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.     

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.     

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.     

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.     

Natural enemy specialization and the period of population cycles

The dynamical consequences of multiple‐species interactions remain an elusive and fiercely debated topic. Recently, Murdoch and colleagues proposed a general rule for the dynamics of generalist natural enemies: when periodic, they exhibit single generation cycles (SGCs), similar to single species systems. This contrasts markedly with specialists, which tend to show classic (longer period) consumer–resource cycles. Using a well‐studied laboratory system, we show that this general rule is contradicted when we consider resource age‐structure.     

Linking climate change to population cycles of hares and lynx

The classic 10‐year population cycle of snowshoe hares (Lepus americanus, Erxleben 1777) and Canada lynx (Lynx canadensis, Kerr 1792) in the boreal forests of North America has drawn much attention from both population and community ecologists worldwide; however, the ecological mechanisms driving the 10‐year cyclic dynamic pattern are not fully revealed yet. In this study, by the use of historic fur harvest data, we constructed a series of generalized additive models to study the effects of density dependence, predation, and climate (both global climate indices of North Atlantic Oscillation index (NAO), Southern Oscillation index (SOI) and northern hemispheric temperature (NHT) and local weather data including temperature, rainfall, and snow). We identified several key pathways from global and local climate to lynx with various time lags: rainfall shows a negative, and snow shows a positive effect on lynx; NHT and NAO negatively affect lynx through their positive effect on rainfall and negative effect on snow; SOI positively affects lynx through its negative effect on rainfall. Direct or delayed density dependency effects, the prey effect of hare on lynx and a 2‐year delayed negative effect of lynx on hare (defined as asymmetric predation) were found. The simulated population dynamics is well fitted to the observed long‐term fluctuations of hare and lynx populations. Through simulation, we find density dependency and asymmetric predation, only producing damped oscillation, are necessary but not sufficient factors in causing the observed 10‐year cycles; while extrinsic climate factors are important in producing and modifying the sustained cycles. Two recent population declines of lynx (1940–1955 and after 1980) were likely caused by ongoing climate warming indirectly. Our results provide an alternative explanation to the mechanism of the 10‐year cycles, and there is a need for further investigation on links between disappearance of population cycles and global warming in hare–lynx 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.     

Life cycles shape parasite evolution: comparative population genetics of salmon trematodes

Little is known about what controls effective sizes and migration rates among parasite populations. Such data are important given the medical, veterinary, and economic (e.g., fisheries) impacts of many parasites. The autogenic-allogenic hypothesis, which describes ecological patterns of parasite distribution, provided the foundation on which we studied the effects of life cycles on the distribution of genetic variation within and among parasite populations. The hypothesis states that parasites cycling only in freshwater hosts (autogenic life cycle) will be more limited in their dispersal ability among aquatic habitats than parasites cycling through freshwater and terrestrial hosts (allogenic life cycle). By extending this hypothesis to the level of intraspecific genetic variation, we examined the effects of host dispersal on parasite gene flow. Our a priori prediction was that for a given geographic range, autogenic parasites would have lower gene flow among subpopulations. We compared intraspecific mitochondrial DNA variation for three described species of trematodes that infect salmonid fishes. As predicted, autogenic species had much more highly structured populations and much lower gene flow among subpopulations than an allogenic species sampled from the same locations. In addition, a cryptic species was identified for one of the autogenic trematodes. These results show how variation in life cycles can shape parasite evolution by predisposing them to vastly different genetic structures. Thus, we propose that knowledge of parasite life cycles will help predict important evolutionary processes such as speciation, coevolution, and the spread of drug resistance.     

Moving forward in circles: challenges and opportunities in modelling population cycles

Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non‐intuitive ways, the high‐dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco‐evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem‐level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.     

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.