Climate change impacts on population growth across a species’ range differ due to nonlinear responses of populations to climate and variation in rates of climate change

assumes a linear response of population growth rate to climate. We then assessed the climate responsiveness as in Fig 1. Specifically, we regressed median annual population growth rate (deterministic lambda from the annual kernels; median calculated across the bootstrapped samples of regression coefficients) against splines of all annual climate variable present in the vital rate functions using a generalized additive model (GAM) in the mgcv package [23–25]. We used AIC to ensure that each population’s GAM was a better fit than an analogous linear model. To account for the nonlinearity of climate responsiveness, we used a decomposition approach to estimate the relative contribution of each climate variable to the change in popula- tion growth rate for each population. We first calculated Δλ, the difference between population growth rate in 2086–2100 (future) and 2088–2022 (current), measured as deterministic λ of the mean kernel. We then calculated Δλc, the contribution of climate variable c to Δλ, by com- paring population growth rate of the current sequence to a ‘future’ population growth rate obtained by replacing one climate variable c with the 2086–2100 sequence, maintaining all other climate variables at the 2088–2022 sequence. Δλc isolates the impact of each climate vari- able in generating the difference between the future and current population growth rate, incor- porating both climate responsiveness and differences in the magnitude of climate change across populations or climate variables. We repeated this decomposition for each population

and each climate variable present in the vital rate functions. We found a high correlation (R = 0.85) between the sum of Δλc values across climate variables and Δλ, suggesting that the contri- butions are additive and the decomposition approach is reasonable. We assessed the relative contribution of magnitude of climate change v. climate responsive- ness in generating variation in climate change effects across populations using a multiple regression. For each climate variable, we ran a multiple regression using median Δλc as a response variable (where median is calculated across 500 bootstrap samples of regression coef- ficients). Predictor variables were the amount of change in a climate variable (Δc in Fig 1, mean future, 2086–2100, minus mean current, 2008–2022, climate conditions) and the climate responsiveness value for each climate variable (where climate responsiveness, Δλ/ Δc in Fig 1, is calculated using the GAM predictions, holding all non-focal climate variables at their mean). We used the sums of squares from an ANOVA analysis to partition the total variance of each Δλc into components due to degree of change in a climate variable, climate responsive- ness, and their interaction. Note these results should be interpreted with caution, as the sample size is very low (5 replicate populations per multiple regression). In the analyses in the main text, we use the average climate projections (across GCMs). Pro- jections of population growth rates for individual GCMs are similar and shown in the S1

Appendix. All demographic data are archived on Figshare (10.6084/m9.figshare.13911755). Results We found effects of one or more climate variables on every vital rate that we tested for them, with the exception of variance in size after one year of growth (Table 1). Larger plants were more likely to fruit, but high temperature and high precipitation in the coldest month of the current year reduced the probability of fruiting (Table 1, Fig 3C). Larger size reduced the num- ber of fruits per unit size given fruiting, and high temperature in the coldest month of the current year further reduced the number of fruits per unit size (Table 1, Fig 3D). Higher pre- cipitation in the coldest month of the current year decreased survival (Fig 3A). Given that fruiting tended to be fatal, and that larger plants were more likely to fruit, the linear effect of size on survival was negative; a negative quadratic term suggests that survival may have been even lower for very large plants (Table 1). In addition, higher precipitation during the coldest PLOS ONE Nonlinear responses of population growth rate to climate change PLOS ONE | https://doi.org/10.1371/journal.pone.0247290 March 3, 2021 7 / 20