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High rates of habitat loss and fragmentation, as a result of habitat destruction, climate change and other types of disturbance, have potentially serious consequences for maintenance of biodiversity (e.g. Sinclair et al. 1995; Moilanen & Cabeza 2002). Fragmented habitat patches are often separated by large expanses of relatively unsuitable habitat where individuals of some species cannot survive. Once restricted to small and isolated patches, some species will rapidly disappear (Turner 1996). Nevertheless, many species naturally persist in a network of isolated populations or a ‘metapopulation’, in which smaller subpopulations are connected by dispersal or the movement of individuals (Hanski 1999).
Metapopulation models examining the effects of patch size and isolation on rates of extinction and recolonization have been well studied (e.g. Hanski 1994; Hanski et al. 1996; Moilanen & Hanski 1998). Larger population sizes, often approximated by patch area, are believed to be less prone to extinction resulting from demographic stochasticity, while the colonization probability of an empty patch is largely determined by its isolation to other surrounding populations. These models have tended to assume that patch size and isolation are sufficient for predicting extinction and colonization of local populations over time.
Previous work suggests that talus-dwelling pikas (Lagomorpha: Ochotonidae) represent a ‘classical’ metapopulation structure (Smith 1980, 1987; Hanski & Gilpin 1991; Smith & Gilpin 1997; Peacock & Smith 1997; Moilanen, Smith & Hanski 1998). However, these dynamics have been adequately quantified for a only single population of the American pika (Ochotona princeps, Richardson) in California (Moilanen et al. 1998), so additional research on other pika populations would enhance the generality of results from earlier studies. Metapopulation dynamics of pikas are generally tractable because (1) they are territorial and live in spatially distinct or naturally fragmented landscapes (talus or boulderfields separated by meadows) (Smith 1974); (2) pikas infrequently disperse long distances and therefore the spatial configuration of the habitat patches will influence the dynamics of the populations (Moilanen et al. 1998); and (3) the overall population size is thought to be relatively stable (Southwick et al. 1986), and even though subpopulations may experience extinctions and colonizations, these dynamics are largely asynchronous, which appears to prevent extinction of all subpopulations simultaneously (Moilanen et al. 1998).
Our primary objectives were (1) to test the assumption of general metapopulation models that patch size is largely responsible for predicting patch extinction, and connectivity of patches is the best predictor of colonization events, and (2) to explicitly examine the relative importance of patch size, connectivity and selected attributes of habitat quality on patch occupancy, local extinction and recolonization rates in a population of collared pikas (Ochotona collaris, Nelson), a close relative of O. princeps, in the south-west Yukon during a seven year period (1995–2001).
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Collared pikas are generalist alpine herbivores endemic to the mountains of central and south-eastern Alaska, the Yukon, and north-western British Columbia (MacDonald & Jones 1987). They are territorial animals that live in a naturally patchy landscape consisting of isolated talus patches separated by expanses of alpine meadows. Our study site was located in the Ruby Ranges, Yukon (61°12′N, 138°16′W; 1700–2100 m), and included 27 discrete talus patches ranging in size from 0.07 ha to 15.7 ha and separated by meadow ranging in distance of 15 m to 1140 m within a 4 km2 study area (Fig. 1, Table 1). A 50 × 50 m grid system covering the study site allowed us to map individual talus patches. The size and isolation of the patches were calculated using arcview (Environmental Systems Research Institute, Inc. 1999).
Figure 1. Talus patches at the Ruby Ranges, Yukon study site. Shaded areas represent talus surrounded by meadow (white), lines indicate shallow creeks. See Table 1 for patch details.
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Table 1. Patch area, perimeter, number of times surveyed, number of times occupied by adults, number of times went extinct, number of times recolonized, range in population size and connectivity measure (Si) for each patch shown in Fig. 1
|Patch||Area (m2)||Perimeter (m)||No. years surveyed||Adult pop. range||Times occupied||Times recolonized (years)1||Times extinct (years)2||Range of connectivity|
|CCk|| 78201||2744||4||13–29||4||na3||0|| 3·6–8·8|
|EGH||100177||1830||7|| 1–13||7||2 (99, 00)||1 (98)||10·5–27·0|
|snowplot||156875||1801||7|| 0||0||0||na|| 4·9–20·8|
|WO|| 31712||1704||7|| 0–15||6||1 (01)||1 (99)|| 3·5–22·3|
|GILL|| 59741||1663||2 || 7–9||2||na||0|| 3·0–15·4|
|WS|| 63897||1488||7|| 0–7||5||0||1 (99)|| 3·5–23·8|
|EK9|| 23954||1060||7|| 3–16||7||na||0|| 7·6–20·9|
|WM|| 19374|| 992||7|| 0–7||4||0||1 (98)|| 5·2–30·5|
|EM8|| 14063|| 956||7|| 0–6||6||4 (97, 98, 99, 01)||1 (96)||10·0–28·4|
|EP-T|| 19973|| 734||7|| 0–8||5||0||1 (99)||10·1–25·0|
|OBL|| 12561|| 656||2|| 0–4||2||1 (01)||1 (00)|| 3·6–10·9|
|HAW|| 7797|| 623||3|| 1–4||3||na||0|| 7·3–16·25|
|WPQ2|| 8793|| 480||7|| 0–4||5||1 (99)||1 (98)|| 5·4–31·4|
|WQ17|| 6481|| 421||4|| 0||0||0||na|| 1·1–14·2|
|WQ12|| 3871|| 405||7|| 0–2||0||0||1 (98)|| 2·0–27·9|
|WHH3|| 1775|| 378||4|| 0||0||0||na|| 7·8–12·5|
|WS3|| 3661|| 334||7|| 0–3||5||0||1 (99)|| 5·5–25·8|
|ELL4|| 3571|| 319||3|| 0–2||2||1 (01)||1 (99)|| 8·0–16·1|
|FF7|| 2557|| 290||4|| 1–2||4||na||1 (00)||14·5–42·5|
|WO3|| 4504|| 277||7|| 0–4||6||2 (99, 00)||1 (98)|| 4·7–31·62|
|WP9|| 1793|| 220||7|| 0||0||1 (95)||na|| 2·7–31·4|
|ENN4|| 1184|| 175||3|| 0–1||2||1 (01)||1 (99)|| 6·5–15·2|
|KK0|| 1571|| 172||2|| 0–2||1||1 (01)||na|| 7·6–15·8|
|EK5|| 1316|| 156||7|| 0–2||6||4 (98, 99, 00, 01)||1 (97)|| 7·5–33·2|
|EJJ3|| 654|| 152||3|| 0||0||0||na|| 6·7–16·7|
|EII5|| 949|| 117||3|| 0||0||0||na|| 9·4–25·7|
Pikas were live-trapped in summer 1995–2001 using Tomahawk traps baited with native vegetation. Animals trapped for the first time were marked with numbered metal ear tags and a unique combination of coloured wires to allow for subsequent observation and identification of individuals without handling. The age and sex of each individual was also determined (Franken 2002). Because pikas are diurnal, vocal and build large distinctive haypiles, we were able to determine the number and location of all pikas in the study area with confidence.
Each summer talus patches were surveyed to determine the occupancy (presence or absence) of pikas on a patch. A patch was considered to be recolonized if pikas were absent the previous summer and present the current summer. Clinchy, Haydon & Smith (2002) suggested that because juveniles are the main dispersers and they tend to have lower survival than adults, that there would be a higher probability of extinction following recolonization events. To avoid this problem, we defined a patch as becoming extinct if adult pikas were present in the previous summer, but absent in the subsequent summer. Because adults are philopatric (O. princeps, Smith 1974; O. collaris, this study; see Franken 2002), we assumed that the absence of adult pikas from previously occupied patches indicated death rather than dispersal.
A patch was defined as the area with a population of pikas in which most of behavioural interactions occur within the patch rather than among patches (Harrison 1991). We were able to define populations, and thus patches, using mark–recapture studies. It is possible that pikas may have made brief movements to these other patches for mating; however, pika movements away from the talus are inhibited due to the threat of predation (Ivins & Smith 1983; Holmes 1991). Pikas will rarely move more than 6 m from the talus edge to forage, even though forage availability might improve further out (Huntly 1987; Roach, Huntly & Inouye 2001; McIntire & Hik 2002; Morrison et al. 2004), suggesting that movements between talus patches separated by large expanses of meadow are infrequent. The smallest distance between our patches was 15 m and more often this distance was much larger (Table 1).
In metapopulation models, patch size and population size are assumed to be correlated and therefore patch size is often used as a surrogate for population size because it is easier to measure. At our study site, we were able to determine both the population size and the patch size. We used population size in determining the probability of extinction, and patch size when determining the probability of recolonization. Patch size was measured as both the total area (hectares) and the perimeter of a talus patch (metres). Previous work on pikas has used perimeter as an indication of habitat because pikas tend to live and forage at the patch edge (Smith 1974). We correlated patch area and perimeter with population size to determine which was better at describing the relationship between patch size and population size.
We used a measure of connectivity described by Hanski (1994), which takes into account distances to all potential source populations and their population size. This connectivity measure is determined based on the movement ability of individuals in a spatially structured landscape (Moilanen & Hanski 2001):
where Si is a measure of connectivity for patch ‘i’ to other potential source populations ‘j’, α scales the effect of distance to migration (1/α is the average migration distance), dij is the distance from patch i to j, and Nj is the population size of the potential source population.
We initially tested the significance of size (perimeter) and connectivity on the patch dynamics in our study site using univariate logistic regression to model the probability of occupancy, recolonization and extinction. These analyses also permitted direct comparison with earlier studies of patch dynamics of pikas, and allowed us to examine the relative importance of the individual variables. We then used generalized linear models (GLM, McCullagh & Nelder 1989) with binomial errors (splus; Mathsoft Inc. 1997) to model extinction and recolonization of talus patches by pikas incorporating both size and connectivity measures, as well as other patch characteristics. Terms were added in a forward stepwise sequence starting with a null model (intercept only) and using the Cp statistic as the criteria for addition of terms, until no additional variables improved model fit significantly. Additional non-linear effects were tested for by fitting splines to the variables using generalized additive models (gam; Hastie & Tibshirani 1990), but did not improve model fit significantly. Whether a patch went extinct and whether it was recolonized was modelled as a function of (1) patch size (population size for extinction and perimeter for recolonization); (2) connectivity, Si; (3) aspect, measured as the sine of radians; (4) amount of meadow within the talus; (5) year (1995–2000); and (6) average survival (habitat quality); all variables are described in more detail below.
We attempted to determine the quality of each patch by correlating a number of measured habitat variables with survival; however, different habitat characteristics were important in different years and we were unable to develop a set of habitat characteristics that could be used to predict quality for all the years (Franken 2002). While it is possible that we were not measuring the correct habitat characteristics, there is likely to be significant variation in the resources that are important for survival from one year to the next. Consequently, we determined the fate of all individuals and used average survival values over all years as an index of habitat quality for a patch. This provided an indication of patch quality, as we assumed that patches with higher survival rates indicated better quality. While the rationale for this measure is potentially circular, it was considered to be the best option because of the variability in individual habitat characteristics (also see Sergio & Newton 2003).
We used two additional measures of habitat quality: talus aspect and the amount of meadow within a patch. The aspect of the patch was measured in degrees and then converted to a sine wave by taking the sine of the radians to linearize aspect. Observations suggest that southwest facing slopes have higher pika survival owing to the increased solar exposure and plant productivity and therefore was set equal to 1. Patches with a northeast aspect were considered least productive and were set to −1; all other aspects fell between 1 and −1. We also examined the proportion of meadow within the patch that would provide foraging opportunities. The percentage of meadow located within a talus patch was estimated from photographs taken of each patch.
The above variables were used to predict patch occupancy, recolonization and extinction. All patches that were measured in the study site had indications of previous pika use (old haypiles or pellets); however, we used patches in the analysis only if adults had lived there during our study. This approach allowed us to determine average survival of pikas in the patch. Although juveniles dispersed and colonized vacant patches at the end of each summer, many of these events were transient within the season. Consequently, including these juveniles would have introduced substantial additional variation and so we chose a conservative approach that was also more consistent with some other studies (e.g. Clinchy et al. 2002).
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Adult population size and total population size were correlated more strongly with perimeter (r2 = 0·33, P < 0·001; r2 = 0·38, P < 0·001, respectively) (Fig. 2a), than with patch area (ha) (r2 = 0·06, P = 0·004; r2 = 0·071, P < 0·001, respectively) (Fig. 2b). Therefore, perimeter was used as our size measure for recolonization and occupancy analyses. We recorded a total of 18 colonization events and 15 extinction events from 1995 to 2001 (Table 1), most of them during 1998–2001 when the population density was low (Franken 2002).
Figure 2. Correlations between (a) perimeter (m) or (b) patch area and adult population (dotted line) and total (solid circles and lines) population sizes.
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A high proportion (minimum of 31–50%) of juveniles at this site made interpatch movements and there was no significant difference between the number of males and females moving, nor the distance that the different sexes moved (Franken 2002). The majority of pikas at our site moved short distances from their natal territories, with a few pikas making larger movements. The average minimum dispersal distance moved by juvenile pikas at this site was 332 m (n = 35) (for more detail on dispersal movements see Franken 2002). This value was used to calculate α (the effect of distance to dispersal), which was set to 3·0. This is similar to the value of α (2·5) used by Moilanen et al. (1998) for the American pika.
The results of the univariate logistic regression showed that connectivity and the perimeter of a patch (Table 2) significantly influenced the probability of a patch being occupied. Patches were more likely to be occupied if they had higher connectivity and were larger in perimeter. Although these variables were important, very little of the total deviance was explained; connectivity only explained approximately 11% of the deviance in occupancy. The probability of a patch being recolonized was influenced significantly by the connectivity among patches, where more connected patches had a greater probability of being colonized (Table 2). Although this logistic regression was significant, it was only able to explain approximately 17% of the deviance in colonization.
Table 2. Univariate logistic regression predicting patch occupancy, recolonization and extinction of collared pikas based on patch size (adult population and perimeter) and patch isolation (connectivity)
|Patch process||Coefficient||SE||Deviance explained of total (d.f.)||P (χ2)|
| Connectivity|| 0·1121||0·0273|| 20·26/181·86 135||0·0000|
| Perimeter|| 0·0008||0·0003|| 7·98/181·86 (135)||0·0047|
| Connectivity|| 0·0928||0·0431|| 5·04/79·23 (65)||0·0248|
| Perimeter|| 0·0000||0·0005||0·0045/79·23 (65)||0·9460|
| Connectivity||−0·0278||0·0389|| 0·52/68·05 (60)||0·4727|
| Adult population size||−0·2537||0·1431|| 4·89/68·05 (60)||0·0270|
| Perimeter||−0·0009||0·0005|| 3·26/68·05 (60)||0·0711|
The probability of a patch going extinct was significantly influenced by the adult population size, with smaller populations having a greater probability of going extinct (Table 2), but only explained approximately 7% of the deviance in extinction. Thus, the results from the univariate logistic regression suggest that there are likely to be other variables that could explain the patch dynamics of pikas at this site in addition to patch size (population size) and connectivity.
factors affecting recolonization
Aspect, connectivity, average survival and the amount of meadow were all important in predicting the probability of recolonization of a patch by pikas (Table 3). Aspect had a large effect on which patches were recolonized. This was the first variable added to the model; all other terms were assessed after holding the effect of aspect constant. Patches orientated southwest had a higher probability of being recolonized (Table 3). Connectivity, measured as the proportion of surrounding patches that could contribute colonizing individuals, also had significant effects on whether or not a patch was recolonized. Patches that had high connectivity were more likely to be recolonized (Table 3). The recolonization of a patch was also significantly affected by the average survival of individuals in the patch (our measure of habitat quality); patches where the average survival of individuals was higher were also more likely to be recolonized (Table 3). The proportion of meadow within a patch also affected the probability of recolonization of a patch, such that patches with less meadow interspersed throughout the talus had a higher probability of being recolonized (Table 3). Year (1995–2001) and the size or perimeter of a patch did not contribute significantly when added to the model and were subsequently excluded from it. Aspect, connectivity, average survival and amount of meadow within the talus explained approximately 41% of the deviance in recolonization.
Table 3. Final models of recolonization and extinction of collared pikas. Significant terms were added stepwise based on the Cp statistic at each step. The change in deviance of the model by the inclusion of the term (and all variables above) is tested against a χ2 distribution
|Model||Variables included in final model||Coefficient (SE)||Residual d.f.||Change in deviance||P for χ2 test on deviance|
|Aspect|| 1·057 (0·62)||46||51·93||0·0004|
|Connectivity (Si)|| 0·2698 (0·09)||45||45·51||0·0113|
|Average survival|| 8·375 (3·66)||44||41·69||0·051|
|Meadow||−7·744 (4·15)||43||38·03 R = 0·41||0·0556|
|Extinction||Constant|| 3·994 (1·80)||60||68·05||–|
|Average survival||−8·962 (2·83)||59||53·89||0·0002|
|Connectivity (Si)||−0·0907 (0·06)||58||50·59 R = 0·26||0·0832|
Although year and connectivity were considered to be moderately correlated (r = −0·68), these variables were not added into the same model. Aspect and meadow were also moderately correlated r = −0·54; all other variables were weakly correlated (r < 0·4).
factors affecting extinction
The average survival and the connectivity of the talus patch were both important in predicting the probability of a patch going extinct (Table 3). Average survival of the patch had a strong influence and was added into the model first. All other terms were therefore assessed after holding the effect of average survival constant. Patches were less likely to go extinct if they had higher average survival, as well as higher connectivity (Table 3). The talus aspect, amount of meadow within a talus patch, population size and year (1995–2001) did not contribute significantly to the model. Average survival and connectivity explained approximately 26% of the total deviance in extinction events.
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Several studies have examined the influence of patch size, which is assumed to be correlated with population size, and isolation on the persistence of populations (e.g. Smith 1980; Peltonen & Hanski 1991; Hanski et al. 1995; Forys & Humphreys 1999), and many have shown that smaller, more isolated patches are more subject to extinction and less likely to be recolonized than larger, closer patches. Our results, however, suggest that population size is only marginally important in predicting extinction of pikas, and connectivity explains only partially colonization of patches at our site. Other habitat quality features such as aspect, amount of meadow, and average survival (a proxy measure of patch quality) were also found to influence pika persistence. Although our population declined from 1998 to 2000 (Franken 2002) there was still a balance between the number of colonization and extinction events, consistent with evidence for equilibrium metapopulation structure (Hanski 1999).
One constraint of our study is that several of the patches in the study area were surveyed only during the last 4 years (1998–2001) and therefore population sizes and connectivity to these patches was not included in the early surveys (1995–98). This may have underestimated the importance of connectivity with respect to extinction, but is unlikely to have affected the importance of connectivity on recolonization, as most recolonization occurred in recent years. However, three common parameterization errors discussed by Moilanen (2002: inaccurate measurement of patch area, unknown patches, inaccurate patch occupancy) were not applicable to our study. Pikas are present throughout the Ruby Ranges, and although we were unable to assess the influence of long-distance dispersal onto our study site (i.e. edge effects), our core area (Fig. 1) was relatively isolated from other large talus patches occupied by pikas (approximately 400 m to the east; > 600 m to the south and north; and > 1000 m to the west). We suspect that few individuals were coming from these peripheral areas.
Recolonization of talus patches by pikas at our site was higher when there was greater patch connectivity. Connectivity was also important in preventing local extinctions of pikas, consistent with other empirical evidence showing that as populations become more isolated the risk of extinction increases (e.g. Smith 1980; Fahrig & Merriam 1985; Sjögren 1991; Johst, Brandl & Eber 2002). We also did not find a strong relationship between population size and extinction. Although univariate analysis indicated that population size had a significant influence on extinction, little variation was explained. When other variables were included in the analysis, adult population size did not appear to be important in predicting extinction. It is possible that we did not see an affect of population size on extinction because of a low variation in the sizes of populations. Additionally, low over-winter survival of pikas at this site and moderate to high interpatch movement rates (Franken 2002) may have weakened the effect of population and patch size on extinction.
Clinchy et al. (2002) argued that spatial patterns of patch occupancy may be related to processes other than dispersal, such as weather, anthropogenic changes and predation. They found that spatially correlated extinctions of American pikas in California are probably not a result of the rescue effect, but may be explained by predation. They argued that there was very little dispersal in their population of pikas, and therefore another mechanism explained the recolonization and extinction patterns. However, at our site there are few predators (Hik, McColl & Boonstra 2001) and interpatch dispersal is common and seems to be an important process in both the recolonization and extinction patterns observed.
We had accurate population sizes for every patch in the study area, and therefore did not have to rely on patch size as a surrogate of population size (Hanski 1999). Although patch area and patch perimeter were both correlated with population size, patch perimeter explained more variation, while patch area actually explained very little variation in population size. Because pikas often establish haypiles along the edge of the talus patch (Smith 1974), it is not surprising that population size would be correlated with perimeter.
The assumption that population size correlates with patch size may be risky in a conservation situation if large patches of poor habitat are conserved over small patches of high quality habitat. One patch (snowplot –Fig. 1, Table 1), the largest patch in terms of area and perimeter, was never occupied by pikas during our study. There are two possibilities as to why pikas are absent from this site. Pikas may not have colonized this area because of lack of conspecifics, which suggests that animals will disperse to patches where conspecifics are located and will avoid unoccupied patches regardless of quality (e.g. Stamps 1988). However, unoccupied patches were often recolonized at our site, and it is more likely that this particular patch cannot support pikas because of low habitat quality associated with persistent late season snow cover.
Thomas et al. (2001) and Fleishman et al. (2002) found habitat quality contributed more to species persistence than area or isolation. Although habitat quality is more difficult to measure than area and isolation, Thomas et al. (2001) suggested its importance in metapopulation studies. In our case, pikas were more likely to recolonize patches with more talus and less meadow interspersed in the talus. The main foraging opportunities for pikas are on the talus–meadow interface or patch perimeter (Huntly 1987; Holmes 1991), and although meadow interspersed within the talus patch may be beneficial in terms of shorter travel distance to forage, there may be greater threat of predation. More meadow within a patch means less continuous talus, which may be important for escape terrain from their main predators, such as weasels and birds of prey (Ivins & Smith 1983; Holmes 1991).
The aspect of talus was also important in recolonization, such that pikas recolonized patches that were southwest-facing more often than patches that were northeast-facing. The length of growing season and the quality of vegetation surrounding the talus patches may account for this result, as patches facing north and east are more likely to have longer periods of snow cover and reduced growth of forage plants. Average survival was also a significant predictor for recolonization, and provided a useful measure of habitat quality in this system.
Although pikas at our site exhibited high population turnover, patch size and connectivity did not appear to explain the dynamics entirely. Habitat characteristics associated with aspect and amount of meadow also influenced persistence of pikas. It is not surprising that populations are more likely to persist when living on patches with higher habitat quality (Verboom et al. 1991; Klok & DeRoos 1998; Thomas et al. 2001; Fleishman et al. 2002). Measures of habitat quality may be particularly useful when combined with patch size and isolation to enhance the ability of metapopulation models to predict occupancy patterns. More generally, our results and others suggest that large areas and even large population sizes are not secure from extinction risks. Connectivity plays an important role in both recolonization and extinction; however, habitat quality must also be considered in models and in conservation planning to ensure population persistence (e.g. Moilanen & Cabeza 2002).