Nonlinear effects of climate on boreal rodent dynamics: mild winters do not negate high‐amplitude cycles

Small rodents are key species in many ecosystems. In boreal and subarctic environments, their importance is heightened by pronounced multiannual population cycles. Alarmingly, the previously regular rodent cycles appear to be collapsing simultaneously in many areas. Climate change, particularly decreasing snow quality or quantity in winter, is hypothesized as a causal factor, but the evidence is contradictory. Reliable analysis of population dynamics and the influence of climate thereon necessitate spatially and temporally extensive data. We combined data on vole abundances and climate, collected at 33 locations throughout Finland from 1970 to 2011, to test the hypothesis that warming winters are causing a disappearance of multiannual vole cycles. We predicted that vole population dynamics exhibit geographic and temporal variation associated with variation in climate; reduced cyclicity should be observed when and where winter weather has become milder. We found that the temporal patterns in cyclicity varied between climatically different regions: a transient reduction in cycle amplitude in the coldest region, low‐amplitude cycles or irregular dynamics in the climatically intermediate regions, and strengthening cyclicity in the warmest region. Our results did not support the hypothesis that mild winters are uniformly leading to irregular dynamics in boreal vole populations. Long and cold winters were neither a prerequisite for high‐amplitude multiannual cycles, nor were mild winters with reduced snow cover associated with reduced winter growth rates. Population dynamics correlated more strongly with growing season than with winter conditions. Cyclicity was weakened by increasing growing season temperatures in the cold, but strengthened in the warm regions. High‐amplitude multiannual vole cycles emerge in two climatic regimes: a winter‐driven cycle in cold, and a summer‐driven cycle in warm climates. Finally, we show that geographic climatic gradients alone may not reliably predict biological responses to climate change.     

Vole population cycles in northern and southern Europe: is there a need for different explanations for single pattern?

1. Students of population cycles in small rodents in Fennoscandia have accumulated support for the predation hypothesis, which states that the gradient in cycle length and amplitude running from southern to northern Fennoscandia reflects the relative influence of specialist and generalist predators on vole dynamics, itself modulated by the presence of snow cover. The hypothesized role of snow cover is to isolate linked specialist predators, primarily the least weasel, Mustela n. nivalis L. and their prey, primarily field voles Microtus agrestis L., from the stabilizing influence of generalist predators. 2. The predation hypothesis does not readily account for the high amplitude and regular 3-year cycles of common voles documented in agricultural areas of western, central and eastern Europe. Such cycles are rarely mentioned in the literature pertaining to Fennoscandian cycles. 3. We consider new data on population cycles and demographic patterns of common voles Microtus arvalis Pallas in south-west France. We show that the patterns are wholly consistent with five of six patterns that characterize rodent cycles in Fennoscandia and that are satisfactorily explained by the predation hypothesis. They include the: (a) existence of cycle; (b) the occurrence of long-term changes in relative abundance and type of dynamics; (c) geographical synchrony over large areas; (d) interspecific synchrony; and (e) voles are large in the increase and peak phase and small in decline and low phase, namely. There is a striking similarity between the patterns shown by common vole populations in south-west France and those from Fennoscandian cyclic rodent populations, although the former are not consistent with a geographical extension of the latitudinal gradient south of Fennoscandia. 4. It is possible that the dominant interaction leading to multiannual rodent oscillations is different in different regions. We argue, however, that advocates of the predation hypothesis should embrace the challenge of developing a widely applicable explanation to population cycles, including justifying any limits to its applicability on ecological and not geographical grounds.     

Persistent Chaos of Measles Epidemics in the Prevaccination United States Caused by a Small Change in Seasonal Transmission Patterns

Epidemics of infectious diseases often occur in predictable limit cycles. Theory suggests these cycles can be disrupted by high amplitude seasonal fluctuations in transmission rates, resulting in deterministic chaos. However, persistent deterministic chaos has never been observed, in part because sufficiently large oscillations in transmission rates are uncommon. Where they do occur, the resulting deep epidemic troughs break the chain of transmission, leading to epidemic extinction, even in large cities. Here we demonstrate a new path to locally persistent chaotic epidemics via subtle shifts in seasonal patterns of transmission, rather than through high-amplitude fluctuations in transmission rates. We base our analysis on a comparison of measles incidence in 80 major cities in the prevaccination era United States and United Kingdom. Unlike the regular limit cycles seen in the UK, measles cycles in US cities consistently exhibit spontaneous shifts in epidemic periodicity resulting in chaotic patterns. We show that these patterns were driven by small systematic differences between countries in the duration of the summer period of low transmission. This example demonstrates empirically that small perturbations in disease transmission patterns can fundamentally alter the regularity and spatiotemporal coherence of epidemics.     

Population cycles in voles and lemmings: state of the science and future directions

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Multi-annual density fluctuations and habitat size enhance genetic variability in two northern voles

In order to gain a better understanding of the consequences of population density cycles and landscape structure for the genetic composition in time and space of vole populations, we analyzed the multiannual genetic structure of the two numerically dominant, sympatric small rodent species of northernmost Fennoscandia. Red voles Myodes rutilus and grey-sided voles M. rufocanus were trapped in the subarctic birch forest along three fjords over five years. Along each fjord, there were four or five altitudinal transects each with five trapping stations. Spring and fall population densities were estimated from mark–recapture data. Grey-sided voles exhibited higher amplitude density fluctuations than red voles. Polymorphism at eight or nine microsatellite loci, determined in 1228 voles, was used to estimate local genetic diversity and differentiation among samples. Genetic diversity was higher in grey-sided voles than in red voles. Spring densities had no effect on local genetic diversity or on differentiation. The amplitude of density fluctuations and the extent of favorable habitat (sub-arctic birch forest) surrounding each site had a positive effect on genetic diversity, and the amplitude of density fluctuations had a negative effect on differentiation in red voles, for which fluctuating populations were compared with more stable populations. The harmonic mean of densities, reflecting average population sizes, had a negative effect on genetic diversity in red voles, but a positive effect in grey-sided voles, for which only fluctuating populations were compared. No other effects were significant for grey-sided voles. A temporal assignment test showed that the spatial structure was more stable in time for populations with more stable population dynamics. Altogether our results suggest that high amplitude density fluctuations lead to more gene flow and higher genetic diversity in vole populations.     

Flexibility in a changing arctic food web: Can rough‐legged buzzards cope with changing small rodent communities?

Indirect effects of climate change are often mediated by trophic interactions and consequences for individual species depend on how they are tied into the local food web. Here we show how the response of demographic rates of an arctic bird of prey to fluctuations in small rodent abundance changed when small rodent community composition and dynamics changed, possibly under the effect of climate warming. We observed the breeding biology of rough‐legged buzzards (Buteo lagopus) at the Erkuta Tundra Monitoring Site in southern Yamal, low arctic Russia, for 19 years (1999–2017). At the same time, data on small rodent abundance were collected and information on buzzard diet was obtained from pellet dissection. The small rodent community experienced a shift from high‐amplitude cycles to dampened fluctuations paralleled with a change in species composition toward less lemmings and more voles. Buzzards clearly preferred lemmings as prey. Breeding density of buzzards was positively related to small rodent abundance, but the shift in small rodent community lead to lower numbers relative to small rodent abundance. At the same time, after the change in small rodent community, the average number of fledglings was higher relative to small rodent abundance than earlier. These results suggest that the buzzard population adapted to a certain degree to the changes in the major resource, although at the same time density declined. The documented flexibility in the short‐term response of demographic rates to changes in structure and dynamics of key food web components make it difficult to predict how complex food webs will be transformed in a warmer Arctic. The degree of plasticity of functional responses is indeed likely to vary between species and between regions, depending also on the local food web context.     

Duplication and population dynamics shape historic patterns of selection and genetic variation at the major histocompatibility complex in rodents

Genetic variation at the major histocompatibility complex (MHC) is vitally important for wildlife populations to respond to pathogen threats. As natural populations can fluctuate greatly in size, a key issue concerns how population cycles and bottlenecks that could reduce genetic diversity will influence MHC genes. Using 454 sequencing, we characterized genetic diversity at the DRB Class II locus in montane voles (Microtus montanus), a North American rodent that regularly undergoes high‐amplitude fluctuations in population size. We tested for evidence of historic balancing selection, recombination, and gene duplication to identify mechanisms maintaining allelic diversity. Counter to our expectations, we found strong evidence of purifying selection acting on the DRB locus in montane voles. We speculate that the interplay between population fluctuations and gene duplication might be responsible for the weak evidence of historic balancing selection and strong evidence of purifying selection detected. To further explore this idea, we conducted a phylogenetically controlled comparative analysis across 16 rodent species with varying demographic histories and MHC duplication events (based on the maximum number of alleles detected per individual). On the basis of phylogenetic generalized linear model‐averaging, we found evidence that the estimated number of duplicated loci was positively related to allelic diversity and, surprisingly, to the strength of purifying selection at the DRB locus. Our analyses also revealed that species that had undergone population bottlenecks had lower allelic richness than stable species. This study highlights the need to consider demographic history and genetic structure alongside patterns of natural selection to understand resulting patterns of genetic variation at the MHC.     

Unstable dynamics and population limitation in mountain hares

The regular large-scale population fluctuations that characterize many species of northern vertebrates have fascinated ecologists since the time of Charles Elton. There is still, however, no clear consensus on what drives these fluctuations. Throughout their circumpolar distribution, mountain hares Lepus timidus show regular and at times dramatic changes in density. There are distinct differences in the nature, amplitude and periodicity of these fluctuations between regions and the reasons for these population fluctuations and the geographic differences remain largely unknown. In this review we synthesize knowledge on the factors that limit or regulate mountain hare populations across their range in an attempt to identify the drivers of unstable dynamics. Current knowledge of mountain hare population dynamics indicates that trophic interactions--either predator-prey or host-parasite--appear to be the major factor limiting populations and these interactions may contribute to the observed unstable dynamics. There is correlative and experimental evidence that some mountain hare populations in Fennoscandia are limited by predation and that predation may link hare and grouse cycles to microtine cycles. Predation is unlikely to be important in mountain hare populations in Scotland as most hares occur on sporting estates where predators are controlled, but this hypothesis remains to be experimentally tested. There is, however, emerging experimental evidence that some Scottish mountain hare populations are limited by parasites and that host-parasite interactions contribute to unstable dynamics. By contrast, there is little evidence from Fennoscandia that parasitism is of any importance to mountain hare population dynamics, although disease may cause periodic declines. Although severe weather and food limitation may interact to cause periodic high winter mortality there is little evidence that food availability limits mountain hare populations. There is a paucity of information concerning the factors limiting or regulating mountain hare populations in the Alps of Central Europe or in the tundra and taiga belts of Russia. Future research on mountain hare population dynamics should focus on the interactions between predation, parasitism and nutrition with stochastic factors such as climate and anthropogenic management including harvesting.     

Dynamics and responses to mortality rates of competing predators undergoing predator-prey cycles

Two or more competing predators can coexist using a single homogeneous prey species if the system containing all three undergoes internally generated fluctuations in density. However, the dynamics of species that coexist via this mechanism have not been extensively explored. Here, we examine both the nature of the dynamics and the responses of the mean densities of each predator to mortality imposed upon it or its competitor. The analysis of dynamics uncovers several previously undescribed behaviors for this model, including chaotic fluctuations, and long-term transients that differ significantly from the ultimate patterns of fluctuations. The limiting dynamics of the system can be loosely classified as synchronous cycles, asynchronous cycles, and chaotic dynamics. Synchronous cycles are simple limit cycles with highly positively correlated densities of the two predator species. Asynchronous cycles are limit cycles, frequently of complex form, including a significant period during which prey density is nearly constant while one predator gradually, monotonically replaces the other. Chaotic dynamics are aperiodic and generally have intermediate correlations between predator densities. Continuous changes in density-independent mortality rates often lead to abrupt transitions in mean population sizes, and increases in the mortality rate of one predator may decrease the population size of the competing predator. Similarly, increases in the immigration rate of one predator may decrease its own density and increase the density of the other predator. Proportional changes in one predator's birth and death rate functions can have significant effects on the dynamics and mean densities of both predator species. All of these responses to environmental change differ from those observed when competitors coexist stably as the result of resource (prey) partitioning. The patterns described here occur in many other competition models in which there are cycles and differences in the linearity of the responses of consumers to their resources.     

Dynamics of voles and small mustelids in the taiga landscape of northern Fennoscandia in relation to habitat quality

In the forests of northern Fennoscandia during the I980's, the dynamics of microtine rodents changed from multiannual high amplitude fluctuations (cycles) to, depending on species, fluctuations with a strong seasonal component or fluctuations with smaller amplitude and lower frequency. Microtine and predator data from the Pallasjarvi area, Finnish Lapland, suggest that this transition took place at different rates in different parts of the taiga landscape. Generally, densities in forest habitats have been primarily seasonal since 198S-86. In mesic spruce taiga and in drier forest habitats microtines had a prolonged peak in 1981-83 and a crash in 1984-83. At the timberline, however, microtine populations dropped from peak to low densities already in 1982-83 but the final crash did not occur until spring 1985. The synchronous decrease in microtines densities in all habitat types in 1984-85 coincided with increase in weasel activity. Activity of other carnivores was consistently high in mesic lowland habitats. The data support following three conjectures. 1) Periodic abundance of least weasels is crucial for sustained vole cycles. 2) Predominance of stoats and other generalist predators lead to less regular fluctuations with a strong seasonal component where density declines occur in autumn and early winter. 3) In barren tundra areas, the vegetation cannot sustain high densities of microtines and. consequently, predation is not a necessary condition for population crashes.     

Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication

Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of ‘subbarrel’ patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.     

Second-order feedback and climatic effects determine the dynamics of a small rodent population in a temperate forest of South America

 The multiannual cyclic fluctuations exhibited by arvicoline rodents in the Northern Hemisphere have attracted the attention of population ecologists. However, despite the abundant information on small rodent dynamics in South America, there are no studies reporting cyclic population dynamics. Here, we report evidence of cyclic population dynamics in a South American small rodent, the longhaired field mouse (Abrothrix longipilis) from southern temperate forests in Chile. The time-series analyses showed that longhaired field mice dynamics are better represented by a second-order autoregressive model characterized by 3-year cyclic dynamics. The 3-year cycles are clearly shown in the autocorrelation factor (ACF) pattern and in the dominant frequency of the spectral analysis. In addition, we determined nonlinear effects of the Antarctic Oscillation Index (AAOI). The results shown here pointed out that we need the integration of studies about cyclic small rodent populations from the different continents and beyond the Northern Hemisphere to resolve the enigma underlying the cyclic population dynamics exhibited by many small rodent species. Received: September 19, 2002 / Accepted: February 4, 2003     

Long-term decline in numbers of cyclic voles in boreal Sweden: analysis and presentation of hypotheses

Cyclic vole populations, defined as showing fairly regular 3–4 yr density fluctuations but with variable amplitudes, were monitored in boreal Sweden in spring and fall 1971–2002, starting in fall 1971. Voles were snap-trapped on permanent sampling plots at the landscape level within a 100 by 100 km study area north of Umeå. The predominating species trapped were Clethrionomys glareolus, C. rufocanus and Microtus agrestis. In addition to the 3–4 yr cycles, there was a long-term decrease in numbers and amplitude of the fluctuations, which was especially conspicuous in C. rufocanus. In this latter species there was a persistent decline of both spring and fall densities, apparently bringing the population close to extinction in the area. However, the decline of spring densities from the 1970s to the 1980s and onwards was also evident in C. glareolous and M. agrestis. The declines in numbers and amplitude were largely linked to an increased frequency and/or accentuation of winter declines, which more or less neutralized or even overrode the density increase during the reproductive season in the previous summer, especially so in the second year of the cycles. Thereby the gradual two-large-step build-up of high spring densities, very much founding the base for the very large peak densities and amplitudes in the 1970s, was successively replaced by a one-smaller-step build-up of more modest spring densities, leading to lower peak densities and amplitudes in the 1980s, 1990s and early 2000s. Understanding the causes of the increased frequency and/or severeness of winter declines appears critical to understanding the observed long-term changes in numbers. However, the underlying causes of the increase of winter declines and the decrease of densities and amplitudes are unknown, but some hypotheses are presented and discussed here. Also, some implications from the decreased vole abundance for reproduction and densities of predators on the voles, and on predators’ alternative prey species, are briefly discussed.     

Analysis of period mRNA cycling in Drosophila head and body tissues indicates that body oscillators behave differently from head oscillators.

The period (per) gene is thought to be part of the Drosophila circadian pacemaker. The circadian fluctuations in per RNA and protein that constitute the per feedback loop appear to be required for pacemaker function, and have been measured in head neuronal tissues that are necessary for locomotor activity and eclosion rhythms. The per gene is also expressed in a number of neuronal and nonneuronal body tissues for which no known circadian phenomena have been described. To determine whether per might affect some circadian function in these body tissues, per RNA cycling was examined. These studies show that per RNA cycles in the same phase and amplitude in head and body tissues during light-dark cycles. One exception to this is the lack of per RNA cycling in the ovary, which also appears to be the only tissue in which PER protein is primarily cytoplasmic. In constant darkness, however, the amplitude of per RNA cycling dampens much more quickly in bodies than in heads. Taken together, these results indicate that circadian oscillators are present in head and body tissues in which PER protein is nuclear and that these oscillators behave differently.     

Complex seasonal patterns of primary producers at the land-sea interface

Seasonal fluctuations of plant biomass and photosynthesis are key features of the Earth system because they drive variability of atmospheric CO₂, water and nutrient cycling, and food supply to consumers. There is no inventory of phytoplankton seasonal cycles in nearshore coastal ecosystems where forcings from ocean, land and atmosphere intersect. We compiled time series of phytoplankton biomass (chlorophyll a) from 114 estuaries, lagoons, inland seas, bays and shallow coastal waters around the world, and searched for seasonal patterns as common timing and amplitude of monthly variability. The data revealed a broad continuum of seasonal patterns, with large variability across and within ecosystems. This contrasts with annual cycles of terrestrial and oceanic primary producers for which seasonal fluctuations are recurrent and synchronous over large geographic regions. This finding bears on two fundamental ecological questions: (1) how do estuarine and coastal consumers adapt to an irregular and unpredictable food supply, and (2) how can we extract signals of climate change from phytoplankton observations in coastal ecosystems where local‐scale processes can mask responses to changing climate?     

Short‐term variations in gene flow related to cyclic density fluctuations in the common vole

In highly fluctuating populations with complex social systems, genetic patterns are likely to vary in space and time due to demographic and behavioural processes. Cyclic rodents are extreme examples of demographically instable populations that often exhibit strong social organization. In such populations, kin structure and spacing behaviour may vary with density fluctuations and impact both the composition and spatial structure of genetic diversity. In this study, we analysed the multiannual genetic structure of a cyclic rodent, Microtus arvalis, using a sample of 875 individuals trapped over three complete cycles (from 1999 to 2007) and genotyped at 10 microsatellite loci. We tested the predictions that genetic diversity and gene flow intensity vary with density fluctuations. We found evidences for both spatial scale‐dependant variations in genetic diversity and higher gene flow during high density. Moreover, investigation of sex‐specific relatedness patterns revealed that, although dispersal is biased toward males in this species, distances moved by both sexes were lengthened during high density. Altogether, these results suggest that an increase in migration with density allows to restore the local loss of genetic diversity occurring during low density. We then postulate that this change in migration results from local competition, which enhances female colonization of empty spaces and male dispersal among colonies.     

The dynamics of production and destruction: Analytic insight into complex behavior

This paper analytically explores the properties of simple differential-difference equations that represent dynamic processes with feedback dependent on prior states of the system. Systems with pure negative and positive feedback are examined, as well as those with mixed (positive/negative) feedback characteristics. Very complex time dependent behaviors may arise from these processes. Indeed, the same mechanism may, depending on system parameters and initial conditions, produce simple, regular, repetitive patterns and completely irregular random-like fluctuations.For the differential-delay equations considered here we prove the existence of: (i) stable and unstable limit cycles, where the stable cycles may have an arbitrary number of extrema per period; and (ii) chaos, meaning the presence of infinitely many periodic solutions of different period and of infinitely many irregular and mixing solutions.     

Qualitative analysis of a predator-prey system with limit cycles

Fairly regular multiannual microtine rodent cycles are observed in boreal Fennoscandia. In the southern parts of Fennoscandia these multiannual cycles are not observed. It has been proposed that these cycles may be stabilized by generalist predation in the south.We show that if the half-saturation of the generalist predators is high compared to the number of small rodents the cycles are likely to be stabilized by generalist predation as observed. We give examples showing that if the half-saturation of the generalist predators is low compared to the number of small rodents, then multiple equilibria and multiple limit cycles may occur as the generalist predator density increases.     

Uncertainty and predictability in population dynamics of a bitrophic ecological model: Mixed-mode oscillations,bistability and sensitivity to parameters

We consider a two-trophic ecological model comprising of two predators competing for their common prey. We cast the model into the framework of a singular perturbed system of equations in one fast variable (prey population density) and two slow variables (predator population densities), mimicking the common observation that the per-capita productivity rate decreases from bottom to top along the trophic levels in Nature. We assume that both predators exhibit Holling II functional response with one of the predators (territorial) having a density dependent mortality rate. Depending on the system parameters, the model exhibits small, intermediate and/or large fluctuations in the population densities. The large fluctuations correspond to periodic population outbreaks followed by collapses (commonly known as cycles of “boom and bust”). The small fluctuations arise due to a singular Hopf bifurcation in the system, and are ecologically more desirable. However, more interestingly, the system exhibits mixed-mode oscillations (which are concatenations of the large amplitude oscillations and the small amplitude oscillations) that indicate the adaptability of the species to prolong the time gap between successive cycles of boom and bust. Numerical simulations are carried out to demonstrate the extreme sensitivity of the system to initial conditions (chaos and bistability of limit cycles are observed) as well as to the system parameters (here we only show the sensitivity to the density dependent mortality rate of the territorial predator). This model throws light at the uncertainties in long term behaviors that are associated with a real ecological system. We show that even very small changes in the system parameters due to natural or human-induced causes can lead to a complete different ecological phenomenon, thus affecting the predictability of the density of the prey population. In this paper, we explain the mechanisms behind the irregular fluctuations in the population sizes in an attempt to understand the dynamics occurring in a natural population and also comment on the inherent uncertainties associated with the system.     

川西平原农田啮齿动物群落动态：年间变动和季节变动

为了研究农田啮齿动物群落的动态规律,用标志重捕的方法给出了川西平原农田的啮齿动物群落的物种数、结合种群密度、生物量、物种多样性的Shannon指数与Simpson指数等5个变量的时间序列资料,并分析了这些时间序列的年间变动和季节变动的特点。结果表明：（1）5个变量总是处于不断的变化之中,特别是年间交替升降十分明显;（2）群落的全部8个物种从未同时出现过,同一个月最多有5个物种,最少只有1个物种;（3）5个变量季节变动的幅度均较大并各具有1至3个不等的明显的峰值,而年间变动的幅度则相对较小;（4）5个变量的最大值均出现在夏季,最小值则出现在春季、夏季或冬季;（5）5个变量的季节性均不强;（6）优势种大足鼠（Rattus nitidus)的种群密度分别与群落结合种群密度、生物量的年间变动和季节变动均具有相似的变动规律;此外,优势种大足鼠的种群密度、生物量分别占群落结合种群密度、生物量的比例均较高,而且这两个比例季节变动的幅度都较大而年间变动则较为稳定。