Limit cycles in Norwegian lemmings: tensions between phase–dependence and density-dependence

Across the boreal forest of North America, lynx populations undergo 10-year cycles. Analysis of 21 time series from 1821 to the present demonstrates that these fluctuations are generated by nonlinear processes with regulatory delays. Trophic interactions between lynx and hares cause delayed density-dependent regulation of lynx population growth. The nonlinearity, in contrast, appears to arise from phase dependencies in hunting success by lynx through the cycle. Using a combined approach of empirical, statistical, and mathematical modeling, we highlight how shifts in trophic interactions between the lynx and the hare generate the nonlinear process primarily by shifting functional response curves during the increase and the decrease phases.

I review the regular multiannual population fluctuations in voles and lemmings of northern latitudes. Periodically fluctuating small rodent populations all exhibit a clear two-dimensional density-dependent structure. This implies both a direct and a delayed annual density dependence, and suggests that either a predator-prey type of interaction or a specialised plant-herbivore type of interaction (but not both) may be the underlying cause of these multiannual density cycles. Clear-cut experimental testing relating to these propositions is, however, lacking. A two-dimensional annual density-dependent structure is typically non-linear in a way which may be modelled as a threshold type of non-linearity and interpreted as a phase dependence in the density-dependent structure (implying that the density-dependent structure is different in the increase and the decrease phase). Two clear geographic gradients in the annual density-dependent structure are reviewed: the Fennoscandian gradient and the Hokkaidian gradient. The seasonal nature of the annual density-dependent structure is furthermore reviewed: for voles in both Fennoscandia and Hokkaido the direct annual density dependence during the winter (measured per time unit) is concluded to be the strongest. I close with a survey of the main challenges within the field of small rodent cycles' - the greatest of which is suggested to be the integration of demography and population dynamics. I recommend to look at other populations for potentially applicable model systems. I conclude that multiannual population cycles seen in voles and lemmings will continue to be a strong source of conceptual and methodological developments within the field of population ecology.

One of the fundamental determinants of survival and growth of individuals is population density. Typically, individuals exhibit negative density dependence, but positive density dependence (Allee effect) may occur. Understanding patterns of density dependence is important for conservation and management of species that have low densities as a result of recent population declines. June sucker (Chasmistes liorus) is an endangered species that was formerly abundant but now is found at low densities in Utah Lake. We tested the hypothesis that young June sucker exhibit positive density dependence (i.e., Allee effects) in growth and survival at low densities. In addition, we tested the hypothesis that patterns of density dependence in growth and survival of young June sucker are consistent across years. We conducted a series of 5 experiments in 5 separate years. All 5 experiments included similar levels of density manipulations of young June sucker. June sucker exhibited Allee effects in both growth and survival in some years, but patterns of density dependence varied widely among years. Growth exhibited consistent patterns of negative density dependence, especially at higher densities. Survival was less affected by density, exhibiting no response to density in about half of the experimental comparisons. Overall, intermediate densities around 50 individuals · m-2 seemed to provide the best tradeoff between growth and number produced.

The presence of direct and delayed density dependence in populations of three sympatric rodent species (Clethrionomys rufocanus, Apodemus speciosus, and A. argenteus) in Hokkaido, Japan, was evaluated using triannual census data (spring, summer, and fall) spanning 30 years (1963–1992) on 79 populations for each species. The average abundance and population variability (the s-index) generally increased from spring to fall in C. rufocanus but were typically highest in summer for the Apodemus populations. Based on a comprehensive and comparative review of the population and community biology of the species we made four explicit predictions about the pattern of density dependence: (1) the three species were expected to exhibit socially induced direct density dependence, but (2) this was expected to be weaker in the Apodemus species than C. rufocanus; (3) delayed density dependence caused by predation was only expected in C. rufocanus; thus (4) time series of C. rufocanus were expected to reflect a second-order dynamic process, and those of the Apodemus species were expected to reflect a first-order process. Dennis and Taper's method based on the Gompertz model was used to test for direct and delayed density dependence and thereby to test the predictions. Direct density dependence was detected in most series (81.0–97.5%) for all three seasons and for all three species. A significant proportion of the time series of C. rufocanus (11.8–18.5%) exhibited negative delayed density dependence, whereas detection rates in the two Apodemus species did not differ from that expected by chance alone. Autoregressive analyses corroborated this: a second-order process was commonly found to be the appropriate model for the time series of C. rufocanus, whereas a first-order process was preferred for most time series of the Apodemus species. The high incidence of direct density dependence in all three species and the contrasting results on delayed density dependence between C. rufocanus and the Apodemus species are discussed with reference to social and trophic interactions. Territoriality, delayed maturation, and reduced pregnancy rates are probable causes for the high incidence of direct density dependence in all species. The more unpredictable variability in Apodemus food resource is argued to have a potential to disrupt social regulation and thus to lower the incidence of direct density dependence. A candidate mechanism for the incidence of delayed density dependence is differential vulnerability to predation: the demography of C. rufocanus is much more affected by predators than Apodemus.

Specialized enemies, such as predators and parasitoids, play an important role in the population cycles of small animals by generating delayed density dependence. We investigated the role of predation in population cycles in an undisturbed large-mammal system using long-term data on the sustained density fluctuations of wolves and moose on Isle Royale (Michigan, USA). Nonlinear time-series analysis revealed that wolves display phase-dependent dynamics with stronger density dependence during the decline phase than during the increase phase. This phase dependence was also reflected in predation rates: the number of moose killed daily by wolves was greater during the wolf increase phase than during the wolf decline phase. Accordingly, moose displayed multi-annual cycles generated by an interaction between weak self-regulation and strong delayed density dependence during periods of wolf increase, and strong self-regulation with negligible delayed density dependence during periods of wolf decline. This constitutes, to our knowledge, the first formal documentation of population cycles in large mammals. By making use of long-term data at both trophic levels, as well as data on predator behavior, this analysis may shed light on the mechanisms through which predators contribute to population cycles of prey in other taxa.

The presence of direct and delayed density dependence in populations of three sympatric rodent species (Clethrionomys rufocanus, Apodemus speciosus, and A. argenteus) in Hokkaido, Japan, was evaluated using triannual census data (spring, summer, and fall) spanning 30 years (1963-1992) on 79 populations for each species. The average abundance and population variability (the s-index) generally increased from spring to fall in C. rufocanus but were typically highest in summer for the Apodemus populations. Based on a comprehensive and comparative review of the population and community biology of the species we made four explicit predictions about the pattern of density dependence: (1) the three species were expected to exhibit socially induced direct density dependence, but (2) this was expected to be weaker in the Apodemus species than C. rufocanus; (3) delayed density dependence caused by predation was only expected in C. rufocanus; thus (4) time series of C. rufocanus were expected to reflect a second-order dynamic process, and those of the Apodemus species were expected to reflect a first-order process. Dennis and Taper's method based on the Gompertz model was used to test for direct and delayed density dependence and thereby to test the predictions. Direct density dependence was detected in most series (81.0-97.5%) for all three seasons and for all three species. A significant proportion of the time series of C. rufocanus (11.8-18.5%) exhibited negative delayed density dependence, whereas detection rates in the two Apodemus species did not differ from that expected by chance alone. Autoregressive analyses corroborated this: a second- order process was commonly found to be the appropriate model for the time series of C. rufocanus, whereas a first-order process was preferred for most time series of the Apodemus species. The high incidence of direct density dependence in all three species and the con- trasting results on delayed density dependence between C. rufocanus and the Apodemus specieNare discussed with reference to social and trophic interactions. Territoriality, delayed maturation, and reduced pregnancy rates are probable causes for the high incidence of direct density dependence in all species. The more unpredictable variability in Apodemus food resource is argued to have a potential to disrupt social regulation and thus to lower the incidence of direct density dependence. A candidate mechanism for the incidence of delayed density dependence is differential vulnerability to predation: the demography of C. rufo- canus is much more affected by predators than Apodemus.

Population cycles in voles are often thought to be generated by one-year delayed density dependence on the annual population growth rate. In common voles, however, it has been suggested by Turchin (2003) that some populations exhibit first-order cycles, resulting from strong overcompensation (i.e. carrying capacity overshoots in peak years, with only an effect of the current year abundance on annual growth rates). We focus on a common vole (Microtus arvalis) population from western France that exhibits 3-year cycles. Several overcompensating nonlinear models for populations dynamics are fitted to the data, notably those of Hassell, and Maynard-Smith and Slatkin. Overcompensating direct density dependence (DD) provides a satisfactory description of winter crashes, and one-year delayed density dependence is not responsible for the crashes, thus these are not classical second-order cycles. A phase-driven modulation of direct density dependence maintains a low-phase, explaining why the cycles last three years instead of two. Our analyses suggest that some of this phase dependence can be expressed as one-year delayed DD, but phase dependence provides a better description. Hence, modelling suggests that cycles in this population are first-order cycles with a low phase after peaks, rather than fully second-order cycles. However, based on the popular log-linear second-order autoregressive model, we would conclude only that negative delayed density dependence exists. The additive structure of this model cannot show when delayed DD occurs (here, during lows rather than peaks). Our analyses thus call into question the automated use of second-order log-linear models, and suggests that more attention should be given to non-(log)linear models when studying cyclic populations. From a biological viewpoint, the fast crashes through overcompensation that we found suggest they might be caused by parasites or food rather than predators, though predators might have a role in maintaining the low phase and spatial synchrony.

In species with polygynous mating systems, females are regarded as food-limited, while males are limited by access to mates. When local density increases, forage availability declines, while mate access for males may increase due to an increasingly female-biased sex ratio. Density dependence in emigration rates may consequently differ between sexes. Here, we investigate emigration using mark-recovery data from 468 young red deer Cervus elaphus marked in Snillfjord, Norway over a 20-year period when the population size has increased sixfold. We demonstrate a strong negative density-dependent emigration rate in males, while female emigration rates were lower and independent of density. Emigrating males leaving the natal range settled in areas with lower density than expected by chance. Dispersing males moved 42 per cent longer at high density in 1997 (37 km) than at low density in 1977 (26 km), possibly caused by increasing saturation of deer in areas surrounding the marking sites. Our study highlights that pattern of density dependence in dispersal rates may differ markedly between sexes in highly polygynous species. Contrasting patterns reported in small-scale studies are suggestive that spatial scale of density variation may affect the pattern of temporal density dependence in emigration rates and distances.

A key issue in metapopulation dynamics is the relative impact of internal patch dynamics and coupling between patches. This problem can be addressed by analysing large spatiotemporal data sets, recording the local and global dynamics of metapopulations. In this paper, we analyse the dynamics of measles meta-populations in a large spatiotemporal case notification data set, collected during the pre-vaccination era in England and Wales. Specifically, we use generalized linear statistical models to quantify the relative importance of local influences (birth rate and population size) and regional coupling on local epidemic dynamics. Apart from the proportional effect of local population size on case totals, the models indicate patterns of local and regional dynamic influences which depend on the current state of epidemics. Birth rate and geographic coupling are not associated with the size of major epidemics. By contrast, minor epidemics--and especially the incidence of local extinction of infection--are influenced both by birth rate and geographical coupling. Birth rate at a lag of four years provides the best fit, reflecting the delayed recruitment of susceptibles to school cohorts. A hierarchical index of spatial coupling to large centres provides the best spatial model. The model also indicates that minor epidemics and extinction patterns are more strongly influenced by this regional effect than the local impact of birth rate.

Disentangling empirically the many processes affecting spatial population synchrony is a challenge in population ecology. Two processes that could have major effects on the spatial synchrony of wild population dynamics are density dependence and variation in environmental conditions like temperature. Understanding these effects is crucial for predicting the effects of climate change on local and regional population dynamics. We quantified the direct contribution of local temperature and density dependence to spatial synchrony in the population dynamics of nine fish species inhabiting the Barents Sea. First, we estimated the degree to which the annual spatial autocorrelations in density are influenced by temperature. Second, we estimated and mapped the local effects of temperature and strength of density dependence on annual changes in density. Finally, we measured the relative effects of temperature and density dependence on the spatial synchrony in changes in density. Temperature influenced the annual spatial autocorrelation in density more in species with greater affinities to the benthos and to warmer waters. Temperature correlated positively with changes in density in the eastern Barents Sea for most species. Temperature had a weak synchronizing effect on density dynamics, while increasing strength of density dependence consistently desynchronised the dynamics. Quantifying the relative effects of different processes affecting population synchrony is important to better predict how population dynamics might change when environmental conditions change. Here, high degrees of spatial synchrony in the population dynamics remained unexplained by local temperature and density dependence, confirming the presence of additional synchronizing drivers, such as trophic interactions or harvesting.

Previous articleNext article No AccessNotes and CommentsMore Thoughts on Vertebrate Predator Regulation of PreySam Erlinge, Gorgen Goransson, Goran Hogstedt, Goran Jansson, Olof Liberg, Jon Loman, Ingvar N. Nilsson, Torbjorn von Schantz, and Magnus SylvenSam Erlinge Search for more articles by this author , Gorgen Goransson Search for more articles by this author , Goran Hogstedt Search for more articles by this author , Goran Jansson Search for more articles by this author , Olof Liberg Search for more articles by this author , Jon Loman Search for more articles by this author , Ingvar N. Nilsson Search for more articles by this author , Torbjorn von Schantz Search for more articles by this author , and Magnus Sylven Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The American Naturalist Volume 132, Number 1Jul., 1988 Published for The American Society of Naturalists Article DOIhttps://doi.org/10.1086/284842 Views: 3Total views on this site Citations: 21Citations are reported from Crossref Copyright 1988 The University of ChicagoPDF download Crossref reports the following articles citing this article:Anders Pape Møller, Timothy A. Mousseau Assessing effects of radiation on abundance of mammals and predator–prey interactions in Chernobyl using tracks in the snow, Ecological Indicators 26 (Mar 2013): 112–116.https://doi.org/10.1016/j.ecolind.2012.10.025Alexandre Millon, Jan Tøttrup Nielsen, Vincent Bretagnolle, Anders Pape Møller Predator-prey relationships in a changing environment: the case of the sparrowhawk and its avian prey community in a rural area, Journal of Animal Ecology 78, no.55 (Jul 2009): 1086–1095.https://doi.org/10.1111/j.1365-2656.2009.01575.xCornelia Kraus, Heiko G. Rödel Where have all the cavies gone? Causes and consequences of predation by the minor grison on a wild cavy population, Oikos 105, no.33 (Jun 2004): 489–500.https://doi.org/10.1111/j.0030-1299.2004.12941.xA. R. E. Sinclair Mammal population regulation, keystone processes and ecosystem dynamics, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 358, no.14381438 (Aug 2003): 1729–1740.https://doi.org/10.1098/rstb.2003.1359G. L. Blackwell, M. A. Potter, J. A. McLennan, E. O. Minot The role of predators in ship rat and house mouse population eruptions: drivers or passengers?, Oikos 100, no.33 (Apr 2003): 601–613.https://doi.org/10.1034/j.1600-0706.2003.11026.xTero Klemola, Miia Tanhuanpää, Erkki Korpimäki, Kai Ruohomäki Specialist and generalist natural enemies as an explanation for geographical gradients in population cycles of northern herbivores, Oikos 99, no.11 (Nov 2002): 83–94.https://doi.org/10.1034/j.1600-0706.2002.990109.xG.L Blackwell, M.A Potter, E.O Minot Rodent and predator population dynamics in an eruptive system, Ecological Modelling 142, no.33 (Aug 2001): 227–245.https://doi.org/10.1016/S0304-3800(01)00327-1Ilkka Hanski, Heikki Henttonen, Erkki Korpimäki, Lauri Oksanen, Peter Turchin SMALL-RODENT DYNAMICS AND PREDATION, Ecology 82, no.66 (Jun 2001): 1505–1520.https://doi.org/10.1890/0012-9658(2001)082[1505:SRDAP]2.0.CO;2Lisa M Sheffield, Jamie R Crait, W Daniel Edge, Guiming Wang Response of American kestrels and gray-tailed voles to vegetation height and supplemental perches, Canadian Journal of Zoology 79, no.33 (Mar 2001): 380–385.https://doi.org/10.1139/z00-220JAN LINDSTRÖM, ESA RANTA, HANNA KOKKO, PER LUNDBERG, VEIJO KAITALA From arctic lemmings to adaptive dynamics: Charles Elton's legacy in population ecology, Biological Reviews 76, no.11 (Jan 2007): 129–158.https://doi.org/10.1111/j.1469-185X.2000.tb00061.xT. 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Density dependence in population growth rates is of immense importance to ecological theory and application, but is difficult to estimate. The Global Population Dynamics Database (GPDD), one of the largest collections of population time series available, has been extensively used to study cross-taxa patterns in density dependence. A major difficulty with assessing density dependence from time series is that uncertainty in population abundance estimates can cause strong bias in both tests and estimates of strength. We analyse 627 data sets in the GPDD using Gompertz population models and account for uncertainty via the Kalman filter. Results suggest that at least 45% of the time series display density dependence, but that it is weak and difficult to detect for a large fraction. When uncertainty is ignored, magnitude of and evidence for density dependence is strong, illustrating that uncertainty in abundance estimates qualitatively changes conclusions about density dependence drawn from the GPDD.

Research on mammals has had an important role in our understanding of population ecology and the development of population models. Important areas of research have included studies on density dependence, predator-prey theory, disturbance dynamics, the use of models for synthesis of knowledge and as management tools, and approaches to validating models of population dynamics. This overview briefly discusses these areas of research and notes the relevant contributions of the following chapters in this volume. A common feature of these chapters is the use of models for assessing management strategies, a task for which stochastic population models such as RAMAS Metapop seem most suited. One area of research that requires further work is the development of efficient methods for analyzing these models so that optimal management strategies can be determined. Research on the population ecology of mammals has played an important part in many developments in population ecology. Chapter 39 on snowshoe hares by Griffin and Mills reminds us of the snowshoe hare–lynx cycle in Canada. It is perhaps one of the most widely known examples of predator-prey dynamics, has one of the longest time series, and has contributed substantially to our understanding of predator-prey dynamics (Krebs et al. 2001). The potential influence of predation (or other trophic interactions) is either ignored in most models of population viability or subsumed within the vital rates.

Some of the most interesting debates in population ecology have taken place within the context of population cycles. Their study has been a fertile ground for the development of ideas on how population models should be formulated and confronted with data. It is the setting in which the use of field experiments became established in ecology (e.g., Krebs and DeLong 1965), and also the context of many methodological and conceptual developments in the fields of population demography (Leslie and Ranson 1940), pest management (Berryman 1982), and community dynamics (Sinclair et al. 2000). Yet, as with many other issues in population dynamics, identifying without ambiguity the causes of population cycles in general, and for any organism in particular, continues to prove an extraordinarily difficult task. The major purpose of this book is to review recent research developments on the role of food web architecture, and more specifically on the effects of food, predators, and pathogens in population cycles. Its stated aim is to present evidence that population cycles could be caused by food web architecture in some natural systems. Whereas in chapter 1 Alan Berryman promotes a research program centered on the analysis of time series data for formulating, selecting, and even testing hypotheses on population cycles, the case studies encompass a much broader diversity of research approaches. The authors and coworkers of the seven case studies have combined time series analysis, model building, natural history observation, and experiments in different proportions to reach the conclusion that trophic interactions play an important role in generating cyclic dynamics. This diversity of approaches reflects, in part, a taxonomic divide between vertebrates and invertebrates, experiments being more common with the former, but also profound differences in research traditions. Indeed, the investment required to estimate population size and quantify the causes of mortality of moths and beetles is substantially less than that required for estimating the abundance of voles, hares, and grouse and their predators. From these practical constraints, divergent research traditions have evolved.

Long‐term studies of cyclic rodent populations have contributed fundamentally to the development of population ecology. Pioneering rodent studies have shown macroecological patterns of population dynamics in relation to latitude and have inspired similar studies in several other taxa. Nevertheless, such studies have not been able to disentangle the role of different environmental variables in shaping the macroecological patterns. We collected rodent time‐series from 26 locations spanning 10 latitudinal degrees in the tundra biome of Fennoscandia and assessed how population dynamics characteristics of the most prevalent species varied with latitude and environmental variables. While we found no relationship between latitude and population cycle peak interval, other characteristics of population dynamics showed latitudinal patterns. The environmental predictor variables provided insight into causes of these patterns, as 1) increased proportion of optimal habitat in the landscape led to higher density amplitudes in all species and 2) mid‐winter climate variability lowered the amplitude in Norwegian lemmings and grey‐sided voles. These results indicate that biome‐scale climate and landscape change can be expected to have profound impacts on rodent population cycles and that the macro‐ecology of such functionally important tundra ecosystem characteristics is likely to be subjected to transient dynamics.