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

(and their interaction) during four time periods shorter than a year: 1) snow-covered season, 2) snow-free season, 3) coldest month, and 4) warmest month. We then selected, using AICc, the single best fit model across these five time periods, and used it in all subsequent analyses. Note that this approach does not allow for different windows of time to have effects on the same vital rate (e.g., warmest and coldest month temperatures cannot both affect a given vital rate), nor for quadratic temperature or precipitation effects reflecting an optimum, as we did not have sufficient data to test for these effects. We modified the model selection approach for probability of survival, which likely depends on both climate variables over the year of interest and, given the plant’s semelparity, the probability of fruiting in the prior year (which itself depends on the climate conditions in the prior year). Specifically, we tested the same 5 global models as described above, but also allowed these models to include terms for coldest month temperature and precipitation in the year prior, because coldest month conditions affected the probability of fruiting (see Results). The global model for survival also included log size in the prior year, the square of log size in the prior year, as well as interactions between log size and coldest month temperature, as well as between log size and precipitation in the year prior (S1 Appendix). We used a generalized linear model with a binomial distribution for probability of

fruiting and survival, and a linear model for all other vital rates including variance in log size (note that using log size improved normality of residuals). Our approach assumes that varia- tion in climate results in different vital rates across populations, rather than other non-climate factors that may also differ across populations, such as soil type. In addition, our approach assumes that populations respond similarly to climate, and does not allow for local adaptation resulting in different responses to climate. We used the vital rate regressions to construct climate-driven population-specific integral projection models (IPMs) for current (2008–2022) and future (2086–2100) conditions using SNAP projections of climate over these time periods. While the demographic data span only one annual transition for each site, we used population growth rate over a longer time period (2008–2022) to represent current conditions, in an effort to guard against effects of unusual climate conditions in the year of the measurements. We substituted SNAP temperature values into the fitted regression equations to predict vital rates, correcting for population-specific dif- ferences between soil (iButton) and air (SNAP) temperature estimates, as described in S1 Appendix. Note that analogous to the vital rate fitting procedure, we allowed the warmest and coldest month to vary across populations, years, and GCMs. Because some vital rate predic- tions were unrealistic, we limited our vital rate values to 30% more or less than the observed

maximum and minimum values for a size class in the discretized kernel (45% for binomial vital rates’ observed values). The degree of limitation does not affect our results (S1 Appendix). We calculated deterministic population growth rates for the current (2008–2022) and future (2086–2100) time periods using the mean kernel over these time periods. We included param- eter uncertainty in the predictions by performing a parametric bootstrap, sampling 500 times from the multivariate Normal distribution of parameter estimates for each vital rate function and recalculating current and future population growth rates for each set of parameter esti- mates (note that this approach assumes that vital rates are independent). See S1 Appendix for more details on the construction of the IPMs. We used an LTRE and a decomposition approach to estimate the relative contributions of each climate variable present in the vital rate functions to the change in growth rate for each population (where change is defined as future minus current). First, we used a LTRE approach to approximate the impact of each climate variable on population growth rate; specifically, we calculated the numerical derivative of the population growth rate with respect to each climate variable (using a perturbation approach; S1 Appendix) and multiplied it by the change in that variable (mean future, 2086–2100, minus mean current, 2008–2022, value). This approach PLOS ONE Nonlinear responses of population growth rate to climate change PLOS ONE | https://doi.org/10.1371/journal.pone.0247290 March 3, 2021 6 / 20