Scale-free extinction dynamics in spatially structured host-parasitoid systems

Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.     

Approach to equilibrium in age structured populations with an increasing recruitment process

This paper considers a model for the dynamics of an age structured population subject to a density dependent factor which regulates the recruitment. Certain properties of biological interest are obtained and the stability of the equilibrium age distributions is investigated. Finally some applications to known fishery models are considered.Work done under the contract 80.02333.01 of C.N.R.     

Evolution of condition-dependent dispersal under kin competition

Dispersers often differ in body condition from non-dispersers. The social dominance hypothesis explains dispersal of weak individuals, but it is not yet well understood why strong individuals, which could easily retain their natal site, are sometimes exposed to risky dispersal. Based on the model for dispersal under kin competition by Hamilton and May, we construct a model where dispersal propensity depends on body condition. We consider an annual species that inhabits a patchy environment with varying patch qualities. Offspring body condition corresponds to the quality of the natal patch and competitive ability increases with body condition. Our main general result balances the fitness benefit from not dispersing and retaining the natal patch and the benefit from dispersing and establishing somewhere else. We present four different examples for competition, which all hint that dispersal of strong individuals may be a common outcome under the assumptions of the present model. In three of the examples, the evolutionarily stable dispersal probability is an increasing function of body condition. However, we found an example where, counterintuitively, the evolutionarily stable dispersal probability is a non-monotone function of body condition such that both very weak and very strong individuals disperse with high probability but individuals of intermediate body condition do not disperse at all.     

Distribution and coexistence of shrews in patchy landscapes: A field test of multiple hypotheses

Despite the important role of shrews (Soricomorpha: Soricidae) in the functioning of ecosystems, as predators and prey, the effects of habitat loss and fragmentation on this guild of mammals are still unclear. We studied the distribution of 5 species (the greater white toothed shrew Crocidura leucodon; the lesser white toothed shrew Crocidura suaveolens; the pigmy shrew Sorex minutus; the Appennine shrew Sorex samniticus and the Etruscan shrew Suncus etruscus) in a fragmented landscape in central Italy.Shrews were trapped with pitfall traps made from plastic water bottles, the number of traps increased with patch size. A total of 170 individuals, of 5 species of shrews were captured. Shrews were widely distributed in our study area, however patch occupancy was determined mainly by vegetation and geometrical characteristics of the patches. Our data supports the hypotheses that patterns of habitat selection and the dynamics of seasonal abundance (habitat and temporal partitioning between similarly sized species) reduce competitive pressure, thus allowing coexistence of shrews in relatively species-rich assemblages, for such small amounts of habitat. The most important outcome of our results is the crucial role played by vegetation structure in determining distribution patterns. These results strongly suggest that measurements of the vegetation structure of habitat patches should always be included as explanatory variables when studying the distribution of shrews in fragmented landscapes.     

The Role of Complex Formation and Deleterious Mutations for the Stability of RNA-Like Replicator Systems

In the RNA world hypothesis, RNA(-like) self-replicators are suggested as the central player of prebiotic evolution. However, there is a serious problem in the evolution of complexity in such replicators, i.e., the problem of parasites. Parasites, which are replicated by catalytic replicators (catalysts), but do not replicate the others, can destroy a whole replicator system by exploitation. Recently, a theoretical study underlined complex formation between replicators--an often neglected but realistic process--as a stabilizing factor in a replicator system by demonstrating that complex formation can shift the viable range of diffusion intensity to higher values. In the current study, we extend the previous study of complex formation. Firstly, by investigating a well-mixed replicator system, we establish that complex formation gives parasites an implicit advantage over catalysts, which makes the system significantly more vulnerable to parasites. Secondly, by investigating a spatially extended replicator system, we show that the formation of traveling wave patterns plays a crucial role in the stability of the system against parasites, and that because of this the effect of complex formation is not straightforward; i.e., whether complex formation stabilizes or destabilizes the spatial system is a complex function of other parameters. We give a detailed analysis of the spatial system by considering the pattern dynamics of waves. Furthermore, we investigate the effect of deleterious mutations. Surprisingly, high mutation rates can weaken the exploitation of the catalyst by the parasite.     

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.     

A model for the length of tracts of identity by descent in finite random mating populations

Linkage disequilibrium (LD) reflects coinheritance of an ancestral segment by chromosomes in a population. To begin to understand the effects of population history on the extent of LD, we model the length of a tract of identity-by-descent (IBD) between two chromosomes in a finite, random mating population. The variance of an IBD tract is large: a model described by (Genet. Res. Cambridge 35 (1980) 131) underestimates this variance. Using Fisher's concept of junctions, we predict the mean length of an IBD tract, given the age of the population and the population sizes over time. We derive results also for subdivided populations, given times of subdivision events and sizes of the resulting subpopulations. The model demonstrates that population growth and subdivision strongly affect the expected length of an IBD tract in small populations. These effects are less dramatic in large populations.     

The importance of dispersal in determining seed versus safe site limitation of plant populations

The traditional dichotomy of seed versus safe site limitation of plant populations is an oversimplification. While most plant models implicitly assume that the number of safe sites colonized will increase directly with increased seed production by each plant, the number of sites colonized may also strongly depend on patterns of seed dispersal relative to the parent plant, since the majority of a plant’s seeds are deposited very close to it and so not all safe sites are equally accessible. I created a series of spatially explicit individual based plant population models exploring how seed versus safe site limitation is jointly affected by the number of seeds produced per plant and mean dispersal distances. While increased dispersal distance led to reduced seed limitation (more saturation of available safe sites) when a parent plant’s site was temporarily unsuitable following its death, increased dispersal distances could increase seed limitation, especially at low per-plant fecundities, if safe sites did not turn over through time. Models comparing localized to global seed dispersal indicated substantially different degrees of seed limitation for constant per-plant fecundities. Thus seed addition experiments need to be designed to add seeds in realistic spatial patterns to yield meaningful results.     

Mathematical models of microbial growth and competition in the chemostat regulated by cell-bound extracellular enzymes

A mathematical model of growth and competitive interaction of microorganisms in the chemostat is analyzed. The growth-limiting nutrient is not in a form that can be directly assimilated by the microorganisms, and must first be transformed into an intermediate product by cell-bound extracellular enzymes. General monotone functions, including Michaelis-Menten and sigmoidal response functions, are used to describe nutrient conversion and growth due to consumption of the intermediate product. It is shown that the initial concentration of the species is an important determining factor for survival or washout. When there are two species whose growth is limited by the same nutrient, three different modes of competition are described. Competitive coexistence steady states are shown to be possible in two of them, but they are always unstable. In all of our numerical simulations, the system approaches a steady state corresponding to the washout of one or both of the species from the chemostat.Research supported by NSF grant DMS-90-96279Research supported by NSERC grant A-9358     

Equilibria in systems of interacting structured populations

The existence of a stable positive equilibrium density for a community of k interacting structured species is studied as a bifurcation problem. Under the assumption that a subcommunity of k–1 species has a positive equilibrium and under only very mild restrictions on the density dependent vital growth rates, it is shown that a global continuum of equilibria for the full community bifurcates from the subcommunity equilibrium at a unique critical value of a certain inherent birth modulus for the kth species. Local stability is shown to depend upon the direction of bifurcation. The direction of bifurcation is studied in more detail for the case when vital per unity birth and death rates depend on population density through positive linear functionals of density and for the important case of two interacting species. Some examples involving competition, predation and epidemics are given.     

Spatial dynamics of Microtus vole populations in continuous and fragmented agricultural landscapes

Small mammal populations often exhibit large-scale spatial synchrony, which is purportedly caused by stochastic weather-related environmental perturbations, predation or dispersal. To elucidate the relative synchronizing effects of environmental perturbations from those of dispersal movements of small mammalian prey or their predators, we investigated the spatial dynamics of Microtus vole populations in two differently structured landscapes which experience similar patterns of weather and climatic conditions. Vole and predator abundances were monitored for three years on 28 agricultural field sites arranged into two 120-km-long transect lines in western Finland. Sites on one transect were interconnected by continuous agricultural farmland (continuous landscape), while sites on the other were isolated from one another to a varying degree by mainly forests (fragmented landscape). Vole populations exhibited large-scale (>120 km) spatial synchrony in fluctuations, which did not differ in degree between the landscapes or decline with increasing distance between trapping sites. However, spatial variation in vole population growth rates was higher in the fragmented than in the continuous landscape. Although vole-eating predators were more numerous in the continuous agricultural landscape than in the fragmented, our results suggest that predators do not exert a great influence on the degree of spatial synchrony of vole population fluctuations, but they may contribute to bringing out-of-phase prey patches towards a regional density level. The spatial dynamics of vole populations were similar in both fragmented and continuous landscapes despite inter-landscape differences in both predator abundance and possibilities of vole dispersal. This implies that the primary source of synchronization lies in a common weather-related environment.     

Spatial dynamics of colony interactions in young populations of the fire ant Solenopsis invicta

Newly founded colonies of the fire ant Solenopsis invicta compete intensely by brood raids, which result in a rapid reduction of colony density. Experimental plantings of colonies and analyses of sequential maps were used to examine the importance of spatial pattern in the dynamics of young populations. Colony positions were initially clumped in naturally founded cohorts, but were regular in most mature populations. Incipient colonies planted in clumped patterns were more likely to engage in brood raids than colonies planted in regular hexagonal patterns at the same average density. However, contrary to what would be expected if local crowding increased mortality, no significant increases in spatial regularity were observed during brood raiding either in the experimentally planted populations or in a natural population of more than 1200 incipient colonies. These results show that it may be difficult to infer the degree of past or current competition by passive analysis of spatial data even when field experiments show that the probability of mortality depends on local spacing.     

The role of predation and competition in determining the distribution of common bream,roach and white bream in Dutch eutrophic lakes

Synopsis Most of the lakes in The Netherlands are turbid and without vegetation. This is regarded as the result of increasing eutrophication within the last decades. Under these conditions common bream, roach, and white bream are the most common cyprinids. In six shallow (1–3 m), wind exposed lakes the abundance of common bream and roach was linked to the abundance of pikeperch; bream dominated when pikeperch was abundant, but when the latter species was rare, roach was dominant and the biomass of bream was reduced. The biomass of white bream was always relatively low. In lake Tjeukemeer the distribution of roach < 20 cm fork length (FL) and bream was also related to the distribution of pikeperch. Only roach > 20 cm FL managed to coexist with pikeperch in the open water area, whereas roach < 20 cm was confined to the littoral zone where pikeperch was nearly absent. Bream occurred mainly in the open water and avoided the littoral zone where it competed with roach. White bream occupied an intermediate position, occurring in relatively low density both in the littoral zone and in open water. The importance of predation and competition in determining the distribution and abundance of roach and common bream in the eutrophic lakes of The Netherlands is discussed.     

Tiller demography in seashore populations of Agrostis stolonifera,Festuca rubra and Poa irrigata

Abstract. The dynamics of tillers in natural populations of three cohabiting perennial grass species, Agrostis stolonifera, Festuca rubra and Poa irrigata (= Poa pratensis ssp. irrigata) were studied for five years in a Baltic seashore meadow. The process of tiller population maintenance was very dynamic. Both birth and death rates of tillers were high, particularly in A stolonifera, and the turnover rate of the populations was high. Recruitment was mainly by vegetative tillers, produced continuously throughout the growing season. The proportion of flowering tillers was low, but varied between years. Considerable year-to-year variation was also found in birth and death rates. Despite this between-year variation and the differences found between species in flowering frequency, pattern of survivorship and tiller longevity, population sizes of the species remained relatively constant.     

Habitat features and genetic integrity of wild grapevine Vitis vinifera L. subsp. sylvestris (C.C. Gmel.) Hegi populations: A case study from Sicily

Wild grapevine represents a valuable genetic resource for both future breeding programmes of cultivated grape and conservation of biological diversity in natural environments. In Sicily, the knowledge of this species is quite scarce and fragmentary. Therefore, in order to assess the presence and the genetic quality of wild grapevine in the island, eight populations from different locations were investigated. Their habitats were characterized and the genetic diversity was measured by microsatellite markers in order to evaluate possible relationships between genetic features and the ecological behaviour of populations.With the exception of one population found in a scree-type habitat, all the others were present in flooded areas. Grapevine populations growing in riparian habitats were characterized by low inter- and intra-population variability. Conversely, the scree-type population proved to be the most compact and distinctive, as well as the most genetically isolated. Interestingly, together with other two populations from the northern mountain range of the island, this scree-type grapevine population was genetically rather distant from local domestic accessions, suggesting a weak gene exchange with the cultivated grapevines in Sicily. On the contrary, the other populations showed evidences of probable introgression events, as a result of either gene flow between domestic and wild plants, or of possible secondary domestication/genetic improving processes, based on the use of native wild material.     

Variation in predation pressure as a mechanism underlying differences in numerical abundance between populations of the poeciliid fish Heterandria formosa

We explored whether a variation in predation and habitat complexity between conspecific populations can drive qualitatively different numerical dynamics in those populations. We considered two disjunct populations of the least killifish, Heterandria formosa, that exhibit long-term differences in density, top fish predator species, and dominant aquatic vegetation. Monthly censuses over a 3-year period found that in the higher density population, changes in H. formosa density exhibited a strong negative autocorrelation structure: increases (decreases) at one census tended to be followed by decreases (increases) at the next one. However, no such correlation was present in the lower density population. Monthly census data also revealed that predators, especially Lepomis sp., were considerably more abundant at the site with lower H. formosa densities. Experimental studies showed that the predation by Lepomis gulosus occurred at a much higher rate than predation by two other fish and two dragonfly species, although L. gulosus and L. punctatus had similar predation rates when the amount of vegetative cover was high. The most effective predator, L. gulosus, did not discriminate among life stages (males, females, and juveniles) of H. formosa. Increased predation rates by L. gulosus could keep H. formosa low in one population, thereby eliminating strong negative density-dependent regulation. In support of this, changes in H. formosa density were positively correlated with changes in vegetative cover for the population with a history of lower density, but not for the population with a history of higher density. Our results are consistent with the hypothesis that the observed differences among natural populations in numerical abundance and dynamics are caused in part by the differences in habitat complexity and the predator community.     

Style morph frequencies in Minnesota populations of Lythrum (Lythraceae)

Style morph frequencies (shortmidlong) were determined for a total of n = 11 918 plants in 16 Minnesota populations of Lythrum salicaria L. Nine populations were in the establishment phase, with population sizes ranging from n = 56 to n = 2 192. Most of these populations exceeded previously reported population sizes in the native European habitat. A nonparametric statistical test, the chi-square (²), can be used to determine if populations are at isoplethic equilibrium (111, shortmidlong); a ² value >5.99 is significant at the 5% level. Only one established population (White Bear Lake, n = 1991, ² = 3.0) fitted the null hypothesis for isoplethy, although all established populations contained all three style morphs. Pooled values for these populations indicated an excess of mids and longs, with shorts being deficient. Colonizing populations had a higher percentage of mids (54%) when compared to established populations (33.7%). Short styles were almost nonexistent (8%) in colonizing populations. Five out of the seven populations lacked at least one style morph. A review of the literature reporting style morph frequencies in tristylous L. salicaria revealed that no statistical analysis for isoplethy has been performed. Darwin originally assumed that all populations would be isoplethic, possessing equal numbers of all three style morphs, but concluded, without statistical analysis, that, instead, populations were anisoplethic. Since tests for statistical deviations from the expected frequencies (111) have not been used, ² analysis was performed. Several of these populations were at isoplethic equilibrium (Nadder su2 = 1.7, Blelham ² = 1.69, Potsdam ² = 1.5, Vestfold ² = 0.4, Buskerud ² = 5.62, Kilchberg ² = 0.35, Lausanne ² = 3.32, Canberra ² = 5.29, Massachusetts ² = 3.13), suggesting that the general conclusion of anisoplethy in tristylous L. salicaria is inappropriate.This is Scientific Journal Series Paper Number 19 128 of the Minnesota Agricultural Experiment Station     

Dynamics of infection with multiple transmission mechanisms in unmanaged/managed animal populations

Deterministic and stochastic models motivated by Salmonella transmission in unmanaged/managed populations are studied. The SIRS models incorporate three routes of transmission (direct, vertical and indirect via free-living infectious units in the environment). With deterministic models we are able to understand the effects of different routes of transmission and other epidemiological factors on infection dynamics. In particular, vertical transmission has little influence on this dynamics, whereas the higher the indirect (direct) transmission rate the greater the tendency to persistent oscillation (stable endemic states). We show that the sustained cycles are also prone to demographic effect, i.e., persistent oscillation becomes impossible in the managed case (in the sense of balanced recruitment and death rates) by comparing with results in unmanaged populations (exponential population dynamics). Further, approximations of quasi-stationary distributions are derived for stochastic versions of the proposed models based on a diffusion approximation to the infection process. The effect of transmission parameters on the ratio of mean to standard deviation of the approximating distribution, used to judge the validity of the approximations and the expected time until fade out of infection, is further discussed. We conclude that strengthening any route of transmission may or may not reduce the expected time to fade out of infection, depending on the population dynamics.