Population dynamics of large and small mammals

Transcription

1 OIKOS 92: Copenhagen 2001 Population dynamics of large and small mammals John Erb, Mark S. Boyce and Nils Chr. Stenseth Erb, J., Boyce, M. S. and Stenseth, N. C Population dynamics of large and small mammals. Oikos 92: We offer an evaluation of the Caughley and Krebs hypothesis that small mammals are more likely than large mammals to possess intrinsic population regulating mechanisms. Based on the assumption that intrinsic regulation will be manifest via direct density-dependent feedbacks, and extrinsic regulation via delayed density-dependent feedbacks, we fit autoregressive models to 30 time series of abundance for large and small mammals to characterize their dynamics. Delayed feedbacks characterizing extrinsic mechanisms, such as trophic-level interactions, were detected in most time series, including both small and large mammals. Spectral analyses indicated that the effect of such delayed feedbacks on the variability in population growth rates differed with body size, with large mammals exhibiting predominantly reddened and whitened spectra in contrast with predominantly blue spectra for small mammals. Large mammals showed less variance and more stable dynamics than small mammals, consistent with, among other factors, differences in their potential population growth rates. Patterns of population dynamics in small versus large mammals contradicted those predicted by the Caughley and Krebs hypothesis. John Erb, Dept of Zoology and Physiology, Uni. of Wyoming, Laramie, WY , USA (current address: Minnesota Dept of Natural Resources, Farmland Wildlife Populations and Research Group, RR1 Box 181, Madelia, MN 56062, USA [john.erb@dnr.state.mn.us]). Mark S. Boyce, Dept of Biological Sciences, Uni. of Alberta, Edmonton, AB, Canada, T6G 2E9. N. C. Stenseth, Di. of Zoology, Dept of Biology, Uni. of Oslo, P.O. Box 1050, Blindern, N-0316 Oslo, Norway. Patterns of temporal variability in animal populations have long been of interest to ecologists from Verhulst s (1845) description of logistic growth, to Elton s (Elton 1924, Elton and Nicholson 1942a, b) focus on population cycles, and modern discussions of complex deterministic dynamics (May 1974a, Hansen 1992, Gatto 1993, Hastings et al. 1993, Ebenman et al. 1996). This focus on population variability is not limited to population ecologists. A primary objective of community and ecosystem ecology, as well as conservation biology, is to understand the nature of variability. One approach to understanding population variability is to evaluate population regulating mechanisms. We define limiting factors as those that cause changes in the rate of production or loss, and determine the equilibrium point (constant or variable) for a population (Sinclair 1989). Regulating factors return a population to this equilibrium. By definition, regulating factors have a density-dependent effect, whereas limiting factors may be density-dependent or -independent. Although a multitude of species-specific factors might limit population abundance, we expect only a limited subset of these exert a significant regulating influence. Further, there probably exists some commonality in the nature of the regulating mechanisms among species. One proposed commonality is whether regulating mechanisms are intrinsically (e.g., Chitty 1960, 1967, 1987, Wynne-Edwards 1962, Christian 1971, Lidicker 1975) or extrinsically (e.g., Nicholson 1933, Andrewartha and Birch 1954, Lack 1954) driven. Populations are said to be extrinsically regulated if, for example, disease or trophic-level interactions (from above or below) are the primary regulatory mechanisms. Intrinsic regulatory mechanisms are those driven Accepted 29 August 2000 Copyright OIKOS 2001 ISSN Printed in Ireland all rights reserved OIKOS 92:1 (2001) 3

2 behaviorally and/or physiologically (e.g., dispersal or reproductive inhibition), and regulate the population prior to the imposition of extrinsic factors. Based on the dynamics of plant-herbivore models and the negative relation between body size and the intrinsic rate of increase (see, e.g., Peters 1983, Calder 1984), Caughley and Krebs (1983) concluded that small mammals ( 30 kg) are likely to evolve intrinsic mechanisms of regulation, whereas large mammals ( 30 kg) might be expected to be regulated by extrinsic factors. Essentially, higher intrinsic rates of increase (r) associated with smaller mammals are more likely to yield greater temporal variability (e.g., limit cycles), which will reduce persistence. At least two possibilities exist by which individual selection can result in the evolution of intrinsic population regulating mechanisms. First, competitive advantage over neighbors can be achieved by interference behaviors such as territoriality. Second, demographic tradeoffs can favor reduced reproductive effort because of advantages to survival of parents or offspring (Goodman 1979). For example, if competition reduces the probability of survival of offspring, physiological mechanisms to reduce reproductive effort may be favored if they can enhance the survival of the parents. Neither of these individually based mechanisms for the evolution of intrinsic population regulating mechanisms are necessarily tied to body size or reproductive rate of the population, however. The mechanism envisaged by Caughley and Krebs (1983) is a group selection process; for example, they state cyclic populations under extrinsic controls are at a high risk of extinction, and that the only cyclic populations which have persisted in evolutionary time are those which are self-regulated. Although such an evolutionary process might operate, we expect that group selection is likely to be a weak force at best (Williams 1966, 1971, Maynard Smith 1976). Furthermore, current research (e.g., Hanski et al. 1991, Krebs et al. 1995a) indicates that the dynamics of many cyclical populations are in fact a result of trophic-level interactions (i.e., extrinsic factors). Although Pimm (1991) documented an inverse relationship between temporal variability and body size, evaluation of persistence time should account for the fact that small mammals are potentially more resilient (higher intrinsic rates of increase), and occur at higher ecological densities (Silva and Downing 1995, and references therein). Foley (1994) has provided a framework for estimating persistence time which accounts for these factors. Caughley and Krebs (1983) suggest that the presence of high population growth rates results in population fluctuations that could lead to local extinctions and the evolution of intrinsic regulation. Yet intrinsic mechanisms that create a selective advantage in a competitive environment, e.g., increased aggression, territoriality, or dispersal, would operate irrespectively of population growth rates. And individual-level selection can favor reduced reproductive output in a competitive environment (see Boyce 1981, Bujalska 1988) competition surely is not limited to small mammals. Thus, we are unaware of any a priori reasons why these intrinsic mechanisms may be limited to small mammals. Also, the mere capability of intrinsic regulation does not require that these mechanisms be manifest. For example, Ostfeld et al. (1993) found stabilizing intrinsic mechanisms (i.e., socially induced reductions in breeding effort) in vole populations, and concluded that extrinsic factors must be responsible for cyclical fluctuations observed in many vole populations. By our definition, then, if extrinsic mechanisms regulate population density prior to intrinsic mechanisms being expressed, then the population is extrinsically regulated. Delayed density dependence suggests that populations are receiving negative feedback from extrinsic factors such as trophic interactions, interspecific competition, or carry-over effects from poor physiological condition (Berryman 1992, Royama 1992). Difficulties arise, using comparative data, in distinguishing between two types of physiologically based carry-over effects. If carry-over effects arise from social strife directly (e.g., decreased survival or reproduction due to fighting or general crowding effects), then the reduction in population growth is intrinsic. However, if carry-over effects on survival or reproduction result from depletion of food quantity or quality, then the reduction in population growth is extrinsic. Intrinsic carry-over effects are not likely to last for more than one generation, making their detection in annual time series of multivoltine species unlikely. The detection of lags in multivoltine species, then, suggests extrinsic regulation, whereas detection in univoltine species leaves room for debate. Hence, with the above note, our primary assumption is that intrinsic mechanisms of population regulation will occur via direct negative feedbacks, whereas extrinsic regulation more likely will occur via delayed negative feedbacks. Translated, then, Caughley and Krebs (1983) hypothesis is that small mammals should have dynamics characterized by first-order density dependence, and large mammals should have second- (or higher-) order dynamics. Furthermore, delayed density effects often lead to greater temporal variability, whereas strong direct effects are assumed to produce more stable patterns (May 1974b, 1976, Hanski et al. 1991, Hanski and Korpimäki 1995). We question Caughley and Krebs s (1983) assertion that body size is a useful predictor of the nature (i.e., extrinsic/intrinsic) of population regulation in mammals. Our objectives were to determine if patterns of temporal variability in mammal populations varied with body size, and if so, to evaluate whether the differences were consistent with Caughley and Krebs s (1983) suggestion of an extrinsic/intrinsic dichotomy 4 OIKOS 92:1 (2001)

3 based on body size. Although we concur with Krebs (1995) that a mechanistic approach based on experimentation is necessary to understand the species-specific mechanisms of regulation, comparison of patterns in population dynamics can be useful in structuring research into regulating mechanisms. Methods We collected 30 mammalian time series (11 species) of annual abundance that extended for 20 years or more (Table 1), and which were based on series of census counts or population estimates. In addition, we in- Table 1. Location, duration, estimated second-order autoregressive coefficients, and estimated order of time series of abundance for large and small mammals. Species Locality Latitude Years 1 2 Region Order a Large mammals a. Alces alces Isle Royale I 1 (0) b. Cer us elaphus National Elk Refuge I 2 c. C. elaphus Yellowstone I 2 d. Bison bison Yellowstone I 1 e. Canis lupus Isle Royale I 0 (1) f. C. lupus* Alberta IV 3 g. C. lupus* British Columbia IV 1 (2) h. C. lupus* Manitoba III 2 i. Ursus americanus* Manitoba I 1 (0) j. U. maritimus* Northwest Territories I 2 (1) k. U. arctos horribilis Yellowstone I 0 Small mammals a. Castor canadensis* Alaska I 1 b. C. canadensis* British Columbia I 1 c. Ondatra zibethicus* Mackenzie District IV 1 d. Alopex lagopus* Ontario I 3 e. A. lagopus* Northwest Territories III 1 (2, 3) f. Vulpes ulpes* Ontario I 2 g. V. ulpes* Alberta I 3 h. V. ulpes* Quebec I 1 i. Martes americana* Ontario I 0 j. M. americana* Alberta I 3 k. M. americana* Quebec I 0 (1) l. Weasels (3 spp.)* Alberta I 0 m. Ar icola terrestris Chateau d Oex IV 3 n. A. terrestris Ste-Croix IV 3 o. A. terrestris Crenit IV 1 (2) p. A. terrestris Brevine IV 3 (2) q. A. terrestris Rougemont IV 3 r. A. terrestris Bulle I 3 s. Clethrionomys rufocanus Hokkaido IV 0 t. C. rufocanus Hokkaido IV 2 (3, 1) u. C. rufocanus Hokkaido III 3 v. C. rufocanus Hokkaido III 3 w. C. rufocanus Hokkaido III 3 x. C. rufocanus Hokkaido IV 3 (2) y. C. rufocanus Hokkaido III 1 z. C. rufocanus Hokkaido I 3 A. C. glareolus Tula III 1 (2, 3) B. C. glareolus Serpukhov I 2 (3) C. C. glareolus Tataria I 1 (2, 3) D. C. glareolus Wytham Wood (wi.) III 2 E. C. glareolus Wytham Wood (spr.) I 2 (1) F. Apodemus syl aticus Wytham Wood (wi.) II 3 G. A. syl aticus Wytham Wood (spr.) II 2 (3, 1) H. All voles Kilpisjärvi (fall) IV 2 (3) J. All voles Kilpisjärvi (spr.) IV 2 (3) K. Lemmus trimucronatus Point Barrow III 2 trimucronatus * denotes fur harvest data. a order estimated as the model with the smallest AICc value. Numbers in parentheses denote models with AICc values which were insignificantly different from the AICc for the selected model. OIKOS 92:1 (2001) 5

4 Fig. 1. Parameter space and patterns of population fluctuation for a second-order autoregressive process (cf. Royama 1992, Stenseth 1999). are shown in Fig. 1 (see Bjørnstad et al for the periodicity gradient within this diagram). We note that these are the typical patterns assuming a deterministic process. Stochasticity alters these patterns somewhat. For example, perturbations generally will keep the patterns in regions II, III, and IV from damping out, whereas the pattern in region I will be more variable when responding to stochastic perturbations. However, our interests were only in broad-scale patterns, and we assume the deterministic approximations to be sufficient. Also, real-world ecological dynamics are inherently nonlinear (Royama 1992), although linear approximations are still useful for identifying broad patterns in the data, and facilitate the comparison of the dynamics of different populations (Bjørnstad et al. 1995, Stenseth 1999). Second, we computed the spectra (Proc SPECTRA; SAS 1993) of the per capita growth rates (r) for each series. Spectra were smoothed using a triangular weighting scheme of the form (SAS 1993). To facilitate comparisons between species, we logarithmically transformed the axes of each power spectrum. We emphasize, though, that such an approach tends to visually dampen any fluctuations in the spectra. What visually may appear as a small increasing trend, for example, actually may constitute a significant increase in power at higher frequencies. Nevertheless, we felt this approach was useful given the broader comparisons for which we were interested. Fig. 2. Location of estimated autoregressive coefficients for time series of abundance for large mammals. cluded 17 time series (nine species; Table 1) of fur harvests for comparison. With the exception of the fur harvest time series, all of the small ( 30 kg) mammal series we analyze are multivoltine species, whereas the large mammal series are from univoltine species. To evaluate the underlying dynamics for individual series, we estimated the appropriate order for each series by computing the small-sample Akaike Information Criterion (AIC c ; Hurvich and Tsai 1989) for autoregressive models of order zero through three. The appropriate model is that which has the smallest AIC c ; a difference of 1 is insignificant (Sakamoto et al. 1986). To compare patterns of temporal variability among species, we used two methods. First, we plotted estimated regression parameters (Proc AUTOREG; maximum likelihood option; SAS 1993) in the appropriate region of the parameter plane (1+ 1, 2 ) for a linear second-order density-dependent process (Royama 1992: 58-59) of the form: r(t)=log e (N t+1 /N t )= log e (N t )+ 2 log e (N t 1 ). The four primary regions of the parameter plane and the typical temporal patterns exhibited for each region Results We detected lagged density dependence in the majority of large mammal series (Table 1). Also, with the exception of the three series of wolf fur harvests, large mammal dynamics were comparatively stable (region I of the stability diagram; Fig. 2; also see Table 1). The spectra of two series (Cer us elaphus [National Elk Refuge], Ursus arctos horribilis [Yellowstone]) were distinctly blue (Fig. 3), consistent with their location to the left of region I near the two-year periodicity contour (see Bjørnstad et al. 1995). Most of the remaining large mammal series generally exhibited white or red spectra (Fig. 3). Small mammal species were dynamically more variable (Fig. 4). However, similar to large mammals, lags were apparent (or could not be ruled out) in the vast majority of cases (Table 1). The small mammal fur harvest series produced results closer to those for large mammals, being located primarily in region I. Also, we found the spectra from these series to be somewhat similar to large mammals. Several spectra (e.g., Castor canadensis and Alopex lagopus) showed increasing power at higher frequencies (i.e., blue spectra), with the remaining spectra being whitened (Fig. 5). Many of these spectra had individual peaks corresponding to the 6 OIKOS 92:1 (2001)

5 Fig. 3. Spectral densities for time series of abundance for large mammals. well-known cycle length of ten years in many Canadian furbearers. The remaining small mammal series, with few exceptions, showed blue spectra (Fig. 5). The spectra did not always monotonically increase. For example, most Ar icola terrestris series showed single peaks superimposed on a blue spectrum. The peaks, here, correspond with 5 7 year periodicity, consistent with their location near the corresponding periodicity contour in the stability plots (see Bjørnstad et al. 1995). Discussion We detected delayed feedbacks in the vast majority of series analyzed. Despite this commonness of lags, we found different patterns of temporal variability between large and small mammals. Lags are often implicated as the mechanism behind oscillatory dynamics (MacDon- Fig. 4. Location of estimated autoregressive coefficients for time series of abundance for small mammals. OIKOS 92:1 (2001) 7

6 Fig. 5. Spectral densities for time series of abundance for small mammals. ald 1978), but as seen here, they are not a sufficient condition. The lower intrinsic rates of increase for large mammals reduce the likelihood of oscillatory dynamics, even in the presence of such lags, i.e., the strength of the delayed feedbacks may be insufficient to override the relative stability produced from lower intrinsic rates of increase. Potentially more important to understanding patterns of variability, then, are the relative strengths of direct and delayed negative feedbacks. In contrast to large mammal results, the detection of lags and high-frequency oscillations in small mammals contradicts the hypothesized patterns of intrinsic regulation proposed by Caughley and Krebs (1983). Our results are in agreement with recent work on small mammals (e.g., Hansson and Henttonen 1985, Hanski et al. 1991, Turchin 1993, Agrell et al. 1995, Bjørnstad et al. 1995, Dobson 1995, Hanski and Korpimäki 1995, Krebs et al. 1995a, b, Norrdahl and Korpimäki 1995, Reid et al. 1995), further supporting the view that strong delayed feedbacks resulting from extrinsic regulation are common for small mammals. Large mammals showed comparatively stable dynamics while small mammals were more variable, consistent with results reported by Pimm (1991: 39 40). The presumed relationship between intrinsic rates of increase and variability formed the basis for Caughley and Krebs s original hypothesis, i.e., that the lower intrinsic rates of increase in large mammals would lead to more stable dynamics and reduce the selective advantage of intrinsic regulation. Conversely, though, strong extrinsic regulation (delayed feedbacks) may itself induce oscillatory dynamics. Further, as noted previously, the detection of lags in large mammals (or univoltine species) does not rule out the possibility that the lags are physiologically based carry-over effects, and thus intrinsically driven. Interestingly, we found most fur-harvest series for small mammals to be dynamically similar to large 8 OIKOS 92:1 (2001)

7 mammals, being located in region I. Given the higher intrinsic rates of increase (compared to the large mammals) and detection of lags for some of these species, coupled with the fact that series of fur harvests tend to amplify actual oscillations (e.g., see Royama 1992), we speculate that the larger spatial scale (i.e., provincial) over which most fur harvest data were compiled results in spatial damping of temporal variability in local dynamics. This assumes the dynamics of local populations are not in synchrony, an assumption worthy of further consideration. Research into spatial synchrony of population dynamics has been increasing (e.g., Ranta et al. 1995, Sutcliffe et al. 1996, Moss et al. 2000), although wide-ranging predictions have not emerged. The lack of direct density dependence suggested for Isle Royale moose (Alces alces) and Yellowstone bison (Bison bison) may be because these populations still are increasing toward equilibrium. Differencing produces a stationary series; little information about density-dependent feedbacks is present until the population has reached an asymptote (Royama 1992). These series both show increasing trends for their entire length. Hence, the lack of density regulation detected in these series is inconclusive. It thus appears that lags, probably resulting from trophic-level interactions, are common in mammals. Recently, Wolff (1997) suggested that the primary ultimate factor determining the nature (i.e., extrinsic or intrinsic) of regulation in mammals is whether species produce altricial or precocial young. He suggested that when breeding space becomes limiting, altricial species tend to exhibit female territoriality as a counter-strategy to infanticide by conspecific females. Additionally, behavioral reproductive suppression is proposed as an adaptive mechanism to avoid inbreeding, or to conserve reproductive effort in response to the threat of infanticide. Although our sample sizes for certain taxonomic groups are low, our results indicate, as Wolff (1997) Fig. 5 (continued). OIKOS 92:1 (2001) 9

8 Fig. 5 (continued). predicted, that rodents and canids exhibit stronger direct density dependence than ungulates. However, these two groups also show the strongest delayed density dependence, contradicting Wolff (1997). However, Wolff (1997) concludes that the necessary conditions he proposes for intrinsic regulation appear to occur only under limited conditions, such that most mammal populations probably are controlled by extrinsic factors. The spectral patterns we observed for the majority of large mammals, as well as small mammal fur harvests, were comparatively redder than small mammals, often appearing white. This is consistent with our speculation that points in region I of the stability plot would show comparatively lower power at high frequencies. Previous work (Pimm and Redfearn 1988, Pimm 1991, Halley 1996) has suggested that reddened spectra will be the dominant color for most species. Our documentation of blue spectra for numerous populations of small mammals challenges this pattern. Noteworthy is 10 the correspondence between our results and the work by Cohen (1995). In an analysis of eight nonlinear population models commonly used in ecology, Cohen (1995) found that, for individual parameter sets in the chaotic region, simulated series for all models unexpectedly produced blue spectra. We note, however, that we computed spectra based on first-differenced (i.e., detrended) data, which may lower the power at low frequencies (i.e., reduce reddening). However, only three of the raw time series exhibited long-term trends (Isle Royale moose, Yellowstone bison, and Yellowstone elk), and the spectrum for Isle Royale moose was distinctly red in spite of such a potential effect. Additionally, all spectra were computed in the same manner, and any possible effects should not affect the comparative nature of our analysis. Perhaps a useful analogy, similar in concept to that originally proposed by Steele (1985) for comparing terrestrial and marine systems (air versus water), is that OIKOS 92:1 (2001)

9 large mammals have an increased ability to buffer themselves against extrinsic (biotic and abiotic) factors, whereas small mammals are less buffered. Lower buffering ability of small mammals will more likely lead to higher system dimensionality, an important precursor to complex dynamics. Buffering by large mammals occurs, in part, because they enjoy greater fasting endurance, thereby are better able to survive food crisis (Lindstedt and Boyce 1985), and because they have greater longevities (Connell and Sousa 1983) and overlapping generations (Bonner 1965). In summary, we found little support for Caughley and Krebs s (1983) suggestion that mechanisms of population regulation can be collapsed into an extrinsic/intrinsic dichotomy based on body size. We did, however, document a consistent pattern among larger mammalslower temporal variability perhaps resulting from a lack of strong delayed density regulation, and a higher resistance to environmental variability. 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