1. World-wide extinctions of amphibians are at the forefront of the biodiversity crisis, with climate change figuring prominently as a potential driver of continued amphibian decline. As in other taxa, changes in both the mean and variability of climate conditions may affect amphibian populations in complex, unpredictable ways. In western North America, climate models predict a reduced duration and extent of mountain snowpack and increased variability in precipitation, which may have consequences for amphibians inhabiting montane ecosystems.
2. We used Bayesian capture–recapture methods to estimate survival and transition probabilities in a high-elevation population of the Columbia spotted frog (Rana luteiventris) over 10 years and related these rates to interannual variation in peak snowpack. Then, we forecasted frog population growth and viability under a range of scenarios with varying levels of change in mean and variance in snowpack.
3. Over a range of future scenarios, changes in mean snowpack had a greater effect on viability than changes in the variance of snowpack, with forecasts largely predicting an increase in population viability. Population models based on snowpack during our study period predicted a declining population.
4. Although mean conditions were more important for viability than variance, for a given mean snowpack depth, increases in variability could change a population from increasing to decreasing. Therefore, the influence of changing climate variability on populations should be accounted for in predictive models. The Bayesian modelling framework allows for the explicit characterization of uncertainty in parameter estimates and ecological forecasts, and thus provides a natural approach for examining relative contributions of mean and variability in climatic variables to population dynamics.
5. Longevity and heterogeneous habitat may contribute to the potential for this amphibian species to be resilient to increased climatic variation, and shorter-lived species inhabiting homogeneous ecosystems may be more susceptible to increased variability in climate conditions.
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Climate change has emerged as one of the greatest threats to global biodiversity, and ecologists and conservation biologists will be increasingly called upon to determine how a changing climate will affect individual species. Studies on climate change impacts have involved tracking changes in phenology (Root et al. 2003), distribution (Walther et al. 2002), survival (e.g. Post & Stenseth 1998) and interspecific interactions (e.g. Kaeriyama et al. 2004) in relation to climatic variables. Documenting changes in phenology and distribution is important, but we ultimately want to know whether changes in climate will affect the viability of plant and animal populations. Predicting changes in population viability is a fundamental challenge, because knowledge of demographic vital rates (i.e. survival, growth and fecundity) is required, and the demographic research needed to quantify these parameters over appropriate time-scales is logistically daunting. However, such studies are necessary to determine the influence of various climatic factors on individual vital rates, population growth rate and risk of extinction.
Most attention in the climate literature has been focused on change in mean climate conditions (Payne et al. 2004; Stewart, Cayan & Dettinger 2004; Mote et al. 2005), and some authors have begun to address how changes in mean climate conditions might affect wild populations (e.g. Post & Stenseth 1998; Brodie & Post 2010; McCaffery & Maxell 2010). However, climate models also predict an increase in climatic variability (Easterling et al. 2000; MacCracken et al. 2001), and fewer researchers have examined how changes in variability of climate across years might affect population viability and species distributions. In one of the few studies to look at variance in climate indices, Zimmermann et al. (2009) found that predictions of spatial distributions of tree species in Switzerland were improved by including climatic extremes in their models. In contrast, studies of three long-lived species found that after other factors were taken into account, mean changes in drought, precipitation and winter temperature, respectively, were more important for population viability than changes in the interannual variation of those variables (Colchero et al. 2009; Jonzen et al. 2010; van de Pol et al. 2010). Determining the extent to which changes in climatic variation affect our predictions of population viability, relative to changes in the mean, is key to developing meaningful forecasts of climate change on individual species.
In this study, we assess the importance of changes in the mean and variance of snowpack for the Columbia spotted frog (Rana luteiventris Thompson, 1913), a frog species that inhabits the Rocky Mountains of western North America. Understanding the impact of climate change on amphibians is an issue of particular urgency; a third of all amphibian species are considered threatened, more than twice as many amphibians are critically endangered compared to mammals or birds (Stuart et al. 2004), and amphibian decline is considered evidence that the sixth mass extinction in the Earth’s history is underway (Wake & Vredenburg 2008). Habitat destruction and disease are considered the principal causes of amphibian declines, but there is little doubt that climate change can and will interact with these factors to influence the rate and extent of declines (Corn 2005). However, we know relatively little about how specific changes in climate may affect the demography of individual amphibian populations. Demographic studies of amphibians are essential to determine which life stages are affected by various stressors and how these impacts combine to affect population growth rates and viability (Biek et al. 2002; Vonesh & De La Cruz 2002; Govindarajulu, Altwegg & Anholt 2005).
Our study of R. luteiventris population viability is based on 10 years of demographic data from a high-elevation population in the US Rocky Mountains (McCaffery & Maxell 2010). From a previous, retrospective analysis examining relationships between survival, growth, and fecundity rates and a suite of winter and summer climate variables, we found that mean juvenile and adult survival rates were inversely correlated with mean peak snowpack over the course of our study period (McCaffery & Maxell 2010). Recent snowpack in western mountains has been reduced in volume and duration, a trend predicted to continue (Stewart, Cayan & Dettinger 2004), and one that has direct consequences for the hydrologic and temperature regimes of montane wetlands (McMenamin, Hadly & Wright 2008; Adam, Hamlet & Lettenmaier 2009). This trend should increase R. luteiventris population viability. However, snowpack is also predicted to become more variable, the consequences of which are unknown.
Here, we forecasted the effects of future changes in mean and variability in snowpack on frog population viability. We built on the previous analysis of this population by using a prospective rather than retrospective approach to examine the relationship between snowpack and population viability, and by including uncertainty in parameter estimates and variability in snowpack using a Bayesian statistical approach. Bayesian statistical methods are useful for examining relationships between climate variables and life-history parameters, because they provide a framework for extending uncertainty in parameter estimates to derived statistics such as stochastic population growth rates and extinction risks (Wade 2000; Ellison 2004; Clark 2005). Parameters are expressed as probability distributions rather than point estimates, which allows a more explicit representation of uncertainty in the estimates; uncertainty can then be translated into ecological forecasts by integrating (or sampling) over the distributions of each empirically estimated parameter. We estimated R. luteiventris survival and transition probabilities using Bayesian capture–recapture methods, established relationships between these vital rates and snowpack, and simulated the distribution of population growth rates and extinction probabilities under possible future climate scenarios. We then compared the sensitivity of population viability metrics to changes in mean snowpack and variance in snowpack across these scenarios for this frog population with highly variable population dynamics.
Materials and methods
Study area and climate data
We conducted demographic monitoring of a R. luteiventris population in the Bitterroot Mountains of western Montana, USA from 2000 to 2009. Our study population was located at 2200 m in the Little Rock Creek drainage of the Selway-Bitterroot Wilderness. This basin is delineated by glacial headwalls, and the frog population here is isolated from other nearby populations (Funk et al. 2005). For a complete description of the study site, see McCaffery & Maxell (2010). We obtained precipitation data from the Twin Lakes SNOTEL site (http://www.wcc.nrcs.usda.gov/snow), located approximately 18 km north-west of our study site at 1950-m elevation. We recorded the peak snow-water equivalence (hereafter ‘SWE’) for each year of our study. SWE is the depth of water that would result if the snowpack were melted instantaneously and is a commonly used metric of snowpack that takes into account both the depth and the density of the snow. We also examined the mean and variance in peak SWE recorded at this site historically (1970–2000).
In the spring, we searched all standing water bodies for egg masses one to two times a week for the duration of the breeding season. Egg masses are conspicuous and distinct from one another, and are found attached to emergent vegetation in shallow water along pond shorelines. We determined the total number of egg masses deposited annually across the basin. Because we surveyed for egg masses multiple times each year and the breeding ponds were small and contained little emergent vegetation, we are reasonably certain that we counted all egg masses.
From 2000 to 2003, we estimated clutch size and variance in a range of egg masses across all breeding ponds using volumetric displacement (Morris & Tanner 1969; Corn & Livo 1989; Werner, Weaselhead & Plummer 1999) and determined that mean clutch size was 812 eggs, which was relatively consistent across ponds and years. To calculate the total number of eggs produced annually, we multiplied the number of egg masses counted by this mean clutch size. Egg mass counts were used to estimate breeding probability, and total egg abundance was use to estimate survival from egg to 1 year (Appendix S1).
We captured frogs in mid-summer following a robust sampling design (Pollock 1982). We monitored three female life stages: juveniles were frogs that were too young to be sexed; subadults were frogs that could be identified as female (>50 mm with no nuptial pads on the thumbs), but were smaller than the smallest documented breeding female; adults were frogs large enough to breed (>62 mm). Each year, we systematically surveyed all the ponds and lake shores in the basin and captured animals by hand or net. Juveniles and adults are commonly found basking on rocks or logs near shorelines or swimming in shallow water, and the species is highly aquatic. Animals were individually marked by clipping unique combinations of toes using an alphanumeric coding system (Waichman 1992) and were measured to determine life stage. To satisfy the assumptions of the robust design, we captured animals for multiple consecutive secondary sessions (days) within the primary sampling period (year). Across the secondary sessions, we assumed that the population was closed to immigration, emigration, births and deaths. This closure allowed population size, corrected for capture probability, to be estimated. Between primary sessions, we estimated survival and transitions among life stages. From these annual surveys, we had 10-year capture histories for 4362 individuals.
We estimated all survival, transition and capture probabilities from the mark–recapture data using robust design, multistate capture–recapture models implemented in a Bayesian framework. We also used Bayesian models to calculate annual breeding probabilities and survival from egg to 1 year using our egg mass and mark–recapture data. Further details about our parameter estimation methods and the mathematical formulation of these estimates can be found in Appendix S1.
Past studies have raised concern about potential effects of toe-clipping on survival (McCarthy & Parris 2004). We explored such effects in preliminary analyses (R. McCaffery, A. Solonen & E. Crone, unpublished data). These revealed no effects on transition probabilities, but noticeable declines in juvenile survival with an increase in the number of clipped toes (Fig. S1). Therefore, we estimated survival separately for each of four toe classes: three, four, five or six toes clipped, and included the number of toes clipped as covariates in analyses of survival vs. SWE. We used functions evaluated at two toes clipped for our models (see ‘Forecasting effects of climate change’).
Forecasting effects of climate change
As the Bayesian sampling approach produces vital rate estimates as a set of samples, we were able to estimate the uncertainty of any function of the vital rates and extend the Bayesian analysis to all calculations made with the estimates. In this study, we used this property in all of our computations of regressions with vital rates and snowpack and in our matrix model predictions.
In all steps of the forecasting process, analyses were repeated over the distribution of estimates generated by the Gibbs sampler (Appendix S1): we calculated predictions separately for the 4000 samples. For transition probabilities, breeding probabilities and survival from egg to 1 year, we performed a logistic regression of annual vital rate parameter distributions with peak SWE measured in that year to determine the relationship between SWE and each vital rate (Y) across the 10 years of the study, that is,
with b0,Y and b1,Y indicating the regression intercept and slope, τ indicating residual error and t indexing years. For juvenile, subadult and adult survival probabilities (S), we also included the number of toes clipped (c) in our regression:
We chose to perform these regressions in this way so as to not make any assumptions about the relationship of SWE to each vital rate, while obtaining vital rate estimates. An alternative would have been to include SWE as a covariate in the parameter estimation, which would have centred the annual estimates around the fitted functions. Preliminary explorations indicate that our results are robust to this decision, but that may not be the case for analyses of smaller data sets.
Juvenile survival decreased with the number of clipped toes (Fig. S1, Table S1). Therefore, we evaluated which values most closely matched population trends by comparing stochastic population growth rates (λs) from models with parameters for various number of toes clipped to the observed growth rate through time (λobs = [N2010/N2000]^(1/10) = 0·86). Observed trends were best matched using survival evaluated at two toes clipped, that is, just below the range of values for marked frogs. In other words, toe-clipping reduced survival of marked frogs, but did not appear to affect population dynamics (R. McCaffery, A. Solonen & E. Crone, unpublished data). Therefore, we used functions evaluated at two toes clipped to analyse population viability as a function of SWE.
We used these relationships to predict vital rate values for various combinations of mean (μ) and variance (σ2) in peak SWE. We added process variance to the vital rates predicted using SWE using the residual differences between the model predictions and the observations (τY). The following equations were used to draw values for each vital rate X:
For consistency, we used the regressions for all vital rates except for clutch size, even if they did not show a strong relationship with SWE. For clutch size (C), we took the mean number eggs/mass from our field measurements, divided it by two to reflect that c. 50% of the eggs were female, and added normally distributed noise to this measurement. Thus, clutch size was modelled as 406 ± 2 female eggs/clutch. We parameterized a four-stage, female-based projection matrix model with the vital rates predicted from the mean and variance in SWE for each year, where numbers correspond to the life stages described above and in Appendix S1:
We used these models to estimate stochastic population growth rates (λs) and extinction probabilities under various scenarios where we changed mean and variance in SWE. General definitions and calculations of λs and extinction probability follow Morris & Doak (2002).
We examined effects of possible future changes in mean and variance of SWE on R. luteventris population viability. Climate models for the north-western United States, which include our study site, predict a 10–40% decrease in mean peak SWE by 2100, depending on the model and the area within this region (Payne et al. 2004). Therefore, we examined scenarios within this range. Although variance in precipitation is expected to change, there are no model predictions for the magnitude of this change, so we picked a range of hypothetical values to explore the effects of changes in this parameter. The mean SWE values encompassed everything from a slight increase in SWE to a 40% decrease in SWE, and the standard deviations cover a 50% reduction in variance to a threefold increase in variance. To quantify how viability would change across different combinations of future mean and variance in SWE, we estimated mean λs, extinction probabilities and the proportion of samples with λs ≥ 1·0 for each of 260 different combinations of mean and variance in SWE. Mean SWE ranged from 64 to 112 cm, and standard deviation in SWE ranged from 18 to 48 cm. For each scenario, we ran 4000 model predictions for 30 years, with different possible values for the vital rates given by our Bayesian vital rate estimation. This was repeated 100 times, changing the random value for SWE at each iteration. We set 10 female frogs as our quasi-extinction threshold. For our starting population size vector, we assumed 100 adult females and the stable stage distribution predicted by the mean matrix (Caswell 2001; Morris & Doak 2002).
Finally, we examined the sensitivity of our population viability metrics to changes in mean peak SWE vs. changes in the variance in peak SWE. To do this, we calculated the slope of the relationship between population viability metrics and the mean versus variance of SWE over the range of possible values for future mean and variance in SWE.
Vital rate estimates and climate variables
Peak SWE values have not changed over the past 40 years (slope = −0·16 [−0·43 to 0·12 CI]; Fig. 1), and variability among years was high. The mean (103 cm) and standard deviation (23 cm) in peak SWE during the years of our study were similar to the 40-year period (mean = 106 cm, standard deviation = 27 cm; Fig. 1).
Breeding probability and first-year survival were extremely variable across the 10 years of our study and showed no relationship with peak SWE (Table S1). Breeding probability ranged from 0·38 to 1·0, with a mean of 0·71 (0·05 SD), and there was considerable uncertainty in many of the estimates. First-year survival ranged from 0·001 to 0·009, with a mean of 0·004 (0·001 SD), and showed a weak inverse relationship with peak SWE (Table S1). Notably, first-year survival was the highest and most variable in one of the lowest snow years and in the highest snow year.
There was an inverse relationship between juvenile survival and peak SWE (Fig. 2). There was no relationship between subadult and adult female survival and SWE. Transition probabilities from juvenile to subadult stage classes had a weak negative relationship with SWE, but there were no relationships between other transitions and SWE (Table S1).
Across all of our scenarios for future changes in the mean and variance of SWE, a decrease in mean SWE had a positive effect on population viability, and an increase in variability had a small negative effect (Fig. 3). Decreases in mean SWE resulted in an increase in mean λs, an increase in the proportion of samples with a λs ≥ 1·0, and a decrease in percentage of runs going extinct. Increases in variance of SWE resulted in a decrease in mean λs, a decrease in the proportion of samples with λs ≥ 1·0 and an increase in the percentage of runs going extinct. Populations mostly changed from decreasing to increasing around a mean of 70 cm SWE, which represents a 33% decrease relative to current conditions. Mean λs had a higher sensitivity to changes in mean SWE than to changes in variance (Fig. 4). All 4000 slopes for the relationship between decreases in mean SWE and increases in λs (−0·012, −0·019 to −0·007 CI) were greater than the slopes for the relationship between increases in the variance of SWE and decreases in λs (−0·003, −0·005 to −0·001 CI). Similarly, the slopes for the relationship between decreases in mean SWE and decreases in the percentage of runs going extinct (0·052, 0·021 to 0·061 CI) were greater than the slopes for the relationship between increases in the variance of SWE and the increase in percentage of runs going extinct (0·011, 0·004 to 0·017 CI).
Interannual climatic variability is predicted to increase along with the changes in mean climate conditions (Easterling et al. 2000), but the impacts of changing mean and variance in climate variables has rarely been examined in conjunction with animal population viability (but see van de Pol et al. 2010). For this population of R. luteiventris in a mountain ecosystem, we found that population viability metrics were more sensitive to changes in mean SWE than to changes in the variance of SWE. Decreases in SWE systematically increased mean λs, increased the probability of population growth, and decreased extinction probabilities; increases in variability had less of an effect. This conclusion contrasts with a previous meta-analysis of population time-series data, in which environmental stochasticity was the most important determinant of extinction risk (Fagan et al. 2001). However, recent research examining the effects of mean versus variability in climatic change on wild populations has corroborated our results. Colchero et al. (2009) found that an increase in mean drought severity had a larger effect on the viability of a population of desert bighorn sheep (Ovis canadensis) than an increase in the variability in drought. Similarly, Jonzen et al. (2010) found that changes in average rainfall had a greater impact on population growth rates of the red kangaroo (Macropus rufus) than increased variability in rainfall. Finally, van de Pol et al. (2010) concluded that changes in mean winter temperature were more important for Eurasian Oystercatcher (Haematopus ostralegus) population viability that changes in variance in temperature.
At least two features of R. luteiventris life history may contribute to the relatively small effects of environmental stochasticity. First, longevity may affect the resiliency of this population to increased environmental stochasticity. Morris et al. (2008) demonstrated that in general, long-lived species are more resilient to increases in climatic variability than short-lived species (insects and annual plants). Rana luteiventris may live up to 10 or more years in our system, and individuals do not become sexually mature until 3–5 years of age at high elevation (Werner et al. 2004). Thus, it may be that for this long-lived frog species, populations can experience substantial environmental variation without adverse effect. Habitat heterogeneity may also contribute to the relative unimportance of environmental stochasticity to population viability in this system. This population uses a network of 12 lakes, permanent ponds and ephemeral ponds for breeding, foraging, and overwintering. This heterogeneous habitat provides consistent breeding and foraging habitat on both wet and dry years (McCaffery 2010), as has been demonstrated for other amphibian species inhabiting heterogeneous landscapes (Karraker & Gibbs 2009). Pond-breeding temperate amphibian species are typically characterized as having extremely stochastic population dynamics (Green 2003), which are thought to be largely driven by stochastic environmental conditions (e.g. Semlitsch et al. 1996). However, studies have typically examined single pond systems, where animals are much more constrained in years where the pond habitat is unsuitable. Amphibians inhabiting simple or isolated ponds may be more affected by environmental variability.
The shape of the relationship between SWE and population viability metrics may also affect the extent to which variability is important for population viability. In our study, decreases in mean SWE resulted in an approximately linear increase in mean λs (Fig. 3a). However, for nonlinear relationships, changes in environmental variance may have greater consequences for population viability (Ruel & Ayres 1999; Drake 2005). If the relationship between SWE and vital rates were convex (positive second derivative), variance in vital rates would be greater than variance in SWE. If the relationship between SWE and vital rates was concave (negative second derivative), then variance in vital rates would be less than variance in SWE (Jensen 1906, see discussion by Ruel & Ayres 1999). This relationship suggests that, in principle, the shape of the relationship between environmental variation and population parameters could be an important indicator of the relative importance of changes in mean vs. variance of environmental variables. In fact, four studies that have investigated these relationships have shown all three functional forms: concave (Jonzen et al. 2010), convex (Colchero et al. 2009), both concave (for survival) and convex (for fecundity; van de Pol et al. 2010), and approximately linear (this study), but all conclude that changes in the mean affect population viability more than changes in variance. Therefore, the general conclusion that changes in mean conditions are more important than changes in variance does not seem to depend critically on the shape of climate-vital rate relationships in practice, at least for long-lived species. In general, stochastic population growth rate scales linearly with changes in mean vital rates, and less than linearly with changes in variance (Tuljapurkar 1982), such that a change in variance would have less effect on viability than a change in mean of the same magnitude.
Our analysis also demonstrated that decreases in mean snowpack promoted population viability of R. luteiventris in this system and that these results were robust to both uncertainty in our vital rate estimates and increasing variation in snowpack. Population growth rates typically changed from decreasing to increasing with a 33% decline in snowpack, which is within the predicted range of decline for this area (Payne et al. 2004). This result challenges the overarching dogma that climate change will generally be negative for amphibians or exacerbate declines (Corn 2005; Wake 2007; McMenamin, Hadly & Wright 2008). Rather, this case study offers the perspective that in some circumstances, climate warming could benefit some populations and species, provided that habitat suitability and prey availability remain unaffected. Frogs in this system persist at the upper elevational limit of their range and endure long cold winters. Populations of R. luteiventris inhabiting these elevations have broad thermal tolerances, and fitness may be enhanced by a warming climate if they are currently spending much of their time below their physiological optimum (Deutsch et al. 2008). Similarly, van de Pol et al. (2010) found that for a long-lived shorebird, increases in mean winter temperatures were predicted to increase population viability via an increase in adult survival, even though these temperature changes were predicted to negatively affect fecundity.
Peak snowpack only explains some of variability in our vital rates and only relates to some vital rates (e.g. juvenile survival). Undoubtedly other intrinsic and extrinsic factors are influencing these rates. For example, timing of spring snowmelt is related to breeding probability in this population (McCaffery & Maxell 2010). Density dependence at either the larval or adult stage could influence vital rates over time (Wilbur 1976; Berven 1990; Harper & Semlitsch 2007), although densities of larvae and frogs at this site are lower than what has been measured in other species. Vital rate variability might also be influenced by current predation rates and resource availability. Furthermore, our models predict the effects of future snowpack decline on R. luteiventris population viability in isolation from other climate-related ecosystem changes that could be occurring alongside declines in snowpack. These may include habitat loss and changes in the abundance and distribution of food resources. Decreases in the total availability of breeding habitat because of drought could have negative impacts on the population (e.g. McMenamin, Hadly & Wright 2008) and be accompanied by reductions in the quality of remaining habitat. Reductions in snowpack could change the timing, quantity or quality of food resources, which may reduce body conditions and survival rates in juvenile and adult frogs. Models that simultaneously evaluate different ways a given species may be impacted by climate by including other potential drivers of variation could help disentangle the relative influences of different effects of climate on population dynamics and viability.
Although 10 years represent a relatively long demographic study for an amphibian species, it can only capture a certain range of demographic and environmental variability. As such, the relationships we have measured may change if we leave the range of parameter space covered in this study (e.g. Coulson et al. 2001). The mean and variance observed in the 10 years of our study were similar to what was measured over a 40-year period, such that we captured high and low snowpack years over our study period, but we can never know how conditions will change into the future and whether the relationships we have observed will hold under future snowpack conditions.
In this study, we demonstrated a case where mean climate conditions were more important to population viability than variance in those conditions. These projected changes in climate predicted overall increases in population viability for a dynamic frog population. These results add to a small, but growing, body of literature examining the relative effect of changing mean vs. variance of climatic variables on the viability of animal populations and demonstrate the power of demographic modelling for synthesizing the effect of climate variables on multiple vital rates. The use of Bayesian methods in this analysis allowed for an explicit characterization of uncertainty in our parameter estimates and our forecasts of future population viability. The relative unimportance of increased environmental stochasticity on population viability was surprising, as it has been considered the most important determinant of population viability (Fagan et al. 2001). However, increased climatic variation can change populations from increasing to decreasing and should not be discounted from analyses of the effects of climate change on wild populations.
We thank B. A. Maxell, who initiated the field component of this study and collected demographic data from 2000 to 2004, and the field volunteers who have assisted with data collection. We thank M. Laine for help with coding the Gibbs sampler, and J. Brodie, L. Eby, M. Ellis, C. Hartway, W. Lowe and two anonymous reviewers for constructive comments on drafts of the manuscript. A.S. received funding from the Fulbright Program to conduct research at the University of Montana. Fieldwork was partially supported by funding from the US Geological Survey’s Amphibian Research and Monitoring Initiative and US Forest Service Region 1 Inventory and Monitoring grants.