Amphibians are rapidly disappearing from habitats around the world and a major cause of these declines is the amphibian chytrid fungus, Batrachochytrium dendrobatidis (“Bd”). The growth rate of Bd is strongly temperature-dependent, and in areas where temperatures are well outside the envelope in which Bd has high growth rates, amphibians may be afforded a refuge from the effects of Bd. This possibility has received considerable empirical support in hot climates, but remains largely untested in cold climates. We conducted a five-year study of the impact of Bd on the declining Sierra Nevada yellow-legged frog (Rana sierrae) across an elevation/temperature gradient in Yosemite National Park using three approaches: (1) resurveys of all 285 R. sierrae populations to describe the landscape-scale patterns of Bd infection intensity, frog population size, and frog population persistence; (2) detailed description of seasonal patterns in temperatures and corresponding Bd infection intensities on R. sierrae; and (3) a frog translocation experiment in which infected R. sierrae from a single source lake were introduced into each of five lakes along an elevation gradient. We predicted that infection intensity should decrease with increasing elevation (i.e., decreasing temperature), and consequently frog survival, population size, and population persistence should increase with elevation. Results from resurveys indicated that frog population size increased with elevation but Bd infection intensity and frog population persistence were unrelated to elevation. Seasonal temperatures varied widely but had no significant effect on Bd infection intensity. Results from the translocation experiment indicated that Bd infection intensity and frog survival following translocation were also unrelated to water temperature. Therefore, contrary to the widely-accepted paradigm that cold environments should strongly limit effects of Bd on amphibians, we found little or no evidence of such limitation at even the highest elevations. Therefore, in temperate montane ecosystems it is unlikely that high elevations will provide amphibians with a refuge from Bd.
Amphibians are declining worldwide at an alarming rate and a recent study suggested that more than 40% of the world's 6000+ species are now threatened with extinction (Stuart et al. 2004). Causes of endangerment include the well-documented effects of habitat alteration (Dodd and Smith 2003) and nonnative species (Kats and Ferrer 2003), but a recently-described disease is increasingly considered a serious threat (Skerratt et al. 2007). Chytridiomycosis is an emerging infectious disease of amphibians caused by the fungus Batrachochytrium dendrobatidis (“Bd”). Diseases are rarely considered as a driving force of host extinctions but the extraordinary virulence of Bd has caused the decline or extinction of hundreds of species during the last several decades (Skerratt et al. 2007) and hundreds more are considered at risk as Bd spreads into new areas (Rödder et al. 2009).
The growth rate of Bd is strongly influenced by temperature. Based on laboratory studies, the relationship between temperature and Bd growth is described by a hump-shaped curve; maximum growth occurs between 15°C and 25°C, no growth occurs below 4°C, and temperatures above 30°C cause rapid mortality (summarized by Rohr et al. (2008), based on Piotrowski et al. (2004) and Woodhams et al. (2008); hereafter referred to as the “temperature-Bd growth relationship”). Given this strong temperature dependence, Pounds et al. (2006) proposed that climate warming could increase exposure of tropical amphibians to temperatures in which Bd growth is maximized and thereby increase the risk of Bd-caused amphibian extinctions. In contrast, in habitats where temperatures fall outside of the envelope in which Bd has high growth rates, amphibians may be afforded a refuge (Puschendorf et al. 2009) from the high infection intensities that cause fatal chytridiomycosis (Vredenburg et al. 2010). Studies conducted in regions characterized by high average temperatures provide considerable support for this hypothesis, with the impact of chytridiomycosis often reduced in hotter regions and seasons. For example, in tropical and subtropical regions, Bd prevalence and infection intensity are generally lower at low versus high elevations (Woodhams and Alford 2005), low versus high latitudes (Kriger et al. 2007), and during summer versus winter (Berger et al. 2004, Kriger and Hero 2007). However, given that nearly all such studies were conducted at the high end of the temperature range over which Bd is active, they provide only a partial description of the temperature regimes that could afford amphibians a refuge from chytridiomycosis.
Amphibian-Bd dynamics in cold climates remain poorly described, but the temperature-Bd growth relationship suggests that cold temperatures may limit the impact of Bd. In the Rocky Mountains (USA), Muths et al. (2008) reported that the probability of Bd occurrence on amphibians was negatively correlated with elevation and positively correlated with temperature. However, Woodhams et al. (2008) provided evidence that due to life history trade-offs, Bd may be able to maintain relatively high fitness across a much wider range of cold temperatures than the temperature-Bd growth relationship would predict, complicating predictions of the effects of cold temperatures on Bd. Given the increasing interest in using temperature data in general and the temperature-Bd growth relationship in particular to predict the global occurrence of Bd and its impacts on amphibian species (e.g., Rödder et al. 2009, Murray et al. 2011) more detailed study of Bd effects on amphibians in cold climates is critically needed.
The mountain yellow-legged frog is a species complex composed of two closely-related taxa, the Sierra Nevada yellow-legged frog, Rana sierrae, and the southern mountain yellow-legged frog, Rana muscosa (Vredenburg et al. 2007). Historically, these frogs were abundant across California's temperate montane habitats, including the Sierra Nevada mountains (Grinnell and Storer 1924). Both species have declined precipitously during the last century and are now absent from more than 90% of historic localities (Drost and Fellers 1996, Vredenburg et al. 2007). The negative effect on mountain yellow-legged frogs of fish introductions into naturally fishless lakes and streams is well documented (Bradford 1989, Knapp and Matthews 2000, Vredenburg 2004, Knapp et al. 2007). However, during the past decade Bd has caused the decline or extirpation of hundreds of mountain yellow-legged frog populations from remaining fishless habitats across the Sierra Nevada (Rachowicz et al. 2006, Vredenburg et al. 2010), and is now widespread in Yosemite's remaining R. sierrae populations (Fellers et al. 2001; R. A. Knapp, unpublished data). As such, the broad elevation gradient within Yosemite provided an opportunity to quantify the effect of chytridiomycosis across the range of temperatures that characterize temperate montane regions.
The objective of this study was to test the hypothesis that the thermal regime experienced by R. sierrae in Yosemite influences Bd infection intensity, with associated effects on frog survival, frog population size, and frog population persistence. Based on the temperature-Bd growth relationship, our expectation was that high elevation habitats in Yosemite would be cold enough to limit Bd growth, resulting in a negative correlation between Bd infection intensity and elevation and positive correlations between elevation and frog survival, frog population size, and population persistence. We tested this hypothesis using three approaches. First, following on a 2000–2002 survey of all R. sierrae populations in Yosemite (Knapp 2005), we resurveyed these populations to describe the landscape-scale patterns of Bd infection intensity, frog population size, and frog population persistence across a wide elevation (i.e., temperature) gradient. Second, we used intensive sampling of three R. sierrae populations across a range of elevations to describe the pattern of seasonal temperatures and corresponding Bd infection intensities. Third, to quantify the relationships between temperature regime and both infection intensity and frog survival in more detail, we conducted an experiment in which infected R. sierrae from a large source population in Yosemite were translocated to five nearby lakes that spanned an elevation gradient, and Bd infection intensities and frog survival were quantified over the subsequent two years.
Yosemite National Park encompasses 3027 km2 of temperate montane habitat in the central Sierra Nevada (latitude = 37.50°–38.18°, longitude = 119.21°–119.88°). Precipitation in Yosemite falls mostly in the winter months and falls as rain and snow at the lowest elevations and only snow at the higher elevations. Yosemite encompasses an ideal geography in which to conduct research related to our study objective because the broad elevation gradient (1300–3700 m) produces a range of temperatures to which frogs and Bd are exposed (air and water temperatures decrease by approximately 5°C for every 1000 m increase in elevation; Livingstone et al. 1999). Yosemite's lentic habitats are generally small (<10 ha) and range from relatively warm water bodies surrounded by forest at lower elevations to high elevation, cold, oligotrophic water bodies surrounded by alpine meadows and rock.
Lake temperature regimes
To describe the annual temperatures experienced by frogs in Yosemite lakes, we deployed temperature loggers at six lakes in 2008–2009 and at three additional lakes in 2009–2010. Lake elevations ranged from 2273 m to 3237 m (Fig. 1; Appendix A: Table A1). Snow pack depths in 2008, 2009, and 2010 were close to the long-term average for the area (109%, 88%, and 99%, respectively; based on April 1 snow water content measured at the Dana Meadows snow course, 1927–2010: 〈http://cdec.water.ca.gov/cgi-progs/snowQuery〉). Water temperatures were recorded using iButton loggers (Maxim Integrated Products, Sunnyvale, California, USA). R. sierrae spend the ice-free season (June to October) in shallow water adjacent to shore and overwinter in deeper water (Bradford 1984). Therefore, to characterize the temperatures experienced by frogs and by Bd on an annual basis, we deployed two loggers in the littoral zone of each lake soon after ice-out and retrieved them in late September. These loggers were attached to a line anchored in 1 m of water, were kept at 20 cm depth by a surface float, and recorded water temperatures once per hour. When the littoral zone loggers were retrieved in late September, we deployed a single logger in the deepest portion of each lake. This deep water logger was retrieved soon after ice-out the following spring and replaced with two littoral zone loggers that recorded temperatures throughout the second summer. Deep water loggers were suspended 10 cm above the bottom with a submerged float, were kept in place with an anchor, and recorded temperature once per day at 1300 h.
Frog population resurvey
During the original 2000–2002 survey of all lentic habitats in Yosemite (n = 2655; Knapp 2005), R. sierrae was detected at 285 sites. For the current study, we resurveyed all 285 sites once during the summers of 2005, 2006, or 2007 (Fig. 1). During the original survey and the resurvey, the occupancy of sites by R. sierrae and the abundance of all life stages (tadpoles, juveniles, adults) were estimated using visual encounter surveys of the entire water body shoreline and the first 100 m of each inlet and outlet stream (Crump and Scott 1994, Knapp 2005; see Appendix A for additional details).
During the resurvey, we estimated Bd infection intensity on R. sierrae in each population using skin swabs collected from adults (≥40 mm snout-vent length (SVL)) and juveniles (<40 mm SVL), and mouthpart swabs collected from tadpoles (Knapp and Morgan 2006, Hyatt et al. 2007). Our goal was to swab 20 individual R. sierrae per site, and animals were collected as available during or after surveys. Swabs were analyzed for Bd using quantitative real-time PCR (hereafter, “qPCR”), and results are expressed in units of “zoospore equivalents” (see Appendix A for additional details).
Seasonal patterns of Bd infection intensity
Frog populations used to describe seasonal patterns were chosen because they were the largest R. sierrae populations in each of three elevation categories in Yosemite (based on Knapp (2005) and the resurveys conducted as part of the current study): low (2401–2700 m), intermediate (2701–3000 m), and high (3001–3300 m). We refer to these study sites as “Tiltill Lake”, “Davison Lake”, and “Conness Pond”, respectively (Fig. 1; Appendix A: Table A1). Large populations were necessary to maximize the number of swabs collected during each sampling period. We originally included an additional elevation category (2101–2400 m), but no frog populations in this elevation range were large enough to be useful for our purposes. In 2008 and 2009, the three frog populations were visited approximately once per month from June to September (4–6 visits per year). During each visit, we conducted a visual encounter survey of the lake and associated streams, and collected skin swabs from R. sierrae adults and juveniles that were analyzed using qPCR. Other amphibian species present at these sites included the Sierra treefrog (Pseudacris sierra; present at all three sites) and Yosemite toad (Anaxyrus [=Bufo] canorus; Conness Pond only).
Frog translocation experiment
Frogs for translocation were collected from a single source population and moved to five lakes that spanned an elevation gradient of 2471 to 3237 m. The source population (Conness Pond; Fig. 1; Appendix A: Table A1) was the largest R. sierrae population in Yosemite (>500 adult frogs), and has been intensively monitored since 2004. In 2005, we initiated a capture-recapture study at Conness Pond to quantify frog survival by tagging 323 adult frogs with PIT tags. No additional frogs were tagged at this site until early summer 2008 when an additional 71 adult frogs were PIT-tagged. This population was first sampled for Bd in 1998 and was found to be Bd-positive (Fellers et al. 2001). qPCR analysis of 563 swabs collected in 2004 and 2005 indicated that Bd prevalence was high (75% of frogs were infected) and that infection intensities were relatively low (median = 83 zoospore equivalents per swab), as is typical for R. sierrae populations in Yosemite (Briggs et al. 2010).
The five translocation sites (Fig. 1; Appendix A: Table A1; McGee Lake, Tioga Pond, Skelton Lake, Miller Lake, Soldier Lake) are all fishless, relatively deep perennial water bodies and were therefore suitable for R. sierrae (Knapp et al. 2003). Unpublished records indicate the historical presence of R. sierrae at Miller Lake, Skelton Lake, and Tioga Pond, but their historical presence at McGee and Soldier Lakes is uncertain (but likely given their historical presence in nearby lakes). Based on repeat visual encounter surveys conducted at the translocation sites between 2001 and 2006, prior to the translocations all sites lacked R. sierrae, but three sites (McGee, Miller, Tioga) contained breeding populations of the Sierra treefrog. Adult Yosemite toads were occasionally seen at Tioga Pond and Skelton Lake but breed in adjacent marshes and not in the lakes themselves.
To reduce impacts to the Conness Pond source population, we conducted three translocations in 2006 (McGee, Tioga, Skelton) and the remaining two translocations in 2008 (Miller, Soldier). In 2006, frogs for translocation to McGee Lake were collected on 17 July. These 50 adult frogs were swabbed, measured, weighed, and PIT-tagged. Following processing, frogs were held individually in wet cloth bags at Conness Pond, and the following morning were transported 10 km on foot to McGee Lake. On release, 43 of the frogs were active and seemingly healthy. The remaining seven frogs were dead for unknown reasons. In an attempt to reduce mortality in the remaining two translocations conducted in 2006, frogs translocated to Tioga Pond and Skelton Lake were placed individually in small wetted plastic containers that had air holes to ensure adequate ventilation and were transported to the two release sites on the day they were collected. All other frog handling procedures were unchanged. Forty adult frogs were translocated to Skelton Lake (6 km) and to Tioga Pond (10 km) on 7 August and 8 August, respectively (80 frogs total). Thirty-nine of the frogs moved to Skelton Lake survived as did all frogs moved to Tioga Pond. All surviving frogs were active and appeared healthy upon release.
For the 2008 translocations, 70 adult R. sierrae were collected on 14 July (35 for each lake), held overnight in mesh cages, and transported to Miller and Soldier Lakes via helicopter. We used a helicopter because although travel distances were similar to those associated with the 2006 translocations (8 and 13 km, respectively) the terrain was much rougher and the longer travel times could have negatively impacted the frogs. All other methods were identical to those used in August 2006. All frogs appeared healthy upon release at Miller and Soldier Lakes.
During the summer of each translocation and the following summer, we visited the five translocated populations 1–3 times per month (average = 1.7 surveys per month). After two summers, site visits were reduced to one per summer if no frogs were seen during three consecutive surveys, and were terminated if no frogs were seen in two consecutive summers (Appendix A: Table A2). For the source population, we visited 1–3 times per month between 2005 and 2009 (average = 1.4 surveys per month; Appendix A: Table A2). During each visit to the source and translocated populations, we first conducted a shoreline visual encounter survey and then recaptured as many frogs as possible. Captured frogs were identified based on their PIT tag and were swabbed, measured, and weighed. The amount of Bd on each swab was determined using qPCR.
At each site, during the year in which frogs were translocated, littoral zone temperatures were measured from July through September at 20 cm water depth using iButton loggers. Two loggers were deployed widely spaced in the littoral zone of each lake, as described in Methods: Lake temperature regimes.
Lake temperature regimes
We calculated two measures of lake temperature: (1) average annual water temperature, and (2) the number of days in which average temperatures were within the 15–25°C range that is optimal for Bd growth. Both measures were calculated using temperature data collected during a 365 day period from the middle of the first summer to the middle of the second summer. The relationship between these measures and elevation was quantified using linear regression.
Frog population resurvey
Twenty-eight of the surveyed sites were immediately adjacent to at least one other surveyed site (e.g., ponds within marshes, marshes abutting lakes). To maximize the independence of survey data, data from these adjacent sites were combined into single sites (clusters contained 2–5 sites each). This produced 268 unique sites for analysis. Given that measuring air and water temperatures at each of these 268 sites throughout the summer was not feasible, in our analyses we used elevation as a proxy for the temperature regimes experienced by Bd and frogs. Water body elevation ranged from 1676 m to 3542 m (see Appendix A for additional details).
We used multivariate generalized linear and generalized additive models to evaluate the strength of associations between elevation and (1) Bd infection intensity in R. sierrae, (2) R. sierrae population size, and (3) the probability of R. sierrae persistence between the original and repeat survey. In all three analyses we were primarily interested in the effect of elevation but included covariates to reduce the chances of confounding effects caused by not including important predictors. Our general regression analysis approach followed the protocol of Zuur et al. (2009, Section 4.2.3; see Appendix B for details). All statistical analyses were conducted using R (R Development Core Team 2009) and the R libraries nlme and mgcv.
To test for an effect of elevation on Bd infection intensity, we developed a full model that included five predictor variables: elevation, R. sierrae life stage (adult, juvenile, tadpole), day of the year (Day 1 = January 1), year, and maximum water body depth (Table 1: Model 1a). Because of the hierarchical structure of the swab data (i.e., swabs nested within site), our regression protocol included a mixed effects model with “site id” included as a random effect (Table 1). Infection intensity could differ between R. sierrae life stages because of the different structures (skin versus mouthparts) or area swabbed, or because of stage-specific differences in the effectiveness of the immune response (Rollins-Smith 1998). We included day of the year because of known effects of season and temperature on Bd growth rate (Berger et al. 2004, Kriger and Hero 2007), and year to account for variation in infection intensity across the three study years. Maximum water depth was included because of its possible effects on Bd zoospore density via differences in water body volume. We also developed a second model in which the response variable was Bd presence/absence instead of infection intensity (Table 1: Model 1b). Bd-negative and Bd-positive swabs were defined as those with zoospore equivalent values <1 and ≥1, respectively.
Table 3. Description of the final regression models used in analysis of data from the frog population resurvey and seasonal Bd patterns study.
In the analysis of the effect of elevation on R. sierrae population size, the response variable was the number of tadpoles counted during the resurvey (Table 1: Model 2). We used the number of tadpoles instead of the number of post-metamorphic frogs because tadpoles are unable to move between sites but frogs can move widely over the course of the active season (Pope and Matthews 2001). This movement by frogs could obscure the effect of elevation on population size. The predictor variables in the starting model were elevation and maximum water depth (Table 1: Model 2). Water body area and perimeter were considered for inclusion because of the possible effect of habitat size on frog population size, but both were highly collinear with each other and with water depth (r > 0.6). Of these three predictor variables, we opted to include maximum water depth because of its well-known association with habitat quality in R. sierrae (Knapp et al. 2003, Knapp 2005), and because univariate analyses indicated that it showed the highest correlation with population size. The number of tadpoles counted during the resurvey and maximum water depth were both square root-transformed to reduce the influence of the largest values.
To test for an effect of elevation on the probability of R. sierrae persistence, the response variable was the population status of R. sierrae during the resurvey, i.e., detection or non-detection of any R. sierrae life stage. Predictor variables were elevation, the number of tadpoles counted during the original survey, maximum water depth, and the number of years between the original and repeat survey (Table 1: Model 3). The population size during the original survey was included as a predictor variable because of the positive effect of population size on population viability (Boyce 1992). The survey interval ranged from 4 to 7 years (average = 5.7), and was included because a longer survey interval might be associated with a lower probability of persistence. Population size (number of tadpoles counted during the original survey) was log-transformed and lake depth was square root-transformed to reduce the weight associated with large values.
For each regression analysis, the relationships between the significant predictor variables and each response variable are shown graphically in separate plots. For the two models with continuous response variables (infection intensity, population size), the plotted terms are based on partial residuals. For the model with a binomial response variable (population persistence), the y-axis represents the log-odds that R. sierrae was detected during the resurvey. In all plots, the y-axis is standardized to have an average value of zero.
Seasonal patterns of Bd infection intensity
We evaluated the seasonal effect of temperature on Bd infection intensity using regression analyses that were very similar to those described above for the effect of elevation on infection intensity. Temperature was described by three variables: average, minimum, and maximum temperatures recorded during a 10 day window that ended on the survey date (Tave, Tmin, and Tmax, respectively). Tmin and Tmax were both highly collinear with Tave (r > 0.7) but were relatively weakly correlated with each other (r = 0.4). Therefore, we developed two regression models, one with Tave and a second with Tmin and Tmax. Additional predictor variables included in both models were frog size (snout-vent length), site, and year (Table 1: Model 4a). Frog size was included because of a general pattern for juvenile frogs to be more susceptible to Bd than adults. We included site and year to account for between-site or between-year differences in infection intensity. Because of the hierarchical structure of the seasonal data (i.e., swabs nested within survey date), our regression protocol included a mixed effects model with “survey event” included as a random effect. Survey event was a sequential number based on survey date, and served to group all swabs collected at a particular site on a particular day. We also developed a companion Tave model in which the response variable was Bd presence/absence (as defined previously) instead of infection intensity (Table 1: Model 4b).
Frog translocation experiment
To assess the general health of translocated frogs, we calculated the weight gain of individual frogs between when they were initially captured for translocation and when they were recaptured in September following the translocation. For frogs that were recaptured on more than one occasion in September, only data from the final recapture event were used. Very few frogs were recaptured at McGee Lake, so this population was not included in the analysis. Weight gain for frogs at the source population was calculated in an identical manner. Because sample sizes were sometimes small, we tested the significance of weight gain by individual frogs using non-parametric Wilcoxon signed-rank tests.
To test whether Bd infection intensity changed after translocation, we compared infection intensities on swabs collected from frogs the day prior to translocation (McGee Lake, Miller Lake, Soldier Lake) or the day of translocation (Tioga Pond, Skelton Lake) with infection intensities on all swabs collected following translocation. Post-translocation swabs included only those swabs collected in the year the translocation was conducted. We also compared infection intensities at the Conness Pond source population before and after frogs were collected for the translocations. Because sample sizes for some tests were small, differences in infection intensities were analyzed using non-parametric Wilcoxon rank-sum tests.
We analyzed capture-recapture data using MARK (White and Burnham 1999) to estimate frog survivorship in (1) the translocated populations during the two-year period following translocation, and (2) in the source population for the entire 2005–2008 period. This estimation process utilized standard methods, including a Cormack-Jolly-Seber (CJS) model (Lebreton et al. 1992), model selection using AICc weights (Burnham and Anderson 2002), and testing of model fit using the median-ĉ procedure (White 2002). Appendix C provides additional details on these analyses.
For the translocated populations, we evaluated the association between water temperature and (1) the proportional change in infection intensity, and (2) frog survival using Spearman-rank correlation analyses. The temperature regime experienced by frogs was estimated by calculating the average littoral zone water temperature between July 26 and September 14 during the year in which each translocation was conducted. We used this range of dates because during this period temperature data were available for all five translocation lakes and the source lake.
Results and Discussion
Lake temperature regimes
Water temperatures in all nine lakes were at their minimum (∼4°C) during approximately November to June when lakes were ice-covered. Following thaw, temperatures increased rapidly and reached their maximum values in July or August (19–28°C; see Results: Seasonal patterns of temperature and Bd infection intensity for details). Average annual temperatures ranged from 6.5° to 10.9°C and were significantly negatively correlated with lake elevation (F1,7 = 110.30, adjusted R2 = 0.93, P < 0.0001; Fig. 2A). The number of days per year during which average temperatures were within the 15–25°C envelope necessary for maximum Bd growth ranged from 0 to 113 and was also significantly negatively correlated with elevation (F1,7 = 24.02, adjusted R2 = 0.77, P = 0.002; Fig. 2B). Based on these temperatures, the temperature-Bd growth relationship would predict that the annual temperature regimes at higher elevations of Yosemite are cold enough to severely limit Bd growth.
Frog population resurvey
Bd infection intensity
We were able to collect skin swabs from R. sierrae at 117 of the 166 sites at which R. sierrae were detected during the resurvey. At these sites, 1–42 R. sierrae were swabbed per site (average = 6). No swabs were collected at the remaining 49 sites due to our inability to capture any frogs or tadpoles. A total of 647 swabs were collected, 316 of which were from adults, 78 from juveniles, and 253 from tadpoles. For the 117 sites at which at least one swab was collected, 20 sites (17%) showed no evidence of Bd (ZE = 0), seven (6%) had maximum ZE values greater than zero and less than one (range = 0.02–0.81), and 90 (77%) had maximum ZE values greater than one (range = 2–103159). This 83% level of Bd occupancy is higher than that reported from most other landscape-scale Bd surveys conducted in other parts of the world (77%: Kriger et al. 2007; 43%: Pearl et al. 2007; <66%: Adams et al. 2010; 10%: Hossack et al. 2010) although some examples of higher occupancy are known (100%: Pearl et al. 2009, Kielgast et al. 2010). Our 83% value clearly indicates a wide distribution for this pathogen among R. sierrae populations in Yosemite, but it is likely an underestimate of the true Bd distribution due to the presence of false-negative swab results (Adams et al. 2010). R. sierrae populations in Yosemite are relatively small compared to those in areas not yet infected by Bd (Vredenburg et al. 2010, results from the current study) and as a consequence we were able to swab only a relatively small number of R. sierrae at most sites. Given that Bd prevalence in R. sierrae populations is typically less than 100% (e.g., 80% in the intensively-sampled populations used in the study of seasonal patterns in infection intensity), this likely resulted in some populations being characterized as Bd-negative when Bd was actually present. Collectively, these results suggest that Bd is likely to be essentially ubiquitous across Yosemite's R. sierrae populations.
The response variable (number of zoospore equivalents per skin swab) in the regression analysis was characterized by an excess of zero values and homogeneity of residuals was not achieved by transforming the original ZE values into count data (by rounding to integer values) and using a Poisson or negative binomial distribution. Instead, homogeneity could only be achieved by dropping all zero-values (n = 225), log-transforming the non-zero values (n = 422), and using a Gaussian distribution. Because of the hierarchical structure of these data, a mixed effects model, in which “site id” was included as a random effect, fit the data slightly better than a model without a random term, suggesting that infection intensities within sites were somewhat more similar than those between sites. A semi-variogram and a plot of residuals from the final model against the spatial coordinates showed no evidence of spatial correlation in residuals, and sites were therefore considered to be spatially independent.
Results from the mixed effects model (Table 1: Model 1a) indicated that, contrary to our prediction, elevation was not significantly related to infection intensity. Maximum water depth and year were also not significant predictors of infection intensity. However, R. sierrae life stage and day of the year had significant effects on the number of zoospore equivalents (Table 2). Zoospore equivalents on swabs collected from juveniles and tadpoles were similar and were significantly higher than those of adults (Table 2, Fig. 3A). Although the swab results may not be directly comparable between life stages because of differences in the structures being swabbed (tadpole mouthparts versus frog skin) and the area swabbed (juveniles versus adults), the higher infection intensities of juveniles than adults cannot simply be a consequence of sampling bias because the area swabbed on juveniles is much smaller than that on adults. Similar patterns in post-metamorphic frogs are known from other species and likely reflect real differences in infection intensity caused by the higher susceptibility of juveniles relative to adults. This will be discussed further in Results: Seasonal patterns of temperature and Bd infection intensity. Infection intensity increased linearly with day of the year (Fig. 3B). This effect could be interpreted as a result of increasing water temperatures over the active season (e.g., Pearl et al. 2009). However, temperature measurements made as part of our study of seasonal patterns indicate that water temperatures in the study lakes actually are relatively high and constant in July and August and decline in September (see Results: Seasonal patterns of temperature and Bd infection intensity). Therefore, the mechanism underlying the effect of day of the year is unclear.
Table 4. Description of the significant predictor variables obtained from a reduced generalized linear mixed model of Bd infection intensity.
The related model in which we replaced the Bd infection intensity response variable with Bd presence/absence (Table 1: Model 1b) indicated that elevation did not have a significant effect on the probability of Bd occurrence (P > 0.45). The only significant predictor variable was life stage, and results indicated that the probability of Bd occurrence was similar in juveniles and adults and significantly lower than in tadpoles (P = 0.001).
Frog population size
The best-fit model of factors affecting R. sierrae population size (Table 1: Model 2) was a generalized additive model with a negative binomial distribution. The spatial distribution of residuals obtained from the final model and a semi-variogram both showed no evidence of spatial correlation. Regression results indicated that elevation and water body depth both had significant associations with frog population size (Table 3, Fig. 4). The relationship between elevation and population size was significantly nonlinear, with a general trend of smaller frog populations at low compared to high elevations, as predicted. However, the complex shape of this relationship (Fig. 4A) makes interpretation difficult and likely, at least in part, reflects correlations between elevation and other unmeasured variables. Population size also increased with water depth (Fig. 4B); the number of tadpoles increased as water depth increased from 0 to 4 m and remained high and relatively constant for water bodies deeper than 4 m. This effect of water depth on R. sierrae population size mirrors that on population occurrence in Yosemite (Knapp 2005) and is likely a consequence of the fact that survival of all R. sierrae life stages requires water bodies that do not dry in summer or freeze to the bottom in winter (Knapp et al. 2003).
Table 5. Description of the significant predictor variables obtained from a generalized additive model of frog population size.
Frog population persistence
During the resurvey, R. sierrae were detected at 166 of the 268 sites (62%) at which they were detected during the original survey 4–7 years previously. The best-fit model of factors affecting frog population persistence (Table 1: Model 3) was a generalized linear model with a binomial distribution. The spatial distribution of residuals obtained from the final model and a semi-variogram both showed no evidence of spatial correlation. Model results indicated that contrary to our hypothesis, elevation was not significantly associated with population status. Survey interval also did not have a significant effect. However, the number of tadpoles counted during the original survey and water body depth were both significant predictors of the probability of R. sierrae population persistence (Table 4, Fig. 5). The probability of frog population persistence increased linearly with both the number of tadpoles counted during the original survey (Fig. 5A) and water depth (Fig. 5B). The positive effect of the previous population size on the probability of persistence may indicate the general importance of population size for population viability in R. sierrae, as has been documented for many other species (Boyce 1992). Water depth provides an important measure of habitat quality for R. sierrae and this likely accounts for the positive correlation between water depth and the probability of persistence (Knapp et al. 2003, Knapp 2005).
Table 6. Description of the significant predictor variables obtained from a generalized linear model of frog population persistence.
Seasonal patterns of temperature and Bd infection intensity
At the three study populations, we collected 1028 skin swabs from juvenile and adult R. sierrae during the 2008 and 2009 ice-free periods. During the ice-free periods, water temperatures during a 10-day window preceding the collection of skin swabs ranged widely, from <5°C soon after ice-out to >20°C in mid-summer (Fig. 6A–C). Despite this large seasonal temperature variation, Bd infection intensity was relatively constant across both ice-free periods (Fig. 6A–C). In all three lakes, infection intensities in early summer 2009 when lakes were still very cold and often still surrounded by snow were similar to (Fig. 6A, B) or slightly higher than (Fig. 6C) the infection intensities recorded in mid-summer of the same or the previous year when temperatures were near 20°C.
The best-fit model describing the effect of seasonal temperatures on Bd infection intensity (Table 1: Model 4a) was a generalized additive mixed model with survey event as a random effect. As was the case in the analysis of infection intensity in the frog population resurvey (Results: Frog population resurvey), infection intensity in this data set was also characterized by an excess of zero values and homogeneity of residuals could not be achieved using standard distributions. Instead, homogeneity was only achieved by dropping all zero-values (n = 214) and log-transforming the non-zero values (n = 814).
Two predictor variables, frog size and site, had significant effects on Bd infection intensity (Table 5). The effect of frog size was strongly non-linear; infection intensity decreased markedly between 28 and 42 mm, and remained low and relatively constant for frogs larger than 42 mm (Fig. 7A). This effect of frog size on infection intensity was also observed in the frog population resurvey data set (Results: Frog population resurvey) and similar patterns have been reported for post-metamorphic frogs of other species (Kriger et al. 2007, Pearl et al. 2009). This effect of frog size is consistent with the fact that immune systems of recent metamorphs are relatively poorly developed compared to those in later-stage juveniles and adults (Rollins-Smith 1998). The significant effect of site was due to infection intensities at the high and low elevation sites being similar (Conness Pond and Tiltill Lake, respectively), but higher than those at the mid-elevation site (Davison; Fig. 7B). This unexplained between-site variation in infection intensity could have contributed to the idiosyncratic relationship between elevation and infection intensity in the frog population resurvey (Results: Frog population resurvey). In contrast to our hypothesis, average water temperature during the preceding 10 days was not significantly related to infection intensity. Replacing Tave with Tmin and Tmax produced very similar results: frog size and site were both significant predictor variables and neither temperature variable was significant. Therefore, Bd infection intensities were relatively constant across the wide range of water temperatures that characterized the ice-free period in the study lakes.
Table 7. Description of the reduced generalized additive mixed model of the effect of seasonal temperatures and other factors on Bd infection intensity across three study basins.
In the related Tave model in which we replaced the Bd infection intensity response variable with Bd presence/absence (Table 1: Model 4b), water temperature also did not have a significant effect on the probability of Bd occurrence (P > 0.88). The only significant predictor variable in this model was site: the probability of Bd occurrence was similar at Conness and Tiltill and significantly higher at these two sites than at Davison (P = 0.011). In summary, these results indicate that across these three intensively sampled sites there were no significant associations between seasonal water temperatures and either the probability of Bd infection or infection intensity. A similar lack of seasonal trends in prevalence and infection intensity was reported by Briggs et al. (2010) for two additional R. sierrae populations in Yosemite and one outside of Yosemite. Collectively, these results are not consistent with expectations based on the temperature-Bd relationship (Piotrowski et al. 2004, Rohr et al. 2008, Woodhams et al. 2008).
Frog translocation experiment
Frogs experienced significant weight gains in the 1–2 months following translocation (average = 5.2 g, range = 4.3–5.8 g; range of P-values: 0.020–0.0002). PIT-tagged frogs at the Conness Pond source population also experienced significant (although smaller) weight gains during these same time periods in 2006 and 2008 (weight gain: 1.2 g and 2.3 g, respectively; P-values: 0.002 and 0.004). These results suggest that translocated frogs were able to adapt to their new environment and forage successfully, a response that is consistent with translocation causing only low levels of stress in the frogs (Teixeira et al. 2007). For the three translocations conducted in 2006, infection intensities increased significantly after translocation and also increased significantly at the Conness Pond source population (Fig. 8A–D). In contrast, neither of the two translocations conducted in 2008 was associated with significant changes in Bd infection intensity and the source population also showed no significant change (Fig. 8E–G). Therefore, increases in Bd infection intensity are not an inevitable consequence of translocation.
Frog population counts at the Conness Pond source population (Fig. 9A) suggested an approximately 50% decrease in the number of adult frogs between 2006 and 2009, but tadpole numbers increased by more than 120% during this same time period. Frog population counts at the translocation sites indicated a failure of four of the five translocated populations to become established. At these four sites (2006 translocations: McGee, Tioga; 2008 translocations: Miller, Soldier), numbers of adult frogs decreased rapidly during the first year, and/or few or no adults were detected in subsequent years (Fig. 9B, C, E, F). No evidence of successful reproduction (i.e., egg masses or tadpoles) was ever observed at these four sites. Two dead PIT-tagged frogs were found at Tioga Pond in early summer 2007 and one was found at Miller Lake in fall 2008. In contrast to the failure of these populations to become established, the Skelton Lake population declined more slowly and showed evidence of successful reproduction in 2007, 2008, and 2009 (Fig. 9D). First-year tadpoles were observed in 2007 and both first and second-year tadpoles were observed in 2008 and 2009. Metamorphosis of second-year tadpoles in fall 2008 and 2009 produced juvenile cohorts, and some of the 2008 juveniles survived to become adults by fall 2009 (Fig. 9D).
Contrary to our prediction that the magnitude of change in Bd infection intensity following translocation would be positively correlated with water temperature, no relationship was evident between these two variables (Fig. 10A; S = 18, P = 0.48). MARK-based estimates of yearly survival of translocated frogs ranged from 0 to 0.62, and survival was unrelated to water temperature (Fig. 10B; S = 34, P = 0.12). Although these translocation results do not support the hypothesis that water temperature limits the effect of Bd on R. sierrae populations, they need to be interpreted cautiously because the statistical power to detect effects was limited by the relatively small number of translocations conducted. For example, the relationship between water temperature and frog survival (Fig. 10B) was not significant due to the low survival at one of the coldest sites (Soldier Lake). Results from the other four translocations do show a negative relationship between temperature and survival, but whether the Soldier Lake result is an outlier or is a true indication of the variability in survival regardless of temperature remains uncertain.
The failure of most of the translocations to create self-sustaining frog populations is likely related to the fact that population establishment from a small number of founding individuals is a highly stochastic process (Caughley 1994) and as a consequence, translocations are prone to failure (Bowles and Whelan 1994). In addition to the usual host of factors responsible for the failure of small populations to become established, the R. sierrae that we translocated were also infected with Bd and if their infected status increased mortality (e.g., Pilliod et al. 2010) this could have further reduced the chances of successful establishment. The importance of Bd infection in reducing the success of translocated populations is suggested by the very high survival of R. sierrae previously translocated from an uninfected source population (R. A. Knapp, unpublished data).
Predictive failure of the temperature-Bd growth relationship
The results of the current study provide little support for the hypothesis that cold temperatures (i.e., those on the low side of the temperature-Bd relationship) limit the effect of Bd on amphibians. Our underlying prediction was that Bd growth would be increasingly limited at higher elevations, producing a negative correlation between elevation and infection intensity and a resulting positive correlation between elevation and frog survival, frog population size, and the probability of frog population persistence. Of these predicted relationships, the only one that was supported by the analyses was the relatively weak positive association between elevation and frog population size. However, in the absence of an effect of elevation on infection intensity it is difficult to attribute this effect of elevation on frog population size to chytridiomycosis, and it may instead be attributable to higher densities of predators at low versus high elevation (Knapp 2005).
The failure of the temperature-Bd growth relationship to predict the consequences of Bd to R. sierrae in Yosemite may have several causes. First, it could be argued that all water bodies in Yosemite are cold, and that Bd was in fact limited by temperature but this effect was difficult to detect because the degree of limitation was similar across the entire study area. In fact, our study lakes were characterized by a wide range of temperatures. For example, water temperatures varied seasonally from 4° to 28°C and the number of days per year during which average water temperatures were within the optimal temperature range for Bd growth (15–25°C) ranged from 0 to 113. Therefore, we suggest that the study lakes represented a gradient of temperatures ranging from those in which Bd growth should have been relatively high to those in which Bd growth should have been strongly limited.
Second, the temperatures to which Bd was exposed may not be accurately described by measurements of water temperature. For example, although water temperatures in the study lakes spanned a wide range, frogs may be able to raise their body temperatures above ambient temperatures by basking or selecting warmer habitats (Brattstrom 1963) and this could reduce the actual range of temperatures to which Bd was exposed. Mountain yellow-legged frogs are able to raise their body temperatures above ambient levels (Bradford 1984) but summer body temperatures of R. sierrae in Yosemite nonetheless closely reflect littoral zone water temperatures (R. A. Knapp, unpublished data). Therefore, although frogs are able to modulate their body temperatures to some extent this is unlikely to eliminate the large differences between lakes in temperature regimes experienced by frogs.
Third, the failure of the temperature-Bd growth relationship to predict the effects of chytridiomycosis may be a consequence of reduced amphibian immunocompetence at low temperatures (Andre et al. 2008). Under this scenario, Bd growth rates do in fact decline with temperature as predicted but do not translate into the expected reduced infection intensities on frogs because both the innate and acquired immune systems of amphibians are less effective at these low temperatures (Carey et al. 1999). For example, amphibians, including mountain yellow-legged frogs, produce a wide variety of antimicrobial skin peptides that strongly suppress the growth of Bd (Rollins-Smith et al. 2002, Rollins-Smith et al. 2006) but production of these peptides is greatly reduced at low temperatures (Matutte et al. 2000, Ribas et al. 2009). Similarly, proliferation of T lymphocytes is much lower at cold temperatures than at higher temperatures (Maniero and Carey 1997). However, whether the amphibian immune system is effective against Bd remains an open question (e.g., Conlon et al. 2009, Rosenblum et al. 2009) and some evidence even suggests that chytridiomycosis is associated with down-regulation of some immune system genes (Rosenblum et al. 2009, Ribas et al. 2009). If amphibians are unable to mount an effective immune response to Bd infection, the inhibitory effects of temperature on the amphibian immune system may be inconsequential.
Fourth, recent findings suggest that Bd may exhibit life history trade-offs that allow higher fitness at low temperatures than that predicted based solely on the temperature-Bd growth relationship (Woodhams et al. 2008). For example, under laboratory conditions Bd responds to decreasing temperatures with trade-offs that increase fecundity as maturation rate slows and increase infectivity as growth decreases. As a consequence, Bd may be able to maintain a relatively high growth rate even at low temperatures (Woodhams et al. 2008). Additional research that quantifies these life history trade-offs at lower temperatures than the 10°C minimum used by Woodhams et al. (2008) is critically needed.
Fifth, laboratory Bd studies of the effect of temperature on Bd growth may provide a poor description of field outcomes due to strong context dependency (e.g., Woodhams et al. 2008, Garner et al. 2009), perhaps due to differences between the laboratory and field in Bd transmission dynamics and the presence of Bd environmental reservoirs. As an example of the former, mountain yellow-legged frogs overwinter underwater where they are known to aggregate in crevices (Matthews and Pope 1999). The resulting close proximity between frogs throughout the 7–8 month winter period may increase zoospore transmission rates (Briggs et al. 2010) and suggests a possible mechanism by which Bd infection intensities could stay relatively constant between summer and winter despite much slower Bd growth rates in the 4°C temperatures typical of winter conditions. In addition, if Bd can persist outside of amphibian hosts (e.g., Johnson and Speare 2003), the presence of an environmental reservoir could strongly influence Bd-frog dynamics (Mitchell et al. 2008). This environmental reservoir (e.g., lake sediment) would likely be reduced or even absent in most laboratory studies.
Bd is widespread in amphibians in temperate montane habitats around the world (Garner et al. 2005, Ouellet et al. 2005, Longcore et al. 2007, Pearl et al. 2007) but its negative effects are often assumed to be limited by the cold temperatures characteristic of such ecosystems (Rödder et al. 2009). However, severe effects of Bd on temperate montane amphibians are well documented (Bosch et al. 2001, Bell et al. 2004, Vredenburg et al. 2010). The current study provides the most detailed analysis to date of how temperature influences the effect of Bd on amphibians in temperate montane regions and may provide a resolution of this paradox. Taken together, the results from the frog population resurvey, seasonal patterns of Bd infection intensity, and frog translocations provide no compelling evidence for a controlling influence of cold water temperatures on Bd, and highlight the inadequacy of the published temperature-Bd growth relationship (Piotrowski et al. 2004, Rohr et al. 2008) for predicting the severity of Bd effects on amphibians. Although this relationship appears to have considerable predictive ability in hot climates where Bd is commonly exposed to lethal temperatures, the cold temperatures typical of the highest elevations included in the current study had no detectable limiting influence on Bd. These results suggest that in temperate montane ecosystems Bd can have considerable negative effects on frog populations regardless of elevation, and thermal refuges in which the effects of Bd are limited by low temperatures are unlikely to exist. This conclusion is supported by the general pattern of decline in mountain yellow-legged frogs across their range, in which frogs have declined to a similar degree across all elevations (Drost and Fellers 1996, Vredenburg et al. 2007). This more complete understanding of the role of temperature in controlling the effect of Bd should make possible improved predictions regarding the risk posed by Bd to the world's amphibian species.
This paper is dedicated to the memory of Jeff Maurer, who died in a climbing accident just prior to the completion of the study. This research was supported by grants from the Yosemite Fund and the joint National Institutes of Health/National Science Foundation Ecology of Infectious Disease Program (R01ES12067, EF-0723563). Invaluable assistance in collecting field data was provided by M. Joseph, N. Kauffman, M. Masten, A. Miller, J. Rosen, E. Sherrill, and T. Spang, and in processing swabs by M. Toothman. Research permits were provided by Yosemite National Park and the Institutional Animal Care and Use Committee at University of California, Santa Barbara (UCSB). Staff from Yosemite National Park, UCSB Marine Science Institute, and the Sierra Nevada Aquatic Research Laboratory assisted with critical logistics. D. Bradford and E. Rosenblum provided helpful comments on an early version of the manuscript.
Additional information on methods
We used a study design without temporal replication based on the fact that population-level detection probabilities for R. sierrae are close to one (R. A. Knapp, unpublished data). This high detectability results from several characteristics of R. sierrae and its habitat. First, during the day post-metamorphic R. sierrae frogs and tadpoles are found primarily in near-shore shallows, making both life stages highly visible during shoreline surveys. Second, these oligotrophic lakes generally have high water clarity and lack aquatic vegetation, making frogs and tadpoles highly visible. Third, tadpoles are present throughout the summer (and during all other seasons) due to the 2–3 year duration of this life stage in R. sierrae (Vredenburg et al. 2005).
Water body elevation was obtained from U.S. Geological Survey 1:24000 topographic maps. Maximum lake depth was determined during the original survey by sounding with a weighted line. In the analyses of the frog population resurvey data, nonnative trout presence/absence was not included as a predictor variable in any of the frog population resurvey analyses because trout were found at only seven of the 268 sites. To ensure that Bd was not spread between frog populations by survey activities, we disinfected all field gear by immersion in 0.01% quaternary ammonia for five minutes (Johnson et al. 2003) whenever moving between water bodies.
For post-metamorphic frogs, we swiped a nylon-tipped swab five times each across the left and right sides of the lower abdomen, left and right inner thighs, and left and right rear feet. For tadpoles, all 30 swipes were made across the mouthparts. Swabbed tadpoles were of at least Gosner stage 30 because R. sierrae tadpoles in earlier developmental stages are generally not yet infected (Knapp and Morgan 2006). Following collection, swabs were air-dried, placed into sterile micro-centrifuge tubes, and stored in the laboratory at room temperature. DNA extraction and qPCR protocols followed Boyle et al. (2004) and Hyatt et al. (2007) except that swab extracts were analyzed in singlicate instead of triplicate (Kriger et al. 2006). We calculated a measure of infection intensity (i.e., the number of Bd zoospores on each swab, “zoospore equivalents”) by multiplying the genomic equivalent values generated during the qPCR by 80; this multiplication accounts for the fact that DNA extracts from swabs were diluted 80-fold during extraction and qPCR procedures.
A description of the water bodies used in the seasonal patterns study, translocation experiment, and annual temperature measurements is provided in Table A1. For the frog translocation study, the number of frog surveys conducted at the source population and the five translocated populations is given in Table A2.
Overview of the statistical analysis approach
Prior to analysis, we evaluated predictor variables for collinearity using Spearman rank correlations. When two variables had a correlation coefficient greater than 0.5, only one of the two was used in the analysis. Analyses started with a generalized linear model that contained all non-collinear predictor variables. Validity of regression assumptions related to homogeneity of residuals was assessed by plotting the standardized residuals versus fitted values and versus each individual predictor variable. If the homogeneity assumption was valid, model selection was conducted as described in the next paragraph. If residual patterns indicated heterogeneity, we used alternative residual variance structures (i.e., different distributions, additive modeling, and/or transformation of the response variable) until homogeneity of residuals was achieved. In addition, when data were hierarchically structured (e.g., when multiple swabs were collected from individual sites), we evaluated whether adding a random effects term (e.g., site id) improved the fit of the model relative to a model containing only a fixed effects term. Models with both random and fixed terms are referred to as “mixed effects” models. Fit of alternative models relative to the original model was determined using likelihood ratio tests.
Once the optimal residual variance structure was found, the significance of explanatory variables was determined by dropping each variable sequentially (variable with the highest P-value dropped first) and iteratively comparing the full and nested model using likelihood ratio tests. This produced a final model that contained only significant variables (P ≤ 0.05). Finally, because our data had the potential to be spatially correlated (i.e., nearby sites may be more similar to each other than to those separated by greater distances), we evaluated the degree of spatial dependence by (1) plotting the residuals of the final model against the spatial coordinates, and (2) variogram analysis. If no spatial patterns were apparent in either analysis we assumed that sites were independent.
Additional information on analysis of capture-recapture data
We used the Cormack-Jolly-Seber (CJS) model (Lebreton et al. 1992) that contains the two parameters, apparent survival (Φ) and capture probability (p).8 Apparent survival over interval i (Φi) is the probability that a marked individual in the population during the sampling period at time i survives and remains in the population until the sampling period at time i + 1. This parameter is referred to as apparent survival, instead of true survival, because permanent emigration cannot be distinguished from death. However, previous research indicated that the probability of R. sierrae emigration in the years immediately following translocation was near zero (R. A. Knapp, unpublished data). Therefore, our estimates of apparent survival should be very close to true survival.
Table 8. Set of models used to estimate survival probability (Φ) of Rana sierrae translocated to (1) three sites in 2006 and (2) two sites in 2008, and (3) in the source population.
We developed three capture-recapture data sets: (1) three populations translocated in 2006, (2) two populations translocated in 2008, and (3) Conness Pond source population. To obtain site-specific survivorship estimates from the two translocation data sets, we developed a set of eight candidate models. Capture probability in all models was time-dependent because weather conditions and water temperature were variable between site visits and both can markedly influence frog activity. Models ranged in complexity from a model in which both Φ and p were dependent on the multiplicative effects of site and time (site × time) to a model in which Φ was independent of site and time and p was time-dependent only. In the candidate model set for the Conness Pond source population, Φ and p were either time-dependent or time-independent (four models). The rates in all models were parameterized in units of “per year”, taking into account the unequal sampling intervals between capture events.
We used ΔAICc values and AICc weights to determine which models had the most support. AICc weights can be interpreted as the probability that the model is the best model of those in the candidate set (Burnham and Anderson 2002). In two of the three analyses, a single model was clearly better than all other candidate models, as indicated by lower-ranked models having ΔAICc values >3. However, in the analysis of the 2008 translocations, the second and third-ranked models had ΔAICc values <1, indicating that of the top three models no single model was clearly better. In this case we used model averaging to derive robust parameter estimates. We first extracted the estimate for a particular parameter from each of the three models and then computed a weighted average using the model-specific AICc weights (Burnham and Anderson 2002).
For each of the three analyses, we tested the fit of the most parsimonious model to the data using the median-ĉ procedure (White 2002). For this procedure, 100 simulations were performed at each of 12 ĉ values (upper and lower bounds plus 10 intermediate points). Estimated ĉ values from all three simulations were <1.18 so no adjustments to AIC values were made (estimated ĉ values of ∼1 indicate good model fit).
Analysis of capture-recapture data produced very similar best-fitting models for the populations translocated in 2006 and 2008 and for the source population. In all cases, survival probability was constant through time and recapture probability was time-dependent (Table C1). The time dependence of recapture probability is likely a consequence of differences between recapture occasions in weather conditions and capture effort. In the analysis of the 2006 translocations, by far the best model was one in which survival was different between sites, and recapture probability was dependent on both site and time (Table C1: Populations = 1). The results from the analysis of the 2008 translocations indicated that the fit of the second and third-ranked models was similar to that of the first-ranked model (ΔAICc < 2; Table C1: Populations = 2). All three models were similar in structure to each other and to the best model from the 2006 translocations, with survival being time-independent and recapture probability being time-dependent in all cases. The analysis of data from the Conness Pond source population produced a single best model in which survival was time-independent and recapture probability was time dependent (Table C1: Populations = 3).
MARK-based estimates of yearly frog survival were highly correlated with a second measure of survival, the proportion of frogs that were recaptured in the year following translocation (F1,3 = 454.14, adjusted-R2 = 0.99, P < 0.001). However, as expected, the survival estimate based on the proportion recaptured underestimated true survival (regression coefficient = 0.66).