Phase switching in population cycles

Oscillatory populations may exhibit a phase change in which, for example, a high–low periodic pattern switches to a low–high pattern. We propose that phase shifts correspond to stochastic jumps between basins of attraction in an appropriate phase space which associates the different phases of a periodic cycle with distinct attractors. This mechanism accounts for two-cycle phase shifts and the occurrence of asynchronous replicates in experimental cultures of Tribolium.     

Resonant population cycles in temporally fluctuating habitats

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. In this paper we derive and analyze a discrete stage-structured mathematical model that explains this phenomenon as a kind of resonance effect. Habitat volume is incorporated into the model by the assumption that all rates of cannibalism (larvae on eggs, adults on eggs and pupae) are inversely proportional to the volume of the culture medium. We tested this modeling assumption by conducting and statistically analyzing laboratory experiments. For parameter estimates derived from experimental data, our model indeed predicts, under certain circumstances, a larger (cycle-average) total population abundance when the habitat volume periodically fluctuates than when the habitat volume is held constant at the average volume. The model also correctly predicts certain phase relationships and transient dynamics observed in data. The analyses involve a thorough integration of mathematics, statistical methods, biological details and experimental data.     

Limit cycles in periodically perturbed population systems

A perturbation method is proposed to calculate approximately the limit cycle type nonequilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicity studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.     

Seasonally limited host supply generates microparasite population cycles

Cycles in biological populations have been shown to arise from enemy-victim systems, delayed density dependence, andmaternal effects. In an initial effort to model the year-to-year dynamics of natural populations of entomopathogenic nematodes and their insect hosts, we find that a simple, nonlinear, mechanistic model produces large amplitude, period two population cycles. The cycles are generated by seasonal dynamics within semi-isolated populations independently of inter-annual feedback in host population numbers, which differs from previously studied mechanisms. The microparasites compete for a fixed number of host insect larvae. Many nematodes at the beginning of the year quickly eliminate the pool of small hosts, and few nematodes are produced for the subsequent year. Conversely, initially small nematode populations do not over-exploit the host population, so the surviving hosts grow to be large and produce many nematodes that survive to the following year.     

The macroecology of population dynamics: taxonomic and biogeographic patterns in population cycles

Regular cycles in population abundance are fascinating phenomena, but are they common in natural populations? How are they distributed among taxa? Are there differences between different regions of the world, or along latitudinal gradients? Using the new Global Population Dynamics Database we analysed nearly 700 long (25 + years) time series of animal field populations, looking for large-scale patterns in cycles. Nearly 30% of the time series were cyclic. Cycle incidence varied among taxonomic classes, being most common in mammal and fish populations, but only in fish did cycle incidence vary among orders. Cycles were equally common in European and North American populations, but were more common in Atlantic fish than Pacific fish. The incidence of cycles increased with latitude in mammals only. There was no latitudinal gradient in cycle period, but cycle amplitude declined with latitude in some groups of fish. Even after considering the biases in the data source and expected type I error, population cycles seem common enough to warrant ecological attention.     

Pathogen interactions, population cycles, and phase shifts

Interspecific pathogen interactions can profoundly affect pathogen population dynamics and the efficacy of control strategies. However, many pathogens exhibit cyclic abundance patterns (e.g., seasonality), and temporal asynchrony between interacting pathogens could reduce the impact of those interactions. Here we use an extension of our previously published model to investigate the effects of cycles on pathogen interaction. We demonstrate that host immune memory can maintain the impact of an interaction, even when the effector pathogen abundance is low or the pathogen is absent. Paradoxically, immune memory can result in pathogens interacting more strongly when temporally out of phase. We find that interactions between species can result in changes to the temporal pattern of the affected species. We further demonstrate that this may be observed in a natural host-pathogen system. Given the continuing debate regarding the relevance of pathogen interactions in natural systems and increasing concern about treatment strategies for coinfections, both the discovery of a shift in cycle in empirical data and the mechanism by which we identified it are important. Finally, because the model structure used here is analogous to models of a simple predator-prey system, we also consider the consequences of these findings in the context of that system.     

Disease effects on reproduction can cause population cycles in seasonal environments

1. Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of different infections. 2. We investigated the consequences for host population dynamics of a disease-induced period of no reproduction, and a chronic reduction in fecundity following recovery from infection (such as may be induced by secondary infections) using a modified SIR (susceptible, infected, recovered) model. We also included a seasonally varying birth rate as recent studies have demonstrated that seasonally varying parameters can have important effects on long-term host-parasite dynamics. We investigated the model predictions using parameters derived from five different cyclic rodent populations. 3. Delayed and reduced fecundity following recovery from infection have no effect on the ability of the disease to regulate the host population in the model as they have no effect on the basic reproductive rate. However, these factors can influence the long-term dynamics including whether or not they exhibit multiyear cycles. 4. The model predicts disease-induced multiyear cycles for a wide range of realistic parameter values. Host populations that recover relatively slowly following a disease-induced population crash are more likely to show multiyear cycles. Diseases for which the period of infection is brief, but full recovery of reproductive function is relatively slow, could generate large amplitude multiyear cycles of several years in length. Chronically reduced fecundity following recovery can also induce multiyear cycles, in support of previous theoretical studies. 5. When parameterized for cowpox virus in the cyclic field vole populations (Microtus agrestis) of Kielder Forest (northern England), the model predicts that the disease must chronically reduce host fecundity by more than 70%, following recovery from infection, for it to induce multiyear cycles. When the model predicts quasi-periodic multiyear cycles it also predicts that seroprevalence and the effective date of onset of the reproductive season are delayed density-dependent, two phenomena that have been recorded in the field.     

Circadian activity patterns,photoperiodic responses and population cycles in voles

Summary Patterns of above-ground activity were recorded in two free-ranging populations of Microtus agrestis (L.) and one population of M. arvalis (Pall.) over several years by means of passage counters. Long-term variations of the circadian patterns were observed, but did not repeat themselves in a 12-month cycle. Variations in all three populations could be described by a sinusoidal function of an 18-month period. Maxima and minima of the sine-function were connected to distinct photoperiods (equinoxes and solstices). In a cyclic North Swedish population, the sine-function was superimposed by a second function which shows saturation behaviour. The relevance of these findings is discussed with respect to vole population cycles.     

Delayed density-dependent season length alone can lead to rodent population cycles

Studies of cyclic microtine populations (voles and lemmings) have suggested a relationship between the previous year's population density and the subsequent timing of the onset of reproduction by overwintered breeding females. No studies have explored the importance of this relationship in the generation of population cycles. Here we mathematically examine the implications of variation in reproductive season length caused by delayed density-dependent changes in its start date. We demonstrate that when reproductive season length is a function of past population densities, it is possible to get realistic population cycles without invoking any changes in birth rates or survival. When parameterized for field voles (Microtus agrestis) in Kielder Forest (northern England), our most realistic model predicts population cycles of similar periodicity to the Kielder populations. Our study highlights the potential importance of density-dependent reproductive timing in microtine population cycles and calls for investigations into the mechanism(s) underlying this phenomenon.     

Patterns of 2-year population cycles in spatially extended host-parasitoid systems.

Coexisting but temporally separated cohorts of insects with a multiannual life cycle may have dissimilar average abundance, resulting in periodically fluctuating population density. In the case of the boreal moth genus Xestia with a 2-year life cycle and a distinct abundance difference between the two coexisting cohorts, empirical results and a simple model suggest that the oscillatory dynamics are maintained by interaction with a parasitoid wasp. Here we report theoretical results on a spatially extended version of the basic model and relate the modeling results to empirical observations. A spatially extended model may have domains oscillating in different phases as is the case between western and eastern Finnish Lapland. Spatial heterogeneity tends to fix the location of phase boundaries. In contrast, spatially homogeneous temporal fluctuations tend to synchronize populations in large regions.     

Competition in size-structured populations: mechanisms inducing cohort formation and population cycles

In this paper we investigate the consequences of size-dependent competition among the individuals of a consumer population by analyzing the dynamic properties of a physiologically structured population model. Only 2 size-classes of individuals are distinguished: juveniles and adults. Juveniles and adults both feed on one and the same resource and hence interact by means of exploitative competition. Juvenile individuals allocate all assimilated energy into development and mature on reaching a fixed developmental threshold. The combination of this fixed threshold and the resource-dependent developmental rate, implies that the juvenile delay between birth and the onset of reproduction may vary in time. Adult individuals allocate all assimilated energy to reproduction. Mortality of both juveniles and adults is assumed to be inversely proportional to the amount of energy assimilated. In this setting we study how the dynamics of the population are influenced by the relative foraging capabilities of juveniles and adults.In line with results that we previously obtained in size-structured consumer-resource models with pulsed reproduction, population cycles primarily occur when either juveniles or adults have a distinct competitive advantage. When adults have a larger per capita feeding rate and are hence competitively superior to juveniles, population oscillations occur that are primarily induced by the fact that the duration of the juvenile period changes with changing food conditions. These cycles do not occur when the juvenile delay is a fixed parameter. When juveniles are competitively superior, two different types of population fluctuations can occur: (1) rapid, low-amplitude fluctuations having a period of half the juvenile delay and (2) slow, large-amplitude fluctuations characterized by a period, which is roughly equal to the juvenile delay. The analysis of simplified versions of the structured model indicates that these two types of oscillations also occur if mortality and/or development is independent of food density, i.e. in a situation with a constant juvenile developmental delay and a constant, food-independent background mortality. Thus, the oscillations that occur when juveniles are more competitive are induced by the juvenile delay per se. When juveniles exert a larger foraging pressure on the shared resource, maturation implies an increase not only in adult density, but also in food density and consequently fecundity. Our analysis suggests that this correlation in time between adult density and fecundity is crucial for the occurrence of population cycles when juveniles are competitively superior.     

Experimental tests of predation and food hypotheses for population cycles of voles

Pronounced population cycles are characteristic of many herbivorous small mammals in northern latitudes. Although delayed density-dependent effects of predation and food shortage are often proposed as factors driving population cycles, firm evidence for causality is rare because sufficiently replicated, large-scale field experiments are lacking. We conducted two experiments on Microtus voles in four large predator-proof enclosures and four unfenced control areas in western Finland. Predator exclusion induced rapid population growth and increased the peak abundance of voles over 20-fold until the enclosed populations crashed during the second winter due to food shortage. Thereafter, voles introduced to enclosures which had suffered heavy grazing increased to higher densities than voles in previously ungrazed control areas which were exposed to predators. We concluded that predation inhibits an increase in vole populations until predation pressure declines, thus maintaining the low phase of the cycle, but also that population cycles in voles are not primarily driven by plant-herbivore interactions.     

The effect of delayed host self-regulation on host-pathogen population cycles in forest insects

Delayed host self-regulation using a Beverton-Holt function and delayed logistic self-regulation are included in a host-pathogen model with free-living infective stages (Anderson and May's model G) with the purpose of investigating whether adding the relatively complex self-regulations decrease the likelihood of population cycles. The main results indicate that adding delayed self-regulation to the baseline model increases the likelihood of population cycles. The dynamics display some of the key features seen in the field, such as cycle peak density exceeding the carrying capacity and a locally stable equilibrium coexisting with a stable cycle (bistability). Numerical studies show that the model with more complex forms of self-regulation can generate cycles which match most aspects of the cycles observed in nature.     

Varroa-Virus Interaction in Collapsing Honey Bee Colonies

Varroa mites and viruses are the currently the high-profile suspects in collapsing bee colonies. Therefore, seasonal variation in varroa load and viruses (Acute-Kashmir-Israeli complex (AKI) and Deformed Wing Virus (DWV)) were monitored in a year-long study. We investigated the viral titres in honey bees and varroa mites from 23 colonies (15 apiaries) under three treatment conditions: Organic acids (11 colonies), pyrethroid (9 colonies) and untreated (3 colonies). Approximately 200 bees were sampled every month from April 2011 to October 2011, and April 2012. The 200 bees were split to 10 subsamples of 20 bees and analysed separately, which allows us to determine the prevalence of virus-infected bees. The treatment efficacy was often low for both treatments. In colonies where varroa treatment reduced the mite load, colonies overwintered successfully, allowing the mites and viruses to be carried over with the bees into the next season. In general, AKI and DWV titres did not show any notable response to the treatment and steadily increased over the season from April to October. In the untreated control group, titres increased most dramatically. Viral copies were correlated to number of varroa mites. Most colonies that collapsed over the winter had significantly higher AKI and DWV titres in October compared to survivors. Only treated colonies survived the winter. We discuss our results in relation to the varroa-virus model developed by Stephen Martin.     

Enrichment can damp population cycles: a balance of inflexible and flexible interactions

Destabilization of one predator–one prey systems with an increase in nutrient input has been viewed as a paradox. We report that enrichment can damp population cycles by a food‐web structure that balances inflexible and flexible interaction links (i.e. specialist and generalist predators). We modeled six predator–prey systems involving three or four species in which the predators practice optimal foraging based on prey profitability determined by handling time. In all models, the balance of interaction links simultaneously decreased the amplitude of population oscillations and increased the minimum density with increasing enrichment, leading to a potential theoretical resolution of the paradox of enrichment in non‐equilibrium dynamics. The stabilization mechanism was common to all of the models. Important previous studies on the stability of food webs have also demonstrated that a balance of interaction strengths stabilizes systems, suggesting a general rule of ecosystem stability.     

The effect of snow cover on lemming population cycles in the Canadian High Arctic

Rising temperatures and changes in the precipitation regime will have a strong impact on the quality of the snow cover in the Arctic. A snow cover of good quality protecting lemmings from cold temperatures and predators is thought to be an important factor for maintaining the cyclic dynamic of their populations in the tundra. We examined if the characteristics of annual fluctuations (amplitude and shape of phases) in brown lemming (Lemmus trimucronatus) density could be determined by snow depth, snow density, sub-nivean temperature and persistence of snow. Using an 18-year time series of brown lemming abundance on Bylot Island in the Canadian Arctic, we tested if snow variables could explain the residual variation between the observed lemming density and the one predicted by models where cyclicity had been accounted for. Our analysis provides support for the hypothesis that snow cover can affect the amplitude and possibly also the periodicity of lemming population cycles in the High Arctic. Summer abundance of brown lemmings was higher following winters with a deep snow cover and a low-density snow pack near the ground but was unaffected by the date of establishment or melting and duration of the snow cover. Two snow variables showed a temporal trend; mean winter snow depth tended to increase and date of establishment of the hiemal threshold occurred earlier over time. These temporal trends, which should be favourable to lemmings, may explain why healthy population cycles have apparently been maintained at our study site contrary to other Arctic sites.