Shawn F. Morrison, Department of Biological Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2E9. E-mail: email@example.com
1Demographic analysis is essential in order to determine which factors, such as survival, fertility and other life-history characteristics, have the greatest influence on a population's rate of growth (λ).
2We used life-table response experiments (LTREs) to assess the relative importance of survival and fertility rates for an alpine lagomorph, the collared pika Ochotona collaris, using 12 years (1995–2006) of census data. The LTRE analysis was repeated for each of three subpopulations within the main study site that were defined by aspect (east, west and south).
3Across the entire study site, the survival and fertility of adults contributed 35·6 and 43·5%, respectively, to the variance observed in the projected population growth rate, V(λ), whereas juvenile survival contributed 20·9%. Adult survival and fertility contributed approximately equal amounts for each subpopulation when considered separately, although their rank order varied spatially.
4Adult survival across the entire site was positively correlated to the Pacific Decadal Oscillation (PDO) with a time lag of 1 year, and was uncorrelated to adult density. The PDO was negatively correlated to the timing of spring snowmelt at our site, implicating the importance of earlier spring conditions and plant phenology on the subsequent winter survival of adults and therefore, population growth.
5When subpopulations were analysed separately, survivals and fertilities were variously correlated to lagged PDO and adult densities, but the patterns varied spatially. Therefore, the mechanisms underlying V(λ) can vary substantially over relatively short distances.
Once the relative importance of multiple vital rates has been established, the next step in understanding population dynamics is to identify the ecological mechanisms underlying their variation (Coulson et al. 2005). For example, recent research has identified global-scale climate indices as having strong influences on wildlife populations (e.g. Post et al. 1997; Post & Stenseth 1999; Stenseth et al. 2003a) and better predictive power than local weather variables because they incorporate multiple weather components (e.g. precipitation and temperature) across appropriate temporal and spatial scales and thus capture the complex relationships between weather and ecological processes (Hallett et al. 2004; Stenseth & Mysterud 2005). Additionally, the population growth rate of different populations of the same species may be concurrently affected by both density-dependent (e.g. a functional relationship between the rate of population change and population density; Turchin 2003) and independent (e.g. weather) forces to shape observed population dynamics (e.g. Karels & Boonstra 2000; Coulson et al. 2005).
We analysed a 12-year (1995–2006) census data set from a south-west Yukon population of collared pikas Ochotona collaris (Nelson 1893), a small (c.140–160 g) alpine lagomorph. Talus-dwelling pikas such as O. collaris are long-lived relative to most small mammals (Smith et al. 1990). Pika abundance at our site has declined since 1995, similar to reports of other Ochotonid species in North America and Asia (McDonald & Brown 1992; Beever, Brussard & Berger 2003; Smith, Li & Hik 2004; Li & Smith 2005). While motivated by theoretical considerations regarding mammalian life-history implications on population dynamics, our analysis may also assist in determining the vital rates contributing to pika declines.
Our primary objectives were to: (1) estimate the survival and fertility rates of collared pikas within three subpopulations; (2) quantify the influence of survival and fertility rates on population growth rate using elasticity analysis and life-table response experiments (LTREs); (3) determine if these patterns varied across relatively short spatial scales; and (4) test the hypothesis that pika vital rates, and therefore λ, were affected by climate influences as suggested by Beever et al. (2003) and Li & Smith (2005).
The study was conducted in a 4-km2 alpine valley within the Ruby Range, east of Kluane Lake, Yukon, Canada (61°13′ N, 138°16′ W; 1600–2200 m a.s.l.). The valley was a mosaic of meadow and tundra vegetation interspersed with patches of talus (pika habitat; also referred to as boulderfields). Vegetation communities were dominated by Dryas octopetala, Salix spp., Cassiope tetragona, and several graminoids (e.g. Carex consimilis) (Hik, McColl & Boonstra 2001; McIntire & Hik 2005). Collared pikas, hoary marmots Marmota caligata (Eschscholtz 1829), and Arctic ground squirrels Spermophilus parryii plesius (Richardson 1825) were the dominant mammalian herbivores.
The valley had three dominant aspects (facing west, east and south) separated by a matrix of gravel slopes, 1–2 m wide streams, and 100–300 m stretches of meadow that were unsuitable for pika colonization or persistence. The south and west aspects were connected at higher elevations by nonhabitat gravel slopes that were unoccupied by pikas. The east aspect had patches of talus at higher elevations, but beyond the boundaries of our study area. The east and west aspects also were connected to talus patches outside of the valley. Census data were collected from 1995 to 2006 for the east and west subpopulations and from 1998 to 2006 for the south subpopulation.
Pikas were uniquely marked and retrapped each summer from mid-June to mid-August using Tomahawk live-traps baited with fresh native vegetation. The entire study was monitored four to five times weekly to detect unmarked individuals that were then targeted for trapping. Pikas are diurnally active within their small (< 25 m radius) individual territories, have distinctive territorial calls, create easily noticed haypiles of cached vegetation (Smith 1974, 1980), permitting observers to readily locate and capture all pikas resident within the study area. These characteristics, combined with intensive trapping and search effort indicate > 95% of all individuals were captured annually. Individuals trapped for the first time were marked with numbered metal ear tags (Monel no. 1) and a unique colour combination of thin wire to allow for later re-identification from a distance. Gender was determined following Duke (1951), and individuals were classified as juveniles (young of the year) or adults (> 1 year old) based on body mass and moult pattern (Franken & Hik 2004b).
Juveniles are most trappable following dispersal when they have acquired a territory and are food-hoarding (D. S. Hik, unpublished data). Because juveniles disperse from their natal territories within several days of emergence, we believe that most of our initial captures of juveniles occurred following dispersal from their natal territory. Adults at our site are philopatric and rarely switch territories (Franken 2002). We calculated population abundance as the sum of all marked individuals of all ages and sexes enumerated each season.
survival estimation (paandpj)
Female pikas were classified as dead if not recaptured or resighted in a subsequent year. This assumption was reasonable because pikas are highly visible (Smith 1974, 1980) and adults are highly philopatric (Smith & Ivins 1983). Our long-term trapping data from an intensive trapping protocol indicated only 0·43% (n = 2 of 467) of pikas (ages and sexes pooled) were missed in any given year (i.e. marked in year t, not detected in year t + 1, but re-trapped in year t + 2). Thus, because the probability of recapturing all living pikas was approximately one, we did not have to account for overlooked individuals. Survival of juveniles (PJ) and adults (PA) was calculated following Caswell (2001) for post-breeding pulse breeders.
Estimating pre-dispersal survival of young was not feasible as young are born beneath the talus and cannot be captured until emergence 30 days post-parturition (Franken & Hik 2004b). Because juvenile pikas are most easily captured once they have dispersed and established a territory, our estimates of PJ are based on female juveniles captured after dispersal.
The date of parturition at our site varied annually, but typically occurred in mid to late June, and does not affect overwinter juvenile survival (Franken & Hik 2004a,b). Juvenile females do not reproduce in the summer of their birth, but are reproductively mature at 1 year of age. Because pika nests are inaccessible under the talus, and juveniles disperse from the natal territory quickly following emergence to the talus surface, we could not estimate mean litter size for specific females (i.e. mA). Therefore, we calculated fecundity as the number of post-dispersal female juveniles (Ndaughters) per adult female (Nadfem) and denote it as . All adult females were assumed to be breeders based on data from the closely related O. princeps indicating > 97% of adult females attempted to breed annually (Millar 1974). The sex ratio of post-dispersal juveniles was approximately 1 : 1, there was no evidence of multiple litters successfully being weaned at our site, and interpatch dispersal behaviour of juveniles was not sex-biased (Franken 2002), so we calculated the number of daughters as 0·5 times the total number of juveniles in the population. Our estimate of fecundity, , therefore includes juveniles born within the study area and those that dispersed into the study area. Fertility (FA) was calculated as the product of and adult survival (PA) as appropriate for post-breeding designs (Caswell 2001).
The three dominant aspects of our study area (west, east and south) appear to represent distinct pika subpopulations and are separated by 1–2-m wide creeks and 100–300 m of alpine meadow. Juvenile pikas at our site typically disperse within their natal talus patch (Franken & Hik 2004a). Since 1995, only one juvenile female moved from the subpopulation on which it was originally trapped to either one of the other two subpopulations, suggesting that movements of juvenile females are relatively uncommon. Actual interaspect movements may be more common than our trapping data suggests because capture of dispersing individuals (i.e. juveniles) is difficult before territory establishment.
model structure and analysis
We parameterized female-only transition matrices according to a birth-pulse post-breeding census design (Fig. 1; Caswell 2001), and analysed the data set in two ways: (1) the valley as a single population (one matrix per year from 1998 to 2006), and (2) stratified by subpopulation in which each was analysed independently (i.e. within-subpopulation analysis). We limited our analysis in (2) to the years 1995–2006 for the east- and west-facing subpopulations and 1998–2006 for the south-facing subpopulation (Fig. 2). In each case, we explored how projected λ responded to changes in vital rates using prospective and retrospective perturbation analysis (Caswell 2000, 2001) using matlab (The Mathworks, version 7·0·1 for Macintosh).
We examined how changes in PJ, PA and FA would be reflected in λ using sensitivity and elasticity analysis on mean matrices. Other studies indicate that, in some species, λ is sensitive to the age at first reproduction (α) and last reproduction (ω) (Oli & Dobson 2003). We did not consider these in our analysis because pikas are reproductively mature at 1 year with no evidence of variation in α or ω (Millar 1973, 1974; Franken 2002). Sensitivity refers to the change in λ resulting from a change in matrix elements and our calculations followed Caswell (2001), where the sensitivity (sij) of λ to a change in matrix element aij is given by:
The elasticity (eij) of λ to aij refers to the proportional response of λ to a proportional change in a matrix element (Caswell 2000, 2001), and often is referred to as proportional sensitivity:
Although sensitivity analyses quantify how changes in vital rates (aij's) would influence λ, they do not consider the actual changes in λ observed as a function of historical changes in vital rates (Caswell 2000).
life-table response experiment
A LTRE is a retrospective analysis that determines how much the variances and covariances in matrix elements (i.e. PJ, PA and FA) have contributed to the variance observed in λ (Caswell 2000, 2001). LTRE requires a set of matrices that represent responses to various treatments (fixed effects), or matrices from different locations or times (random design) (Caswell 2000, 2001). Given a set of matrices, it is possible to determine how variation in PJ, PA and FA have contributed to V(λ) (Caswell 2000). The contribution of each element to V(λ) was calculated according to Horvitz & Schemske (1995):
where cov(aij,akl) is the covariance of aij and akl, and the sensitivities are calculated for the mean matrix. We used a random design because our matrices were a random sample from a distribution of possible matrices based on different subpopulations and years (Caswell 2001). Our results therefore reflect the contributions of variances and covariances of the matrix elements to V(λ).
Census data from 1995 to 2006 allowed us to conduct a LTRE analysis using annual matrices for each subpopulation. Although the population abundances in the three subpopulations were small, they were fully enumerated and represent the entire subpopulation. Therefore, parameter estimation problems associated with small sample sizes were avoided because there is no variance associated with estimates. We did not construct matrices for several census years because of missing age classes.
climate and weather
The Pacific Decadal Oscillation (PDO) is a repeating 20–30 years pattern of climate anomalies in sea surface temperature (SST) across the northern Pacific Ocean (Hare 1996; Mantua et al. 1997). Positive PDO values (warm phase) reflect anomalously cool SSTs in the central Pacific and warm SST along the North American coast. This is closely related to winter weather patterns throughout north-western North America (Mantua et al. 1997; Papineau 2001) such that warm phase PDOs result in above-average winter temperatures and below average winter precipitation and snow pack conditions. The ecological and hydrogeological influence of the PDO is strong enough to be useful at forecasting forest fire activity throughout Alaska (Duffy et al. 2005), and has been implicated in the population dynamics of several taxa in the Pacific north-west, including salmon Oncorhynchus spp. (Mantua et al. 1997; Schindler et al. 2005), Dall sheep Ovis dalli (Hik & Carey 2000), seabirds (Parrish & Zador 2003) and songbirds (Ballard et al. 2003). We correlated vital rates to winter PDO values (defined here as the mean value from November to May) for each study year (source: http://www.cdc.noaa.gov/ClimateIndices/Analysis). We chose this period because of high rates of overwinter mortality during the winter in pikas (Franken 2002). To link the large-scale PDO to local effects we correlated winter PDO values to the timing of snowmelt on 10 permanent plots located at the centre of our study site. The permanent plots are part of a long-term study of vegetation ecology and the date each of these plots became snow free has been documented since 1995 using dataloggers and field observations.
Pika population abundance (using all ages and both sexes) declined on the east- and west-facing subpopulations between 1995 and 2006 (Fig. 2). Densities in the west-facing subpopulation declined from 1·9 pikas ha−1 in 1995 to a low of 0·28 pikas ha−1 in 2003 before recovering to 1·4 pikas ha−1 in 2006. The subpopulation went locally extinct in 2000 but was recolonized the same year. Similarly, the east-facing subpopulation declined from 2·5 pikas ha−1 in 1995 to a low of 0·13 pikas ha−1 in 2003 before recovering to 1·3 pikas ha−1 in 2006. This site went locally extinct during winter 2003–04 but was recolonized by July 2004 by immigrating juveniles. The south-facing subpopulation had consistently higher population densities, greater interyear variation, and never went locally extinct (1998–2006; Fig. 2).
We used a two-way analysis of variance (anova) to determine the effects of aspect (east, west or south), and age (juvenile or adult) on the survival rates of females. There was no evidence of an age–subpopulation interaction on survival (F2,49 = 0·50, P = 0·61), which allowed us to consider the main effects independently. There was no main effect of age (F1,49 = 0·28, P = 0·60), or subpopulation (F2,49 = 1·06, P = 0·35). The ratio of juveniles to female adults (, 3·3 ± 0·81 SE. for pooled sites, 1998–2006) did not differ by subpopulation (one-way anova, F2,22 = 0·09, P = 0·91), nor did female fertility (FA, F2,22 = 0·51, P = 0·61).
correlation of climate and population abundance with vital rates
When the entire study site was analysed as a single population (i.e. pooled subpopulations), adult female survival (PA) was positively correlated to the mean winter PDO with a time lag of 1 year (Pearson's r = +0·77, P = 0·03, Fig. 3A). Adult survival was uncorrelated to the PDO in the absence of a lag (r = –0·01, P = 0·99). Adult survival also was not correlated with population density (r = –0·19, P = 0·65). Adult fertility (FA), and the number of juveniles per adult female (), were negatively correlated to the number of adult pikas (r = –0·68, P = 0·06 and r = –0·62, P = 0·10, respectively). Juvenile survival (PJ) was not correlated to either the PDO (r = +0·571, P = 0·140) or the number of adult pikas (r = +0·02, P = 0·955).
Adult survival and juvenile survival were positively correlated to the lagged winter PDO on the south-facing subpopulation (r = +0·80, P = 0·017, and r = +0·77, P = 0·03, respectively, Fig. 3B). On the east-facing subpopulation, juvenile survival was positively correlated with the lagged PDO (r = +0·65, P = 0·03), while was negatively correlated to adult density (r = –0·64, P = 0·06). On the west-facing subpopulation, PA and were correlated to adult density (r = +0·63, P = 0·10 and r = –0·70, P = 0·06, respectively). No other vital rates were correlated (i.e. P < 0·10) to the PDO or adult density for any subpopulation.
The winter PDO values were strongly correlated to the timing of snowmelt at the permanent plots located at the centre of our study site (r = –0·87, Fig. 4). Negative PDO values were associated with later snowmelt, whereas positive PDO values were associated with an earlier disappearance of snow from the plots.
Population growth rate was most sensitive to changes in PJ and PA when the population was considered as a single population. Growth rate was approximately equally elastic to PA, PJ and FA for the pooled population (Table 1). The rank order of sensitivities varied by subpopulation when considered separately: λ was most sensitive to PA and PJ in the east- and south-facing subpopulations, but to PA and FA in the west-facing subpopulation. Elasticities also varied by subpopulation but the trends were less clear. Growth rates on the east- and south-facing subpopulations were approximately equally sensitive to each nonzero matrix element, whereas λ was more elastic to PA on the west-facing subpopulation.
Table 1. Results of sensitivity, elasticity, and LTRE analysis of three subpopulations of collared pikas in south-western Yukon. It is the property of age-structured matrices that the sum of any row in an elasticity matrix equals the sum of the corresponding column (De Kroon et al. 1986; Heppell et al. 2000). Therefore, the elasticities of λ to FA and PJ will necessarily be equal given projection matrix A. The LTRE contribution refers to the percentage of variance in the projected population growth rate, V(λ), explained by each vital rate
Subpopulation and vital rate
LTRE contribution (%)
Entire valley(subpopulations pooled)
LTRE analysis of the pooled study site suggested that the matrix element(s) that had made the largest contribution to V(λ) were those based on adult vital rates (PA and FA); variation in these combined rates explained 79·1% of V(λ) (Table 1). This pattern was similar when each subpopulation was analysed separately. Variation in PJ contributed only 18·2–20·7% to V(λ) for any subpopulation. Instead, matrix elements based on the vital rates of adults contributed most to V(λ). Adult fertility (FA) contributed most to V(λ) in the east- and south-facing subpopulations (48·9 and 48·8%, respectively), whereas PA contributed most (49·5%) to V(λ) for the west-facing subpopulation. Overall, adults contributed 79·3–81·7% (PA plus FA) to V(λ) in each subpopulation (Table 1).
Population dynamics are determined by the underlying vital rates of the population, which in turn are determined by a number of factors, including environmental conditions, density dependence, and chance events. The demographic basis underlying changes in λ is a fundamental issue in population ecology (Sibly, Hone & Clutton-Brock 2003b), yet it remains poorly understood for many vertebrate populations (Dobson 1995). In this light, our study provides several results relevant to our understanding of mammalian population dynamics in general, and of relatively long-lived small mammals, such as collared pikas, in particular. First, we demonstrated a sequence of strong relationships between large-scale climate patterns (PDO), the timing of snowmelt in spring, adult survival rates, and ultimately, variation in pika population growth rates. Second, the vital rates of some pika subpopulations were concurrently affected by density-independent factors such as climate (e.g. adult survival, PA) while others (e.g. fecundity,) were more affected by density. Post-natal losses of first litters at high population densities have been reported for O. princeps, whereas second litters were lost at all densities (Millar 1974). Our observation of density-dependent (i.e. fecundity) and density-independent (i.e. survival) factors operating simultaneously adds to a growing body of research that suggests both factors often combine to shape population dynamics (e.g. Karels & Boonstra 2000; Stenseth et al. 2003b). Third, the vital rates of nearby subpopulations may show few or no detectable relationships with either climate patterns or density, suggesting the influence of other local factors.
There is accumulating evidence that the vital rates most responsible for variation in population growth vary among populations of the same species. For example, experimental manipulation of food resources indicated that population declines of Columbian ground squirrels were driven by juvenile survival in some, but not all, of the populations (Dobson 1995). Mortality of bighorn sheep in Alberta explained 44% of variance in growth rate in one population, but only 15·3% in another population (Coulson et al. 2005). At our site, adults were responsible for most of the variation in growth rate, whether through survival or fertility. Their relative importance, however, varied spatially at distances < 300 m between subpopulations.
Because fitness is measured by λ, determining those life history traits that most affect λ will also identify the intensity of natural selection on those traits (Benton & Grant 1996; Pfister 1998; Caswell 2001). Spatiotemporal variation in the trait most affecting λ implies that the corresponding fitness response is also spatiotemporally variable (Horvitz & Schemske 1995). Therefore, at our site, the intensity of selection on a given vital rate may also differ by subpopulation.
North American pika populations (O. princeps and O. collaris) have been variously described as stable (Millar 1973; Smith et al. 2004) or variable (Smith 1978; Franken 2002). Fluctuations in population abundance are likely due to environmental variation, such that pikas in regions of high environmental variation tend to have greater variability in population abundance (Smith 1978). Pikas at our site have declined and then increased again in two subpopulations (east and west), but have been variable in the south subpopulation with no clear trend. Variation in winter and spring weather patterns appears to be the most plausible explanation for declining populations at our site. Adult survival was strongly correlated to high PDO values that tend to reflect below average snow-pack conditions (Mantua et al. 1997; Papineau 2001). The effects of the PDO on local conditions at our site are exerted through the timing of snow-pack melt in spring. Earlier snowmelt should result in earlier growth of high-quality vegetation and, subsequently, improved body condition of pikas during the spring breeding season and remainder of the summer. Further, an earlier snowmelt may produce a longer growing season for vegetation allowing pikas additional time to collect vegetation for their haypiles. Conversely, a low snow-pack could result in increased mortality if pikas were exposed to an episode of freezing rain without a protective layer of snow for shelter.
Field observations show that snowmelt is not uniform across the site and this may partially explain differences between aspects. For example, snowmelt seemed to occur earlier on south aspects at our site (D. S. Hik, unpublished data) and may explain why that site has not experienced the same population decline as the east or west subpopulations in a manner similar to that reported by Kreuzer & Huntly (2003). We did not observe a correlation between climate (i.e. PDO) and reproduction, although this relationship has been reported for O. princeps (Millar 1974; Smith 1988). In Millar's (1974) study, the relationship between reproduction and environmental conditions followed an ‘all or none’ pattern. Reproduction was terminated during severe weather conditions, but otherwise occurred in a predictable pattern with low variability relative to other lagomorphs (Millar 1974). Variation in spring snowmelt has also been implicated in the population dynamics of other alpine species such as reindeer Rangifer tarandus (Pettorelli et al. 2005) and hoary marmots (Karels & Hik 2003).
Weather may also be implicated in collared pika declines through catastrophic winter mortality associated with rain that later freezes forming an icy crust over food resources rendering them unavailable; alternatively winter rain may directly cause pika death through exposure (Smith et al. 2004). The frequency of winter freezing and thawing events in alpine and high latitude ecosystems is predicted to increase as a consequence of global warming (IPCC 2001; ACIA 2005). Increasing amounts of winter precipitation falling as rain rather than snow, attributed to the PDO and climate change trends, has recently been documented in western United States (Knowles, Dettinger & Cayan 2006), leading to an expectation of more frequent freeze–thaw events in the future. Such freeze–thaw events have been implicated in the population dynamics of other high-latitude herbivores (e.g. Forchhammer & Boertmann 1993; Aanes, Sæther & Øritsland 2000; Aars & Ims 2002). Alternatively, the trend of earlier snowmelt, also documented by Knowles et al. (2006), could improve pika survival and positively affect pika populations. The relationships we observed between vital rates and the PDO provide support in favour of the hypothesis linking pika population growth to winter weather conditions and warrant further detailed investigation.
To conclude, the decomposition of V(λ) into contributions from matrix elements is a powerful tool in understanding how λ responded to historical environmental variation. Population declines and fluctuations at our site were driven largely by variation in adult vital rates, however, the specific influence of adults varied spatially. The variation in adult survival was well explained by large-scale climate patterns (the Pacific Decadal Oscillation) and demonstrated a strong link between large-scale climate indices and population growth rate through the timing of spring snowmelt and intermediary vital rates.
We thank the many field assistants that have contributed to this long-term data set. Financial and logistical support was provided by the Natural Sciences and Engineering Research Council of Canada, Canada Foundation for Innovation, Canada Research Chairs Program, DIAND Northern Scientific Training Program, Canadian Circumpolar Institute, Steve and Elaine Antoniuk Graduate Scholarship in Northern Research, Alberta Ingenuity Studentship, Jennifer Robinson Memorial Scholarship, and an Izaak Walton Killam Memorial Scholarship. R. Danby, A. Derocher, E. Gillis, T. Karels, M. Lewis, A. Smith, S. Wilson, and two anonymous reviewers provided comments on earlier drafts. This work was conducted under permits issued by the Yukon and Canadian governments and the University of Alberta. We thank Kluane First Nation for permission to conduct this research on their traditional lands.