPOMs derived from IBMs have parameters that relate directly to the life history and behavior of individuals, which is an advantage for model interpretation and parameter estimation. The modeling approach that we describe here provides a unified framework for patchy populations with much movements among habitat patches and classic metapopulations with infrequent movements.     

Single-species metapopulation dynamics: concepts, models and observations

This paper outlines a conceptual and theoretical framework for single-species metapopulation dynamics based on the Levins model and its variants. The significance of the following factors to metapopulation dynamics are explored: evolutionary changes in colonization ability; habitat patch size and isolation; compensatory effects between colonization and extinction rates; the effect of immigration on local dynamics (the rescue effect); and heterogeneity among habitat patches. The rescue effect may lead to alternative stable equilibria in metapopulation dynamics. Heterogeneity among habitat patches may give rise to a bimodal equilibrium distribution of the fraction of patches occupied in an assemblage of species (the core-satellite distribution). A new model of incidence functions is described, which allows one to estimate species' colonization and extinction rates on islands colonized from mainland. Four distinct kinds of stochasticity affecting metapopulation dynamics are discussed with examples. The concluding section describes four possible scenarios of metapopulation extinction.     

Evolutionary dynamics of prey exploitation in a metapopulation of predators

In well-mixed populations of predators and prey, natural selection favors predators with high rates of prey consumption and population growth. When spatial structure prevents the populations from being well mixed, such predators may have a selective disadvantage because they do not make full use of the prey's growth capacity and hence produce fewer propagules. The best strategy then depends on the degree to which predators can monopolize the exploitation of local prey populations, which in turn depends on the spatial structure, the number of migrants, and, in particular, the stochastic nature of the colonization process. To analyze the evolutionary dynamics of predators in a spatially structured predator-prey system, we performed simulations with a metapopulation model that has explicit local dynamics of nonpersistent populations, keeps track of the number of emigrants entering the migration pool, assumes individuals within local populations as well as within the migration pool to be well mixed, and takes stochastic colonization into account. We investigated which of the predator's exploitation strategies are evolutionarily stable and whether these strategies minimize the overall density of prey, as is the case in Lotka-Volterra-type models of competitive exclusion. This was analyzed by pairwise invasibility plots based on short-term simulations and tested by long-term simulation experiments of competition between resident and mutant predator-types that differed in one of the following parameters: the prey-to-predator conversion efficiency, the per capita prey consumption rate, or the per capita emigration rate from local populations. In addition, we asked which of these three strategies are most likely to evolve. Our simulations showed that under selection for conversion efficiency the predator-prey system always goes globally extinct yet persists under selection for consumption or emigration rates and that the evolutionarily stable (ES) exploitation strategies do not maximize local population growth rates. The most successful exploitation strategy minimizes the overall density of prey but does not make it settle exactly at the minimum. The system did not settle at the point where the mean time to co-invasion (i.e., immigration of a second predator in a local prey population) equals the mean local interaction time (an idea borne out from studies on host exploitation strategies in host-pathogen systems) but rather where the mean time to co-invasion was larger. The ES exploitation strategies represent more prudent strategies than the ones that minimize prey density. Finally, we show that-compared to consumption-emigration is a more likely target for selection to achieve prudent exploitation and that prudent exploitation strategies can evolve only provided the prey-to-predator conversion efficiency is subject to constraints.     

Microbial activity and phosphorus dynamics in eutrophic lake sediments enriched with Microcystis colonies

1. Sediments from hypereutrophic Lake Vallentunasjön were enriched with Microcystis colonies from the lake water, thereby simulating the conditions after the autumn sedimentation. Release of phosphorus to the overlying lake water was followed during 2–3 weeks in the laboratory. X-ray microanalysis of individual Microcystis and bacterial cells, and chemical phosphorus fractionation, were used to assess the phosphorus pool size in different fractions of the sediment. 2. Benthic Microcystis colonies, most of these having survived within the sediment for 1 year or more, were less susceptible to decomposition, and the specific growth rate of bacteria in their mucilage was lower than for other sediment bacteria. 3. Pelagic Microcystis colonies from late August were resistant to decomposition, when placed on the sediments. When Microcystis colonies from a declining pelagic population in October were added to the sediments, however, a substantial fraction of these colonies was decomposed. The specific growth rate of mucilage bacteria was five times higher than for other sediment bacteria. 4. Release of molybdate-reactive phosphorus to the overlying lake water was larger from sediment cores enriched with Microcystis colonies than from control cores. Chemical phosphorus fractionation showed a decrease in organic-bound phosphorus (residual P). 5. X-ray microanalysis showed that the phosphorus bound in Microcystis cells decreased by -0.300 mg g^?1 DW in the October experiment, due both to a decrease in biomass (i.e. mineralization) and to a decrease in phosphorus content in the remaining cells. Heterotrophic bacteria increased their cellular concentration of phosphorus. The net release of phosphorus from the Microcystis and bacterial pools corresponded to 74% of the decrease of organic-bound phosphorus in the chemical phosphorus fractionation, and to 65% of the decrease of total phosphorus in the upper 0–1 cm of the sediment. 6. Benthic bacteria and cyanobacteria may thus contribute significantly to changes in phosphorus content and turnover of the sediment by changes in their biomass, turnover rate and cellular phosphorus content.     

Linking extinction-colonization dynamics to genetic structure in a salamander metapopulation

Theory predicts that founder effects have a primary role in determining metapopulation genetic structure. However, ecological factors that affect extinction-colonization dynamics may also create spatial variation in the strength of genetic drift and migration. We tested the hypothesis that ecological factors underlying extinction-colonization dynamics influenced the genetic structure of a tiger salamander (Ambystoma tigrinum) metapopulation. We used empirical data on metapopulation dynamics to make a priori predictions about the effects of population age and ecological factors on genetic diversity and divergence among 41 populations. Metapopulation dynamics of A. tigrinum depended on wetland area, connectivity and presence of predatory fish. We found that newly colonized populations were more genetically differentiated than established populations, suggesting that founder effects influenced genetic structure. However, ecological drivers of metapopulation dynamics were more important than age in predicting genetic structure. Consistent with demographic predictions from metapopulation theory, genetic diversity and divergence depended on wetland area and connectivity. Divergence was greatest in small, isolated wetlands where genetic diversity was low. Our results show that ecological factors underlying metapopulation dynamics can be key determinants of spatial genetic structure, and that habitat area and isolation may mediate the contributions of drift and migration to divergence and evolution in local populations.     

Endogenic development of sediments in a eutrophic lake

Sedimentation in the Gouet reservoir (France), measured for 2 years at 8 stations, was maximal during summer, when river inputs were minimal. Physical and chemical conditions in the deposits indicate that the endogenous part of sedimentation was about 70% and resulted from significant diatom production. The high sedimentation rate on the bottom was favoured by the funnel morphology of the reservoir, the chronic lack of oxygen in the water column, and the repeated copper sulfate treatment. The former river meanders of the reservoir were the preferential deposit sites.     

Sulphate reduction and sulphur cycling in lake sediments: a review

1. The concentration of sulphate is low in lakes and sulphur cycling has often been neglected in studies of organic matter diagenesis in lake sediments. The cycling of sulphur is, however, both spatially and temporally dynamic and strongly influences many biogeochemical reactions in sediments, such as the binding of phosphorus. This review examines the control of sulphate reduction and sulphur cycling in sediments of lakes with different trophic status. 2. The factors that control the rate of sulphate reduction have not been identified with certainty in the various environments because many factors are involved, e.g. oxygen and sulphate concentrations, temperature and organic matter availability. 3. Sulphate reduction is less significant under oligotrophic conditions, where mineralization is dominated by oxic decomposition. The supply of organic matter may not be sufficient to support sulphate reduction in the anoxic parts of sediments and, also, sulphate availability may control the rate as the concentration is generally low in oligotrophic lakes. 4. There is a potential for significant sulphate reduction in eutrophic lakes, as both the availability of organic matter and sulphate concentration are often higher than in oligotrophic lakes. Sulphate is rapidly depleted with sediment depth, however, and methanogenesis is generally the most important process in overall carbon mineralization. Sulphate reduction is generally low in acidic lakes because of low sulphate availability and reduced microbial activity. 5. It is still unclear which of the forms of sulphur deposits are the most important and under which conditions burial occurs. Sulphur deposition is controlled by the rate of sulphate reduction and reoxidation. Reoxidation of sulphides occurs rapidly through several pathways, both under oxic and anoxic conditions. Only a few studies have been able to examine the importance of reoxidation, but it is hypothesized that most of the reoxidation takes place under anoxic conditions and that disproportionation is often involved. The presence of sulphide oxidizing bacteria, benthic fauna and rooted macrophytes may substantially enhance oxic reoxidation. Deposition of sulphur is generally higher in eutrophic than in oligotrophic lakes because of a number of factors: a higher rate of sulphate reduction, enhanced sedimentation of organic sulphur and less reoxidation as a result of reduced penetration of oxygen into the sediments, a lack of faunal activity and rooted macrophytes.     

Exact asymptotic analysis for metapopulation dynamics on correlated dynamic landscapes

We compute the mean patch occupancy for a stochastic, spatially explicit patch-occupancy metapopulation model on a dynamic, correlated landscape, using a mathematically exact perturbation expansion about a mean-field limit that applies when dispersal range is large. Stochasticity in the metapopulation and landscape dynamics gives negative contributions to patch occupancy, the former being more important at high occupancy and the latter at low occupancy. Positive landscape correlations always benefit the metapopulation, but are only significant when the correlation length is comparable to, or smaller than, the dispersal range. Our analytical results allow us to consider the importance of spatial kernels in all generality. We find that the shape of the landscape correlation function is typically unimportant, and that the variance is overwhelmingly the most important property of the colonisation kernel. However, short-range singularities in either the colonisation kernel or landscape correlations can give rise to qualitatively different behaviour.     

Spatial dynamics of two competing specialist parasitoids in a host metapopulation

1. We investigated spatial dynamics in two specialist larval parasitoids, Cotesia melitaearum and Hyposoter horticola , attacking the Glanville fritillary butterfly, Melitaea cinxia , in Finland.
2. Presence of C. melitaearum in a host larval group significantly reduced the rate of parasitism by H. horticola (18 vs. 33% in groups with and without C. melitaearum ), but there was no significant reverse effect. The parasitism rates at the level of local populations showed a similar trend.
3 Hyposoter horticola females moved frequently among larval groups, whereas C. melitaearum females often spent several days at a single larval group. In agreement with these behavioural observations about movements within populations, H. horticola was found to have a higher colonization rate of host populations than C. melitaearum .
4. At the within-population level, C. melitaearum tended to occupy large larval groups in the centre of the host population, whereas H. horticola parasitized also small and more isolated (peripheral) larval groups, especially in the presence of C. melitaearum . At the metapopulation level, host population size had a significant positive effect on the presence of local populations of both parasitoid species, but isolation had a significant negative effect on the presence of C. melitaearum only.
5. These results suggest that C. melitaearum is a superior competitor, but an inferior disperser to H. horticola , which facilitates the co-existence of the two species both at the level of local populations and at the level of a metapopulation.
6. Data from a 50-patch network showed a decline in the number of host populations from 34 to 13 in 4 years. This decline caused a near-extinction of the superior competitor, but inferior disperser, C. melitaearum , whereas the abundance of the inferior competitor, but superior disperser, H. horticola , remained relatively constant, in agreement with the prediction of a theoretical model.     

Extinction dynamics and the regional persistence of a tree frog metapopulation

The concept of a metapopulation acknowledges local extinctions as a natural part of the dynamics of a patchily distributed population. However, if extinctions are not balanced by recolonizations or if there is a high degree of spatial synchrony of local extinctions, this poses a threat to and will reduce the metapopulation persistence time. Here we show that, in a metapopulation network of 378 pond patches used by the tree frog (Hyla arborea), even though extinctions are frequent (mean extinction probability p(e) = 0.24) they pose no threat to the metapopulation as they are balanced by recolonizations (p(c) = 0.33). In any one year there was a pattern of large populations tending to persist while small populations became extinct. The total number of individuals belonging to populations that went extinct was small (< 5%) compared with those populations that persisted. A spatial autocorrelation analysis indicated no clustering of local extinctions. The tree frog metapopulation studied consisted of a set of larger, persistent populations mixed with smaller populations characterized by high turnover dynamics.     

Population dynamics in a Danish metapopulation of spadefoot toads Pelobates fuscus

If an amphibian species has a high degree of site fidelity to its natal pond, subpopulations do not mix, and this may have implications: the subpopulations may get different because of genetic drift, and their status may be affected due to stochastic events. During a four-year period (1994–1997), demographic parameters of a Danish metapopulation consisting of ca 1000 adult Pelobates fuscus in five subpopulations were investigated with the aim of quantifying exchange of individuals in subpopulations and potential differences in demographic parameters, and to clarify population regulating mechanisms. This was done through the use of drift fences surrounding the five breeding ponds, individual marking (PIT-tagging) and weight recordings of the adult females. Metamorphs were recorded when leaving the pond. There was no significant differences between ponds in sex ratio, eggs laid per female, fraction of females breeding and survival of eggs to froglets and of adults. However, there was a significant difference in juvenile survival (52% in one pond and 31% in the others). Sex ratio was 1.70 males:1 female. Mean number of eggs laid per female in the pond was 1762. The number of eggs laid was age-specific, fecundity peaking at age five. Larval survival rate was density dependent: decreasing in an overcompensating fashion at high densities. Exchange rate between ponds was low; 1.09% of the marked and recaptured adult population was found to change pond during the study period. The low exchange rate was confirmed in a simple translocation experiment. This population shows features of a source-sink metapopulation where the identity of the source pond changes due to succession. It is presumably regulated either in the larval stage by density dependent mechanisms (in the subpopulations with many adults) or in the adult stage by density independent mechanisms (in the subpopulations with few adults).     

Finding copepod footprints: a protocol for molecular identification of diapausing eggs in lake sediments

Even though calanoid copepods produce diapausing eggs that stay alive in lake sediments, these eggs have rarely been used paleolimnologically, as they lack diagnostic morphological features. In this study, we developed a method to identify copepod diapausing eggs in Japan as a clue toward reconstructing past plankton populations. We first determined a 28S ribosomal DNA (rDNA) (i.e., nc28S) regional sequence library (240 bp) of various calanoid copepod species using ethanol-fixed plankton samples collected from across the Japanese archipelago. Then we applied the UltraSHOT method to extract DNA from an individual diapausing egg. Finally, the nc28S region of diapausing eggs collected from various lakes was sequenced and compared with the regional library for species identification. In total, 21 haplotypes of the nc28S region were recovered from planktonic samples of 11 Japanese freshwater calanoid copepod species. Despite the short length of this region, no identical haplotypes were shared among the species analyzed, including the Acanthodiaptomus pacificus complex treated as a species. Even different lineages of A. pacificus could be separated. These results indicate that the nc28S region can be used as a barcode in Japan. A total of 112 diapausing eggs collected from various lakes and ponds was processed, and the nc28S region of each was successfully sequenced. All of these egg sequences matched one or the other of the nc28S haplotypes in the regional library mentioned above. The set of protocols we applied (i.e., preparing a comprehensive regional sequence library and sequencing egg DNA) is thus useful for involving copepod diapausing eggs in paleolimnological studies in lakes. The nc28S region treated in this study has a strong potential to uncover the paleodiversity of copepods, at least in Japan.