key: cord-0305605-xxq5ssan
authors: Caruso, Nicholas M.; Staudhammer, Christina L.; Rissler, Leslie J.
title: A demographic approach to understanding the effects of climate on population growth
date: 2019-11-13
journal: bioRxiv
DOI: 10.1101/840512
sha: 6491438a8e7d8ff8317e85918b808587c8df9165
doc_id: 305605
cord_uid: xxq5ssan

Amphibian life history traits are affected by temperature and precipitation. Yet, connecting these relationships to population growth, especially for multiple populations within a species, is lacking and precludes our understanding of how amphibians are distributed. Therefore, we constructed Integral Projection Models (IPM) for five populations along an elevational gradient to determine how climate and season affects population growth of a terrestrial salamander Plethodon montanus and the importance of demographic vital rates to population growth under varying climate scenarios. We found that population growth was typically higher at the highest elevation compared to the lower elevations whereas varying inactive season conditions, represented by the late fall, winter and early spring, produced a greater variation in population growth than varying active season conditions (late spring, summer, and early fall). Furthermore, survival and growth was consistently more important, as measured by elasticity, compared to fecundity and large females had the greatest elasticity compared to all other sizes. Our results suggest that changing inactive season conditions, especially those that would affect the survival of large individuals, may have the greatest impact on population growth. Therefore, we recommend experimental studies focused on the inactive season to determine the mechanism by which these conditions can affect survival.

gradients can be achieved through understanding the traits that drive population growth (Urban 48 et al., 2016) . Likewise, conservation and management of a species requires knowledge of how 49 populations might respond to certain conditions, while developing strategies to maintain or 50 increase abundance are most effective when concentrated on those life stages that have a 51 disproportionately large effect on population growth (Caswell, 2000) . Answering these questions 52 inactive season temperature and snow water equivalent (SWE). The growth model estimated a 121 parameter for standard deviation in growth, and included parameters for asymptotic size for each 122 of the five sites along the elevational gradient. Further details about surveys and models can be 123 found in Caruso and Rissler (2019). 124

The museum surveys included specimens housed at the US National Museum of Natural 125

History and were collected from 1968 to 1999. For each individual, SVL was measured; 126 reproductive condition was confirmed; and the number of eggs for gravid females was counted 127 via dissection. We used estimates of probability of reproducing using the results from a Bayesian 128 logistic regression, which included parameters for body size and temperature seasonality of the 129 location where each individual was collected. Additionally, these museum data were used to 130 obtain the mean number of eggs per female as an estimate of clutch size. Lastly, we used the 131 results of the hierarchical Bayesian growth model from the skeletochronology analyses to 132 calculate mean recruit size for each focal elevation. This model used a von Bertalanffy (1938) 133 growth curve that was parameterized for known ages. The age of each individual was estimated 134 by the number of lines of arrested growth (LAG) present within the periosteal layer of their long 135 bones, which are formed during annual periods of inactivity (reviewed in Castanet and Smirina, 136 1990), i.e., in the winter for montane Appalachian salamanders (e.g., Caruso and Rissler, 2019). 137

Lastly, model-based estimates of mean recruit size for each site were determined by using the 138 site-specific growth rates and asymptotic sizes and setting the age to zero. Additional details 139 about methods and models can be found in Caruso and Rissler (in press). 140

We used the DAYMET database (http://www.daymet.org; Thornton et al. 1997 ) to obtain 143 climate data, utilizing mean maximum temperature ( o C) to describe both active and inactive 144 season temperatures. Active and inactive season precipitation variables were characterized by 145 mean precipitation (mm) and snow water equivalent (SWE; kg/m 2 ) during each seasonal period, 146 respectively. We used data from 1980 to 2017 to obtain a representation of the range of climate 147 experienced at each site, determining the median and 95% quantiles of each of the four climate 148 variables to parameterize the IPMs (Climate values used can be found in the electronic ESM 149 We used the estimates of demographic vital rates, their uncertainty, and climate data to 156 parameterize site-specific and climate-varying deterministic post-reproductive census IPMs. As 157 IPMs estimate population dynamics at discrete time points using individual-level continuous 158 state variables, we defined our IPMs using body size (as measured by SVL in mm), and our 159 discrete time step was defined as a year. Therefore, for each site our IPM describes z', the body 160 size distribution at time y + 1, given z, the body size distribution at time y, as a function of 161 survival, growth and fecundity (Fig. 1) . The function n describes the population size distribution 162 reproducing, b is clutch size, and C is the recruitment size distribution. 164

Survival probability was estimated as a function of body size, elevation of each site ( Elev ), and 165 the elevation-specific active season temperature ( Table 1 ). The growth function was estimated using the Von Bertalanffy growth equation as a 168 function of the body size distribution at time y + 1 given the body size at time y, elevation, and 169 the elevation-specific active season temperature and active season precipitation. The size 170 probability density function of individuals in time y + 1 was described as a normal probability 171 density function, where the mean was the expected size in time y + 1 and the standard deviation 172 G σ that was obtained from the results of the growth model (Table 1) . As both survival and 173 growth were estimated for active and inactive seasons separately, we weighted each by the 174 number of days for each season (138 and 227 respectively; Table 1 ). 175

The probability of reproducing was estimated as a function of body size (z) and 176 temperature seasonality (TempSeasonality) of each site. Clutch size was estimated as the mean 177 number eggs per female multiplied by 0.5, which assumes a 1:1 sex ratio of the offspring 178 (Caruso and Rissler, in press; Table 1 ). Lastly, we describe the elevation-specific recruitment 179 size probability density function during time y + 1 using a normal probability density function 180

where the mean is elevation-specific mean offspring size and a standard deviation of one (Table  181 1). 182 Table 1 ). Generally, λ increased with 214 increasing active season precipitation, whereas increasing temperature did not always lead to an 215 increase in λ , especially at lower elevations ( Fig. 2 ; ESM Table 1 ). Inactive season conditions 216 were relatively more complex and were elevation-specific. At the two lowest elevations, λ 217 increased with increasing temperature but did not show a trend with SWE ( Fig. 3 ; ESM Table 1) . 218

Likewise at the mid elevation, inactive season temperature and λ showed a stronger relationship 219 than SWE and λ , however at this elevation lower temperatures led to higher λ ( Fig. 3 ; ESM 220 Table 1 ). At the next highest elevation (1,300), increasing SWE led to higher λ but at the highest 221 elevation site-specific values of λ did not show patterns with either inactive season temperature 222 or SWE ( Fig. 3 ; ESM Table 1) . 223

Elasticity analyses show that the survival-growth kernel (mean elasticity = 0.879 -0.999) 224 consistently had a greater importance than fecundity kernel (mean elasticity = 0.001 -0.121) to 225 population growth. For all sites and climate conditions, we found that survival of large females 226 was most important to population growth with elasticity values generally decreasing towards the 227 distributed elasticities compared to the lower elevations (Figs. 4, 5, 6). Our elasticity results also 229 demonstrate the relatively low importance of fecundity (represented in the bottom right side of 230 each panel in figs. 4 and 5) compared to survival and growth. Lastly, we found that for all sites 231 average λ generally increased with increasing elasticity evenness (Fig. 6) . Therefore, climate 232 conditions that typically led to higher population growth also led to an increase in the importance 233 of fecundity to population growth and more even elasticities across all body sizes. This could result from a larger range of climate variables included in our models during the 296 inactive season compared to the active season (ESM Fig 1) . However, even when we limit the 297 inactive season conditions to their low and average values, the response of population growth to 298 those varying conditions is still greater than the response to the full range of active season 299 conditions (Figs., 2, 3, ESM 

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