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Availability of food may play a number of different dynamical roles in rodent-vegetation systems. Consideration of a suite of rodent-vegetation models, ranging from very simple ones to a model of medium complexity tailored to a specific system (brown lemmings at Point Barrow, Alaska, USA), suggested several general principles. If vegetation grows logistically following an herbivory event (a standard assumption of previously advanced models for herbivore-plant interactions), then almost any biologically reasonable combinations of parameters characterizing rodent-vegetation systems would result in population cycles. We argue, however, that the assumption of logistic growth of the food supply may be appropriate for only a few species, such as moss-eating lemmings. The dynamics of food supply for many arvicoline (microtine) rodents may be better described by a \"linear initial regrowth\" model, which exhibits globally stable dynamics. If this is so, quantitative interactions with food supply are unlikely to explain multiannual population cycles for most boreal or temperate voles. The role of food in population dynamics, however, is not limited to its potential to generate cycles. A tritrophic model including vegetation, rodents, and their specialist predators suggests that food limitation may provide direct density dependence needed for sustained oscillations in this system (which is usually modeled by a phenomenological logistic term in the prey equation). We relate the general theory that we developed to one specific system where we have enough data to arrive at reasonable estimates for most of the parameters-brown lemmings at Point Barrow. The Barrow model exhibits oscillations of the approximately correct period and amplitude, thus giving some theoretical support to the food hypothesis. Nevertheless, we suggest that this result should be treated cautiously because key events explaining the population cycle in the model occur during winter, but winter biology of lemmings is still poorly understood.

The hypothesis that the regular multiannual population oscillations of boreal and arctic small rodents (voles and lemmings) are driven by predation is as old as the scientific study of rodent cycles itself. Subsequently, for several decades, the predation hypothesis fell into disrepute, possibly because the views about predation and rodent dynamics were too simplistic. Here we review the work that has been done on the predation hypothesis primarily in Fennoscandia over the past decade. Models of predator-prey interaction have been constructed for the least weasel (Mustela nivalis) and the field vole (Microtus agrestis), which are considered to be the key specialist predator and the key prey species in the multispecies communities in the boreal forest region in Fennoscandia. The basic model has been parameterized with independent field data, and it predicts well the main features of the observed dynamics. An extension of the model also including generalist and nomadic avian predators predicts correctly the well-documented and striking geographic gradient in rodent oscillations in Fennoscandia, with the amplitude and cycle period decreasing from north to south. These geographic changes are attributed to the observed latitudinal change in the density of generalist and nomadic predators, which are expected to have a stabilizing effect on rodent dynamics. We review the other observational, modeling, and experimental results bearing on the predation hypothesis and conclude that it accounts well for the broad patterns in rodent oscillations in Fennoscandia. We discuss the application of the predation hypothesis to other regions in the northern hemisphere. The predation hypothesis does not make predictions about multiannual and latitudinal changes in body size, behavior, and demography of rodents, which may have some population-dynamic consequences. With the current evidence, however, we consider it unlikely that the phenotypic and genotypic composition of populations would be instrumental for generating the broad patterns in rodent oscillations.

Four paradigms can be followed to help us understand the dynamics of rodent populations. Natural observations are the traditional way to do ecology and it is important to have a good description of the population changes that are to be explained. Laboratory experiments were used in the 1940s and 1950s but provided little insight into events in the field. Field experiments began in the 1950s and have provided the greatest insights into the factors causing changes in numbers. Six factors have been manipulated in field experiments: food, predators, cover, density, physiological condition, and genetic composition. Field experiments can be used to test single-factor or multi-factor hypotheses of population regulation. They have the additional advantage of defining operationally verbal expressions like \"food-limitation\" that provoke fuzzy thinking. There is no need to separate natural observations from field experiments because they are the \"control\" for any manipulation done in the field. Mathematical modelling would seem to be the best of all possible worlds, but in rodent population dynamics it has been the worst because we do not know what the relevant variables to model are. Mathematical models are not a means of discovery and cannot be used to reject logically impossible ideas in the real world. Stenseth's attempt to reject the Chitty hypothesis as logically impossible is itself logically impossible. Whether the Chitty hypothesis is correct or not can be determined only by field experiments. Nor are mathematical models useful for defining concepts operationally in ecology, and I doubt if models ever produce new principles in ecology. I argue that the only useful goal for mathematical modellers in rodent ecology is to analyze how particular variables (like female territoriality) may affect population dynamics. This goal can be achieved only by a closer liaison between modellers and field ecologists at every step in the analysis.

This is an attempt to answer the question why there are great differences of opinion about the value of mathematical modelling in ecology. Some reasons for the gap between empirical and theoretical ecologists are discussed, examples which show the necessity of mathematical modelling in ecology are presented, and suggestions as to what can be done to close this gap between the empirically and mathematically minded ecologists are offered. Although ecology cannot progress without the applications of mathematical models, such models are of value only when they are applied and tested by field and laboratory ecologists.

Mathematical models attempting to illuminate problems in rodent ecology have not been very successful; fairly few new insights have emerged. It is suggested that models should not be developed for planning or directing new research, or to formulate primary hypotheses, but to check consistency and logic of predictions of important hypotheses generated by empiricists. Important factors in the population ecology of small rodents are thought to be detected by people actively engaged in field research while problems with factor interactions, quantification or range of applicability will be disclosed by modelling, at least in more complicated hypotheses. The latter treatment may also be useful in hypotheses for larger organisms to be tested under crucial field conditions rather than with field experiments. In such cases close cooperation between empricists and modellers is necessary.

Lemmings are a key component of tundra food webs and changes in their dynamics can affect the whole ecosystem. We present a comprehensive overview of lemming monitoring and research activities, and assess recent trends in lemming abundance across the circumpolar Arctic. Since 2000, lemmings have been monitored at 49 sites of which 38 are still active. The sites were not evenly distributed with notably Russia and high Arctic Canada underrepresented. Abundance was monitored at all sites, but methods and levels of precision varied greatly. Other important attributes such as health, genetic diversity and potential drivers of population change, were often not monitored. There was no evidence that lemming populations were decreasing in general, although a negative trend was detected for low arctic populations sympatric with voles. To keep the pace of arctic change, we recommend maintaining long-term programmes while harmonizing methods, improving spatial coverage and integrating an ecosystem perspective.

Winter is energetically challenging for small herbivores because of greater energy requirements for thermogenesis at a time when little energy is available. We formulated a model predicting optimal wintering body size, accounting for the scaling of both energy expenditure and assimilation to body size, and the trade‐off between survival benefits of a large size and avoiding survival costs of foraging. The model predicts that if the energy cost of maintaining a given body mass differs between environments, animals should be smaller in the more demanding environments, and there should be a negative correlation between body mass and daily energy expenditure (DEE) across environments. In contrast, if animals adjust their energy intake according to variation in survival costs of foraging, there should be a positive correlation between body mass and DEE. Decreasing temperature always increases equilibrium DEE, but optimal body mass may either increase or decrease in colder climates depending on the exact effects of temperature on mass‐specific survival and energy demands. Measuring DEE with doubly labeled water on winteringMicrotus agrestisat four field sites, we found that DEE was highest at the sites where voles were smallest despite a positive correlation between DEE and body mass within sites. This suggests that variation in wintering body mass between sites was due to variation in food quality/availability and not adjustments in foraging activity to varying risks of predation.

Competition between individuals of the same or different species affects spatial distribution of organisms at any given time. Consequently, a species geographical distribution is related to population dynamics through density-dependent processes. Small Arctic rodents are important prey species in many Arctic ecosystems. They commonly show large cyclic fluctuations in abundance offering a potential to investigate how landscape characteristics relates to density-dependent habitat selection. Based on long-term summer trapping data of the Norwegian lemming (Lemmus lemmus) in the Scandinavian Mountain tundra, we applied species distribution modeling to test if the effect of environmental variables on lemming distribution changed in relation to the lemming cycle. Lemmings were less habitat specific during the peak phase, as their distribution was only related to primary productivity. During the increase phase, however, lemming distribution was, in addition, associated with landscape characteristics such as hilly terrain and slopes that are less likely to get flooded. Lemming habitat use varied during the cycle, suggesting density-dependent changes in habitat selection that could be explained by intraspecific competition. We believe that the distribution patterns observed during the increase phase show a stronger ecological signal for habitat preference and that the less specific habitat use during the peak phase is a result of lemmings grazing themselves out of the best habitat as the population grows. Future research on lemming winter distribution would make it possible to investigate the year around strategies of habitat selection in lemmings and a better understanding of a fundamental actor in many Arctic ecosystems.

“Bottom‐up” influences, that is, masting, plus population density and climate, commonly influence woodland rodent demography. However, “top‐down” influences (predation) also intervene. Here, we assess the impacts of masting, climate, and density on rodent populations placed in the context of what is known about “top‐down” influences. To explain between‐year variations in bank vole Myodes glareolus and wood mouse Apodemus sylvaticus population demography, we applied a state‐space model to 33 years of catch‐mark‐release live‐trapping, winter temperature, and precise mast‐collection data. Experimental mast additions aided interpretation. Rodent numbers in European ash Fraxinus excelsior woodland were estimated (May/June, November/December). December–March mean minimum daily temperature represented winter severity. Total marked adult mice/voles (and juveniles in May/June) provided density indices validated against a model‐generated population estimate; this allowed estimation of the structure of a time‐series model and the demographic impacts of the climatic/biological variables. During two winters of insignificant fruit‐fall, 6.79 g/m2 sterilized ash seed (as fruit) was distributed over an equivalent woodland similarly live‐trapped. September–March fruit‐fall strongly increased bank vole spring reproductive rate and winter and summer population growth rates; colder winters weakly reduced winter population growth. September–March fruit‐fall and warmer winters marginally increased wood mouse spring reproductive rate and September–December fruit‐fall weakly elevated summer population growth. Density dependence significantly reduced both species' population growth. Fruit‐fall impacts on demography still appeared after a year. Experimental ash fruit addition confirmed its positive influence on bank vole winter population growth with probable moderation by colder temperatures. The models show the strong impact of masting as a “bottom‐up” influence on rodent demography, emphasizing independent masting and weather influences; delayed effects of masting; and the importance of density dependence and its interaction with masting. We conclude that these rodents show strong “bottom‐up” and density‐dependent influences on demography moderated by winter temperature. “Top‐down” influences appear weak and need further investigation. The “bottom‐up” influence of masting, plus population density and climate, was studied by state‐space modelling of a 33‐years live‐trapping data set of bank voles and wood mice in an European ash woodland. There were strong positive effects of masting on bank vole reproductive and population growth rates and weaker influences on wood mouse demographics; density dependence significantly reduced population growth in both species and in bank voles winter temperature appeared to have a modifying influence on winter demography. We conclude that population density and the “bottom‐up” influence of masting both have a strong influence on rodent demography but “top‐down” (predation) influences need further study.

The study of the relative importance of the feedback structure (intrinsic processes) and exogenous (climatic or environmental) factors in determining population dynamics, in particular the interaction between density-dependence and climate, is a major question in population ecology. We sought to explain the numerical fluctuations of 2 sympatric rodent species at one well-studied site in semi-arid Chile using simple theoretically based population dynamics models and Royama's theoretical framework for analyzing the dynamics of populations influenced by exogenous climatic forces. We found that rainfall effects appear to operate in a different manner on the 2 rodent species. For one species (Phyllotis darwini), rainfall appeared to influence the carrying capacity of the environment, whereas for a second (Akodon olivaceus) the rainfall effect had a primarily additive influence on the maximum per capita growth rates.