Fluctuating life-history traits in overwintering field voles (Microtus agrestis) Torbjørn Ergon

Transcription

1 Fluctuating life-history traits in overwintering field voles (Microtus agrestis) Torbjørn Ergon Dissertation presented for the degree of Doctor Scientiarum Department of Biology Faculty of Mathematics and Natural Sciences University of Oslo 2003

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3 Contents 1 INTRODUCTION Volelife-cycles Hypothesesforvariationinlife-historytraits Studysystem SUMMARY OF THE PAPERS Mainresults Paper I A common garden experiment Paper II A transplant experiment Paper III Body size and energy expenditure Paper IV Optimal onset of reproduction in voles that don t know everything Conclusionsfromtheempiricalresults Relevanceformanagement GENERAL DISCUSSION Experimental and observational approaches in population studies 12 4 SUMMARY 23 5 REFERENCES 24 6 LIST OF PAPERS 31

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5 1 Introduction Imagine going to a forest clear-cut to check vole traps an early morning in the spring. You weigh the voles, record their data and release them. All the voles you see are less than 30 grams and no female show signs of reproducing. You then go to another site a few kilometers away. Here the males are all above 40 grams and all the females are either highly pregnant or nursing young - the spring has come! Any curious person would wonder why? So did I, and indeed, so have many before me. Dennis Chitty (1952) was the firsttonotethatoverwinteredfield voles during a population decline at Lake Vyrnwy, Wales, had lower body weights in the spring and initiated spring reproduction later compared to the previous spring when the population reached peak densities 1. This has later been recognised as a widespread phenomenon in fluctuating populations of voles, lemmings and even snowshoe hares: Overwintering animals initiate spring reproduction earlier and reach higher adult body size at increasing and peak densities than in years when population densities are declining 2. Thisdissertationisaboutthecausesofthe variation in these two key life-history traits of overwintering small rodents: body size maintained over winter and the time of reproductive onset in the spring. 1.1 Vole life-cycles Life history patterns of voles and lemmings 3 are characterised by short life-spans (usually less than one year), potentially young age at maturation, high fecundity, short gestation period and repeated breeding within the same reproductive season 4. There is also typically very high flexibility in these life-history traits. This is most evident in seasonal environments where breeding is restricted to the growth season of the food plants. Individuals born early in the breeding season will usually breed at young age whereas those born later in the season may delay maturation until the next year (sometimes more than 8 months). One peculiarity of voles life-histories is that they maintain a lower body size during winter than in the summer: young animals that delay reproduction stop growing at small body size and do not resume growth until the next breeding season, and reproductive animals typically reduce body mass by 20-40% as a response to declining day-length prior to the winter 5. A sketch of this general life-history pattern of 1 The large differences in body mass reported in this pioneering work were probably mainly caused by differences in the time that reproduction was initiated in the spring. However, it has later been demonstrated that individuals grow faster and reach higher adult size during the increase and peak phases of the population fluctuations than when the populations are declining (see Chitty 1996 pp and Paper II). 2 Reviews in Chitty (1996), Boonstra and Krebs (1979), Krebs and Myers (1974), and introduction of Paper III. 3 Subfamily Arvicolinae (= Microtinae). 4 In field voles, females may conceive before 3 weeks of age, gestation period is days and litters usually have 3-8 pups. 5 See introduction of Paper III.

6 2 A - Reproduction B - Growth OW YB Body mass OW NB YB NB Winter Spring Summer Autumn Winter Spring Summer Autumn Figure 1: Seasonal life-history patterns of voles. A, Overwintered animals (OW) will breed repeatedly during the reproductive season (spring and summer in northern and alpine environments). Young of the year may breed in the year of birth (young breeders; YB), or they may delay reproduction until the next spring (non-breeders; NB). B, Overwintered animals maintain a low body mass throughout the winter but grow rapidly at the onset of reproduction in the spring (females start growing when they conceive their first litter). Young breeders grow large, whereas non-breeders suspend growth at as small size and do not resume growing until they become reproductively active in the following spring. Breeding animals loose body mass before the winter. It is mainly the animals that delay reproduction that survive the winter and breed in the following spring. (The sketch is based on descriptions by Agrell et al. (1992), Gliwicz (1996), Gyug and Millar (1980), Lambin and Yoccoz (2001), Negus and Berger (1988), and own observations (see Paper I and Paper II). Note that there is large variation in these patterns between species, environments, and between years within the same population.) volesispresentedinfigure1. The patterns of growth, maturation and reproduction are not just related to the time of the year the individuals are born, but there is typically also large variation in the seasonal patterns between years. Onset of spring reproduction, for example, may in some populations occur more than six weeks earlier in some yearsthaninotheryears 6. The tradition in population studies of small rodent cycles has been to describe such year-to-year variation in life-history traits in relation to cyclic phase (defined by current densities and rate of change 7 )rather than in relation to present and previous densities. There are in particular three traits that have been described to vary in relation to the phases of the population cycles 8 : 1. reproducing animals become heavier during the increase and peak 6 See introduction of Paper IV. 7 See Krebs and Myers (1974) for definitions of the different phases. 8 See reviews by Batzli (1992), Krebs and Myers (1974), and Stenseth and Ims (1993).

7 3 years than in other years, 2. fewer young animals mature in their year of birth when densities are high, and 3. reproduction commences early in the spring when the population is increasing and late during population declines. Body size will in itself not directly affect the population dynamics or the fitness of the individuals. Nevertheless, growth and maintenance of a given body size are generally important life-history traits because they are intimately linked to tradeoffs and constraints involving fecundity, scheduling of reproduction and survival 9. Furthermore, demographic processes of birth and survival may also alter the body-size distribution at the population level. Traditional studies of life-history variation between species see traits such as growth, sexual maturation, fecundity and survival only as functions of the organisms age 10. This approach is obviously of little use when studying variation within populations where there are large differences in the schedules of growth and reproduction between individuals born at different times of the year. Even among animals born at the same time of the year there may be large variation in traits such as onset of spring reproduction and adult body mass. In such cases one must apply a more general approach where life-history traits are considered to be functions of the total internal and external state of the individuals and their surrounding environment 11. Internal state variables describe the condition of the body and include variables such as body size, fat reserves, age and genotype 12, whereas external state refers to environmental variables such as day-length (season), availability of food and density of predators and competitors. Internal state variables may be flexible, such as fat reserves or the state of the immune system, or they may be fixed in the sense that they are not affected by the environment (e.g. age and genotype). Flexible internal state variables typically depend on earlier environmental conditions or previous life-history decisions (e.g., poorer body condition after periods of food shortage or after reproduction), and they may vary in degree of flexibility 13. The ability of a single genotype to produce different phenotypes (e.g. life-history trait values) in different environments is called phenotypic plasticity, and the functional relations between the phenotypic values and the environmental state variables are called norms of reaction See Sauer and Slade (1988) and Sibly (1986). 10 Roff (1992), Stearns (1992). 11 McNamara and Houston (1996). 12 In the context of the hypotheses presented below it is convenient to define age and genotype as internal state variables, although in other contexts they may not be defined as such. 13 Growth in mammals may for example be severely retarded by adverse conditions in early life due to poor conditions of the mother during gestation or lactation, which may affect the condition throughout the lives of the individuals (if compensatory growth (Sibly 1986) is not effective), i.e., maternal effects (Bernardo 1996; Rossiter 1996). 14 Roff (2002).

8 4 Box 1. Hypotheses for general mechanisms of delayed density-dependent patterns in lifehistory traits. Where does the memory of past densities reside? Individual mechanisms Population mechanisms 1. Memory in the environment due to trophic interactions with: a. Food resources (Batzli 1992, see also Discussion in Paper IV). b. Predators (Korpimäki and Krebs 1996; Ylönen 1994). c. Pathogens (Anderson and May 1978; Feore et al. 1997). 2. Memory in the individuals: a. Persistent phenotypic changes in the quality of the individuals due to the environment experienced in early life (including maternal effects) (Boonstra and Boag 1987; Inchausti and Ginzburg 1998). 3. Memory in population composition: a. Genetic differences due to density dependent selection (Charnov and Finerty 1980; Chitty 1967; Nelson 1987). b. Alteration in the age structure of the population due to density dependent demographic processes (Boonstra 1994; Tkadlec and Zejda 1998). Extrinsic regulation Intrinsic regulation Hypotheses 1 and 2 represent individual level mechanisms in the sense that individuals of the same age and genotype are assumed to behave differently depending on earlier population densities (phenotypic plasticity), whereas Hypothesis 3 represents population level changes in the structure of the population with respect to fixed phenotypes. As for mechanisms for population regulation, Hypothesis 1 represents extrinsic mechanisms, whereas Hypotheses 2 and 3 represent intrinsic mechanisms for delayed density dependence (although changes in population structure or the internal state of the individuals may be due to extrinsic trophic interactions in the earlier environment). 1.2 Hypotheses for variation in life-history traits One way to structure hypothesised mechanisms for delayed density dependence in onset of spring reproduction and other life-history traits is to ask the question Where does the memory of past densities reside? (Box 1). If the performance of individuals of the same age and genotype varies in relation to previous densities, then there must either be some memory in the surrounding environment due to trophic interactions (Hypothesis 1 in Box 1) or the individuals must remember past densities through their physiology (Hypothesis 2). Delayed density dependence at the population level may also occur due to changes in the composition of the population with respect to genotypes and age (Hypothesis 3). One of the most stimulating debates in population ecology is about to what degree populations are regulated through trophic interactions with other species

9 5 (Hypothesis 1) or through intra-population (self-regulating) mechanisms (Hypotheses 2 and 3) 15. Population regulation is a result of density dependent (direct or delayed) variation in life-history traits of individuals (including time of death) 16. The studies in this dissertation are hence relevant for the debate about population regulation, although I address mechanisms for delayed density dependence only in some life history traits: body mass and onset of spring reproduction Study system The field studies took place in Kielder forests on the border between England and Scotland, one of the areas where the pioneering work on population fluctuations by Charles Elton and co-workers were carried out 18. In this region, which is largely covered by spruce plantations, field voles (Microtus agrestis) are confined to distinct grassland clear-cuts surrounded by dense tree stands that lack ground vegetation and are hence uninhabitable for voles. The fact that sub-populations of voles inhabiting these clear-cuts fluctuate somewhat asynchronously, but nevertheless with a regular period of 3 5 years, enables replicated short-term studies of density dependence in life-history traits. Studies of wintering voles and onset of spring reproduction are also made easy by the fact that there is no permanent snow cover during winter Summary of the Papers 2.1 Main results In the two first papers of this dissertation we address the question of whether life-history variation in overwintering field voles is due to variation in the internal state of the individuals (Hypotheses 2 and 3 in Box 1) or due to variation in the external state of the immediate environment (Hypothesis 1 in Box 1). Paper I presents a common garden experiment where voles from different areas were bred under standardized conditions in the lab, and Paper II presents a field transplant experiment where voles were swapped between study sites during mid-winter and later monitored by capture-mark-recapture live-trapping. Both these studies suggest that the main cause of variation in life-history traits of field voles are individual responses to the immediate environment. Paper III 15 See Berryman (2002c), Chitty (1996), Krebs (1978) and Stenseth (1999). 16 Density regulation on a local scale may, of course, also be due to immigration and emigration 17 Note, however, that some of my colleagues have studied the impact of weasel predation on survival (Graham and Lambin 2002), and studies on disease dynamics are currently being undertaken (see Cavanagh et al. 2002). 18 See Chitty (1996 pp ); Newcastleton is located within this study area. 19 For detailed descriptions of the study system see Lambin et al. (1998; 2000), MacKinnon et al. (2001) and Paper I and III of this dissertation.

10 6 and Paper IV investigate the mechanisms of these responses in more detail. Paper III focus on the relations between body mass and energy expenditure (measuredbytheuseofdoublylabelledwater)ofwinteringvoles,andpaper IV focus on the optimal time to initiate spring reproduction when animals perceive the state of their environment with varying degrees of precision Paper I A common garden experiment In the study of Paper I we sampled voles from two neighbouring out-of phase valleys and bred them under standardized lab conditions for two generations. We also monitored the source populations by capture-mark-recapture in the field and compared the patterns of reproduction observed in the lab with patterns of maturation and recruitment in the field. In one of the valleys (Kershopearea) densities were high in the previous year, but, unexpectedly, densities did not decline during the year of study but remained at peak densities throughout the breeding season. However, animals in this area initiated spring reproduction late and did not reach very high body mass, and few young animals matured during the following summer. These characteristics are more typical for the decline phase of population cycles than for the peak phase 20. In the other area (Kielder-valley) where densities in the previous year were low, reproduction commenced about six weeks earlier, reproducing animal reached high body mass and juveniles continued to mature until late in the summer (typical increase phase ). Among the overwintered animals brought to the lab, we found that some of these differences were retained under the standardized conditions. However, this may be pertaining to the fact that we sampled voles when some reproduction was already initiated in the increase-area. Among the lab-born generations, on the other hand, we found no differences in the patterns of reproduction, suggesting that the large differences seen in the fieldwerenotduetogeneticdifferences 21 (cf. Hypothesis 3). One interesting observation from the lab was that there was an early seasonal decline in the probability that lab-born females, from both areas alike, would initiate reproduction (conceive). The pattern of decline was similar to the seasonal decline in maturation probability seen in the peak-area (Kershope). As the animals were reared in open sheds with no lighting, the probable reason for this strong seasonal effect was a response to the change in ambient photoperiod (day-length). This difference between animals in the lab versus animals at the increase-phase field-sites may suggest that the voles need some stimuli from their 20 At the time of writing of Paper I, the delayed density dependence in onset of spring reproduction was not well established in this study system. However, data from a larger number of sampling sites and years presented in Paper IV clearly shows that early commencement of the breeding season is associated with low densities in the previous spring (1 year lag) and a population increase during the previous summer. 21 Note however that, due to genotype-environment interactions, two genotypes may display different phenotypes in one environment (the field) but not in others (the lab).

11 7 food plants in order to mature 22. This may also explain why as many as 23% of the overwintered peak-area females never reproduced in the lab Paper II A transplant experiment The transplant experiment, Paper II, was more rigorous than the lab experiment because it took place under natural field condition. Voles were here swapped between four field sites after the breeding season and then monitored by capturemark-recapture in the following spring in order to separate the effects of previous and current environment on life-history traits of the overwintering voles (Hypothesis 1 vs. 2 and 3). Average body mass differed by about 18% between sites at the time of transplant (November/December), but body mass of the transplanted voles had already converged to the values prevailing at the target sites during the first trapping session in January/February. Over the following spring, voles at the different sites showed large variation in individual weight gain, onset of spring reproduction and survival (estimates of the latter are presented in Paper III and Paper IV). At the sites with the lowest overwintering body mass, individuals grew slower in the spring, reproduced later and had lower survival rates, but also for these traits there were no significant effects of source population. Thus, this experiment showed an overriding effect of the current environment on life-history traits of overwintering individuals (Hypothesis 1) Paper III Body size and energy expenditure The study presented in Paper III was carried out in conjunction with the transplant experiment, measuring daily energy expenditure (DEE) by the use of doubly labelled water on voles at the four study sites during mid-winter. Also here were there no significant effect of the source population, but the DEE measurements differed largely between sites. Voles had higher DEE at the sites where average body mass was lowest despite a positive relation between body mass and DEE among individuals within sites. An optimality model, focusing on the trade-off between energy acquisitioning and avoiding mortality risks of foraging, shows that such patterns between body mass and DEE should be expected if voles became smaller at the sites with the lowest body mass because energy was less available in the food plants at these sites. In contrast, if voles had become smaller because they restricted energy intake to avoid predation, then one should expect to see the same relationship between average body mass and DEE between the site-means as the relationship between individuals within sites (assuming a homogenous environment within sites). The model presented in this paper illustrates potential mechanisms for variation in body mass and energy expenditure of non-breeding animals more generally. 22 Animals were fed on unlimited high-quality protein-rich food in the lab, but they did not receive any fresh plant material. See discussion relating to 6-MBOA in Paper IV.

12 8 By explicitly taking into account how energy expenditure, energy assimilation and survival in cold climates are related to body size and foraging time, the model predicts the optimal body size in environments that differ in the energetic costs of maintaining a given size and/or in the survival costs of foraging. Specifically, it may facilitate understanding of how food quality, temperature and risk of predation influence variation in body mass and energy expenditure between seasons, populations (e.g., trends with climate) and species. Although exact mechanisms cannot of course be deduced from observed patterns, the model enables more meaningful interpretations of the variation in body mass and energy expenditure if these two traits are measured together (as a bi-variate response) and when the patterns of variation and co-variations are compared within and between locations/seasons/species 23. As we were mainly interested in studying causes of the variation in body mass of non-breeding wintering animals, the model does not explicitly account for effects of body mass on fecundity and interspecific competition, but it may be modified to do so Paper IV Optimal onset of reproduction in voles that don t know everything Paper IV focuses on the optimal time to commence seasonal reproduction for multivoltine organisms (organisms having several generations per year). In this paper I present a theoretical model focusing on the trade-off between early reproduction and high success of the first breeding attempt, but I also investigate how dependencies between pre-breeding survival and onset of reproduction (due to trade-offs, senescence or seasonal variation in survival) will influence the optimal strategies. In the case where there is only a dependency between time of reproduction and breeding success, and when animals (hypothetically) have perfect information about their environment, the model predicts that: 1) reproduction should start earlier when the difference between population growth in the breeding season and pre-breeding winter survival is high, and 2) breeding success at the optimum depends on how, but not when, breeding conditions improve. The latter implies that a one-week delay in the time that breeding conditions improve will lead to a one-week delay in the optimal time to initiate reproduction (if breeding conditions improve in the same manner). Thus, if the variation on onset of spring reproduction is only caused by variation in the time that breeding conditions improve, then expected success of the first breeding attempt should be constant, whereasifthevariationiscausedbyaresponsetovariationinpopulationgrowth rate and/or winter survival, breeding success should be lower when reproduction is initiated early. 23 In the paper we discuss potential causes of geographical trends (cf. Bergmann s rule ) and reasons for the fact that collared lemmings, unlike most microtines at northern latitudes, maintain a larger body mass during winter than during summer.

13 9 I further investigate how these predictions about breeding success and optimal time to initiate reproduction change when the animals, more realistically, cannot measure the state of their environment without error. I do this by using a simulation approach to search for optimal weightings of uncertain (imprecise) cues about the environmental state variables 24, and I show how the optimal norms of reaction, the expected phenotypic correlations and selection pressures depend on the precision of the cues used by the animals. Specifically, because it is optimaltobeconservativeinrespondingtoimpreciseenvironmentalcues,there should be less variation in the time of reproductive initiation when cues are more unreliable, and breeding success should be highest in years when breeding conditions improve early (and when reproduction is initiated early; i.e., a negative correlation between breeding date and breeding success). The predicted patterns in the variation of optimal breeding date and breeding success will also be greatly modified by dependencies between pre-breeding survival and breeding date. Such dependencies may arise due to trade-offs (i.e., if early reproduction requires the animals to maintain a morphological or physiological state that renders lower winter survival; e.g. body mass, see Paper III), senescence (pre-breeding survival declines with time due to ageing of the individuals) or to seasonal variation in survival (pre-breeding survival declines with time due to increased extrinsic mortality later in the spring; e.g., due to higher predation). If such dependencies are important, expected (optimal) breeding success may be drastically reduced in years when breeding conditions improve late. In this paper I also present data showing that onset of spring reproduction is delayed density dependent: breeding is generally initiated early in the spring when densities in the previous spring were low. However, there is no correlation between onset of spring reproduction and population growth during the previous non-reproductive season (winter survival) or during the following reproductive season in the direction predicted by the model. This is probably because the animals cannot measure these environmental state variables precisely. Also presented in Paper IV is an analysis on survival costs of reproducing at the four study sites included in Paper II and Paper III. This analysis shows that survival was particularly low for reproducing females at the site where reproduction was initiated the latest (a typical decline site with poor survival, low body masses and high rates of energy expenditure). This is consistent with the model if females at this site were forced to reproduce while the environment was still unfavourable due to dependencies between pre-breeding survival and the time that reproduction could be initiated (see above), or that breeding conditions improved very slowly. Such an association between late onset of reproduction (which is delayed density dependent) and low breeding success may greatly reinforce the delayed negative density dependence on population growth. 24 To simplify, I only studied the optimal response to cues about one state variable at a time, but it should be possible to expand the simulation approach to study the optimal responses to a set of dependent cues reflecting several state variables.

14 Conclusions from the empirical results In summary, I have derived at the following conclusions about variation in lifehistory traits of overwintering field voles in the Kielder forest area: 1. The time that spring reproduction is initiated is delayed density dependent with a one-year lag (Paper IV). 2. The memory of past conditions (see Box 1) resides in the environment rather than in the internal states of the individuals (Paper II). 3. Variation in overwintering body mass is due to variation in the energetic constraints rather than foraging responses to variation in risk of predation (Paper III). 4. Variation in onset of spring reproduction is related to variation in the time that breeding conditions improve rather than responses to cues reflecting variationinprospectsofsurvivalandfuturepopulationgrowth(paper IV). Although I have not studied any specific mechanisms explicitly with respect to environmental state variables and trophic interaction, I suggest that variation in the food quality/availability during winter and early spring is a likely cause of these results (Fig. 2). 2.3 Relevance for management Although the basic scientific issues relating to variation in life-history traits and demography are interesting in its own right, these issues are also relevant for conservation and management of endangered or harvested populations. Time-series analyses focusing on describing the direct and delayed densitydependence, as well as influence of density-independent factors, help us to understand how for example climatic change influence the dynamics of populations and the interactions between them 25. However, predictions from such models may fail when environmental state variables (or the covariance between them) are perturbed outside their normal (or previous) range. In building models intended to predict population responses to environmental change, it is essential to understand how individuals respond to their environment. In particular, it is important to know what environmental cues animals use in their life-history decisions and how they respond to these cues. In Paper IV, I discuss how the population s ability to sustain environmental change depends on the precision and accuracy of the environmental cues used by animals in their reproductive decisions. One situation where rapid environmental change may be particularly harmful is when reaction norms evolved under one set of environmental conditions become maladaptive when the covariation in environmental state variables 25 See the review by Stenseth et al. (2002a) for specific examples.

15 11 A Increase phase Spring Summer Winter Spring B Decline phase Spring Summer Winter Spring Figure 2: Hypothesised mechanism for delayed density dependence in winter/spring body mass and onset of spring reproduction. A. When rodent densities are low and grazing is moderate in the spring, perennial plants will accumulate resources in the roots. This provides an abundant energy source for the rodents during the following winter, enabling the maintenance of a larger wintering body mass (see Paper III). The plants use the stored energy reserves in the roots for an early and fast re-growth of assimilating shoots in the following spring, which enables the rodents to initiate spring reproduction early in the season (see Paper IV). B. When rodent densities are high, repeated grazing and re-growth of the emerging plant shoots in the spring depletes the stored energy reserves in the roots. This reduces the energy availability for the voles in the following winter, impede early re-growth of the vegetation in the following spring and hence prohibit an early start of the reproductive season of the rodents. See Discussion of Paper IV for details on the rationale of this hypothesis. are distorted. For example, if the time that food availability becomes sufficient to rear offspring changes, but the animals initiate reproduction at a certain daylength (enabling them to initiate reproduction before food becomes abundant), then there will be a mismatch between the reproductive strategies and food

16 12 availability, possibly causing severe population declines 26. Eco-physiology may help us to understand how individuals will respond to environmental change 27. Knowledge of simple physiological mechanisms will, however, not allow direct predictions of life-history responses when the environment changes. This is because the environmental conditions may affectasetof inter-dependent individual traits in intricate ways. For example, improved food quality may entertain both a higher body mass and a reduced foraging time, but the trade-off between maintaining a high body mass and reducing foraging time may depend on the prevailing risk of predation. The model presented in Paper III is an example of how physiological considerations and life-history trade-offs may be included in the same model to understand and predict individual responses to environmental change. 3 General Discussion Experimental and observational approaches in population studies 28 Thereweretwobearsyesterdayandtherearethree bears today. Does this mean that one bear has been born, or that 101 have been born and 100 have died? Wood (1994) 29 Much, if not most, population studies on small rodents have been motivated by a fascination for the pronounced population cycles observed in many populations of lemmings and voles. At least in Norway, one of the most commonly asked questions addressed to population ecologists by the public is: What causes lemming-years, and why do they occur regularly?. We usually give them answers of the type formulated by the Finnish naturalist Ehrström in 1852, who wisely introduced his report on mass movements of lemmings by saying: We are not aware of the causes of pronounced periodicity, while smaller fluctuations in nature, we understand only incomplete. 30 Although specific mechanisms are controversial, ecologists now seem to agree that small rodent population cycles are due to delayed negative density-dependent feedback processes, most likely caused by trophic interactions 31.Mystudiesare hence relevant to the question of what causes cycles because I address mechanisms for delayed density-dependent life-history traits in the overwintering co- 26 See specific examples in Stenseth and Mysterud (2002). 27 Le Maho (2002). 28 I have elaborated on some of the ideas presented here in an essay written as part of a PhDcourse in philosophy of science that I followed in 1999 (available at Questions, approaches and paradigms in studies of small rodent population cycles; a search for the Holy Grail. 29 Cited from Caswell (2000), p Cited from Klemola (1999) who referred to Ehrstöm (1852). 31 Stenseth (1999) and Berryman (2002c).

17 13 horts. However, as this is just one aspect of the complex demographic processes that shape the multi-annual population fluctuations, I will not speculate on how relevant the mechanisms that I have observed (see section 2.2) are for the occurrence of regular population cycles 32. Instead, I will discuss some approaches that may be taken to understand the mechanisms of such cycles; in particular the roles of experimental and observational studies. Levels of understanding; mechanisms, processes and patterns Population dynamic patterns, such as cycles, may be understood at many levels. At the population level the dynamics may be understood in terms of direct and delayeddensitydependentstructuresofpopulationgrowth(aswellasexogenous forcing). This is often the aim of time-series analysis of animal numbers. The dynamic results of density dependent structures involving non-linearity, seasonality and stochasticity are far from trivial, and mathematical theory is essential in understanding the dynamics at this level 33. Such mathematical modelling may be used to describe and predict the change in animal numbers without understanding the causes of variation in population growth at the demographic or mechanistic levels. With knowledge at the demographic level one understands the causes of variation in population growth in terms of variation in demographic rates such as maturation rates, fecundity and survival without necessarily understanding the causes, or mechanisms, of this variation beyond descriptions relating to present and previous densities, seasons or exogenous variables. With such knowledge one are able to construct population dynamic models as some sort of book-keeping of individuals 34. By knowledge at the mechanistic level I mean that one has some sort of understanding of what causes the variation in the demographic rates (or life-history traits), for example that delayed density dependent variation in survival is due to predation. Such mechanisms may be determined at a general level as in Box 1 or at a much more detailed level with respect to physiological and behavioural responses, and with respect to the nature of the delays in trophic interactions (e.g. Fig. 2). It is a goal of science in general to understand patterns and processes at a much 32 Preliminary simulations of matrix projection models suggest that the delayed density dependence in onset of spring reproduction observed in Paper IV may not be sufficiently strong to cause population cycles on its own. However, if late onset of spring reproduction is associated with particularly low survival during the first breeding attempt (as was observed at one of my study sites, see Paper IV), then regular cycles may occur. I believe, however, that more information about the demographic processes is needed before such specific modelling becomes very relevant (e.g., variation in onset of spring reproduction has less relevance for the multi-annual cycles if population growth is generally high in the summer and direct density dependence is strong). 33 E.g. Turchin (2003). 34 See The individual based reductionistic school in Box 2. Note that population level models may be required to obtain a theoretical understanding of the population level processes of the dynamics, see Turchin (2003).

18 14 as possible detailed mechanistic level. Indeed, this is the motivation for most population studies of small rodents. However, trying to understand population dynamic patterns such as regular cycles in terms of the underlying mechanisms is not an easy task. When undertaking this task I think it is important to reflect upon two points, which may be posed as postulates: Postulate 1 Different mechanisms may lead to the same population dynamics. Postulate 2 The same mechanism may lead to different population dynamics. Postulate 1 is obvious: a reduction in fecundity due to impaired food quality may result in the same change in numbers as decreased survival due to predation. Postulate 2 requires explanation. By the same mechanism I mean structurally or qualitatively the same mechanism. Structurally equal mechanisms may be modelled by the same model, but parameter values may differ 35. Anyone who has played with non-linear dynamic models knows that even minute changes in the (system specific) parameter values may completely change the dynamics of the model 36. The difference in parameter values required to move from a non-cyclic to a cyclic dynamic is often, in parts of the parameter space, far more subtle than one would specify in a specific hypothesis. Thus, in some sense two cyclic populations may have less in common than a non-cyclic and a cyclic population in terms of the underlying demographic mechanisms of the dynamics (although in the latter case the two populations, or systems, would occupy different regions of the variable-space). Further, an apparently drastic change in the population dynamic pattern (e.g. a drastic shift in the amplitude of the cycles) does not imply that there necessarily has been any major change in the underlying mechanisms of the dynamics (especially if non-linear density dependence is involved; see footnote 36). General approaches There are many approaches taken to study the causes of small rodent population cycles. I have described three traditions, or schools, in Box 2. These approaches look at the problem of what causes cycles in different, and largely complementary, ways. There have, however been much discussion about how science should be 35 See McCauley and Murdoch (1987) for a discussion on this topic. 36 For example, consider the discrete logistic equation, N t+1 = rn t(k N t), where N t is the population size at time t, andwherer and K is the system specific parameters ( intrinsic growth rate and carrying capacity ). Even this very simple model may produce a wide range of dynamics including constant population size, cycles of any period and chaotic dynamics, and thedynamicsmayswitchfromonetypetoanotherwithsmallchangesinr (May and Oster 1976; Schaffer 1988). The chaotic dynamics of such models often have a rather regular period but erratic amplitude, and the dynamics may go through phases with highly variable amplitude and periodicity (Schaffer 1986, 1988; see McCauley et al. (1999) for examples of coexisting dynamic attractors in Daphnia algae systems.).

19 15 done between followers of the different traditions 37. Much of this discussion highlights the strengths and weaknesses of the different approaches, and much of the discussion just reflects that people have different scientific interests. However, it is also clear that people genuinely disagree on fundamental science-philosophic issues such as what justifies a conclusion. I will contribute to this debate with some views on how observational and experimental studies may be used to uncover the mechanisms of population dynamic patterns such as cycles. The role of observations and experiments When trying to uncover mechanisms of population dynamics (specifically how life-history traits respond to variation in environmental state variables) one face the problem that a large number of state variables may be relevant, and that these variables do not vary independently. Observational studies aim to describe the variation and covariation in the response variables (e.g. life-history traits) and a set of relevant state variables. Specific causations, or mechanisms, cannot be inferred from such observational data because correlations do not imply that there are any casual links, although one may often be able to narrow down to a set of plausible mechanisms when the patterns of variation and covariation in the data are viewed in the light of general theory or specific models(paper III and Paper IV are examples of this). In experiments one ensures that the focal state variables vary independently (i.e. zero covariance) through manipulations and by assigning the experimental units at random to different treatments 38. Non-focal state variables may be kept constant (to increase precision at the expense of realism and inference space; typical lab-experiments, e.g. Paper I)orbeallowedtovaryandco-varyina natural way (typical field-experiments, e.g. Paper II). Experiments are design to reveal casual mechanisms. However, there will often be a nagging uncertainty about the relevance of experimental results because the background environment may not have been realistic (i.e., interaction effects that were not incorporated in the experimental design may be important in the real system) or because treatments were too extreme. There are additional problems that are often overlooked when using experimental approaches to understand population level phenomena such as cycles or population declines. For example, consider an experiment where predators were removed from a random set of locations and where other random locations were 37 See discussions in Berryman (2002b), Chitty (1996), Krebs (1996; 2002), Lambin et al. (2002), ÃLomnicki (1992), and Stenseth (1999). 38 Iamhereusingaratherstrictdefinition of experiments. Some texts refer to any study that involves manipulation as an experiment. However, the effects of any factors that are not ensured to vary independently of other factors through the experimental design must be interpreted in an observational way (although the observations apply to the manipulated, or perturbed, system). Indeed, both observational and experimental inferences may often be drawn from the same study.

20 16 Box 2. Traditional approaches in studies of small rodent cycles 1. The phenomenological school: This is the oldest and most influential tradition initiated by Dennis Chitty and co-workers after Charles Elton s first descriptions of population cycles in Norwegian lemmings. The approach follows to a large extent the older naturalistic traditions of qualitative descriptions and categorisations (see Łomnicki (1992) and Mayr (1997) for historical reviews). Central classifications in this tradition are the distinction between cyclic and non-cyclic populations and a classification of different phases of the population cycles. The descriptions of such defined classes often involve variation in population structure with respect to life-history traits, but this variation is rarely linked to quantitative dynamic models. The motivation for much of this work has been to find a simple and universal cause of cycles, and workers often assume a priori that all cycles are caused by the same mechanisms (e.g. Krebs 1996; Krebs and Myers 1974). The advocates of this school adhere to the hypothetico-deductive method, and strongly believe that scientific progress is primarily made through proposing and rejecting hypotheses (e.g. Chitty 1996; Lambin et al. 2002). 2. The population level analytical school: This school uses time-series data and mathematical modelling to describe and understand the dynamic properties of single populations as well as trophic interactions between species and population level effects of inter-specific and intra-specific competition (see Stenseth 1999; Turchin 2003). The timeseries data applied often consist of only numbers of individuals (often snap-trap data), and models usually ignore any structure of the populations and incorporate only average rates of birth and death (or even just population growth). Analytical models have often been used to determine the plausibility of proposed hypotheses for population cycles, and timeseries analyses have been used to suggest what types of mechanisms that are likely to operate (especially if the time-series include auxiliary data (e.g., other species or climate) or if data are obtained at two or more times each year so that season-specific parameters can be estimated (e.g. Hansen et al. 1999a; Hansen et al. 1999b; Stenseth et al. 2002b)). 3. The individual based reductionistic school: This school builds models that may be parameterised by estimates of demographic parameters or life-history responses of individuals. Such models may be formulated as a book-keeping of individuals in simulation models (DeAnglies and Gross 1992), but more commonly the structure of the population is modelled through matrix projection models (Caswell 2000; Tuljapurkar and Caswell 1997). Such models are often applied where one has data on individual animals (capture-mark-recapture or radio-telemetry data), and where one is mainly interested in predicting the development of the population rather than explaining any particular class of dynamics. This is a much more bottom-up approach to understand population dynamics than the two approaches mentioned above (Łomnicki 1992), and has only recently been applied in small rodent studies (e.g. Lima et al. 1999; 2001). left unmanipulated as controls (predator removal was done on a large scale and the populations were independent). If, in one season, all control populations consistently declined but the predator-removal populations all remained at high densities, then one might be tempted to conclude that high predation was the cause of the decline in the control populations. This would indeed be an un-

21 17 justified conclusion. The control populations could have declined for almost any reason; the only thing one can conclude is that one was able to compensate for whatever caused the decline in the control populations by removing predation. Similarly, if the predator-removal populations as well as the control populations all declined, then this does not refute the hypothesis that the control populations declined due to predation. It may well be that the manipulated populations declined for other reasons than in the controls. I will chose a somewhat complicated, but not unrealistic, example to illustrate the complexity of the problem: Increased adult survival when predators were removed may have caused a saturation of breeding territories, which together with reduced food availability in the denser populations prevented recruitment, and the population subsequently declined due to a combination of low recruitment and lower survival due to senescence and poor food quality. This could have been a transitory behaviour of the manipulated system. Alternatively, another feedback mechanism (for example interactions with a pathogenic parasite) may have taken effect in the absence of the predator-prey interactions 39. The obvious remedy to the problems described above is to describe the response to the experimental treatment as a detailed account of the demographic processes. This would take the form of detailed observational studies within each of the populations, and direct comparisons of single variables in isolation would be little meaningful because experimental treatments at the population level will affect a set of dynamically interacting demographic variables as well as environmental state variables. Interpretations of the demographic processes in the experimental populations also have to deal with the fact that the structure of eco-system may change after some time with experimental manipulations, making it difficult to distinguish between direct and indirect effects of the experimental treatments. Hence, the demographic processes in the manipulated system may be little helpful in trying to understand the mechanisms in the unmanipulated (control) system, as is usually the purpose of the experiment 40. Another problem with population level manipulations is that it is often difficult to manipulate one state variable without simultaneously affecting others (e.g. it may be difficult to exclude predators without simultaneously excluding competitors, and it is difficult to supplement food in unenclosed areas without attracting immigrants 39 See Berryman (2002a) for a discussion of feedback hierarchies and McCauley et al. (1999) for a specific example in Daphnia laboratory systems. 40 Adifferent situation is if the purpose of the population level experiment is to find out how the system responds to the experimental treatment (e.g. to investigate how the population (or community) dynamics is affected by pollution or the introduction of an alien predator). See Moe et al. (2001; 2002a; 2002b) and Lindgjærde et al. (2001) for good examples of how time-series analysis and mathematical modelling can aid the interpretation of population level experiments investigating the influence of a toxicant on blowfly populations. See also Caswell (2000 chap. 10) for how Life table response experiments can be used to decompose differences in population growth between treatments to differences in the demographic rates.