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

Introduction Effects of climate change on species’ geographic distributions are well-documented and wide- spread [1, 2]. However, the impact of climate change on individual populations within a spe- cies’ range can differ dramatically. In fact, climate-induced range shifts will only occur when climate change effects differ across a species’ range. For example, when populations located where conditions are cooler are able to persist or even grow under climate change, but popula- tions located where conditions are warmer decline to extinction, a species’ range will shift to track its thermal tolerances. Accurately predicting climate change impacts on extant popula- tions and on shifts in species’ ranges requires understanding the factors that generate variation in climate change impacts on population growth rate across a species’ range. For terrestrial widespread species, all populations across the range are unlikely to experience equivalent rates of change in temperature and precipitation. In particular, species with wide latitudinal ranges are likely to experience faster rates of warming at their poleward limits than at their equatorward limits [3]. However, these latitudinal patterns in rates of warming can be complicated by topography, elevation, or buffering impacts of the ocean [4], as well as by changes in precipitation that may counter or exacerbate the negative effects of temperature increases. The variation in magnitude of climate change can contribute to variation in response to climate change among populations; for example, a recent review showed that population

declines are more severe where average annual temperature changes are more substantial [5]. In addition to among-population differences in the magnitude of change in annual climate, the seasonal pattern of change in each climate variable may differ among populations [6]. Moreover, populations of the same species may differ in their intrinsic sensitivity to the same amount of change in a given climate variable [7–9]. One way to measure this climate sen- sitivity is to compute the derivative of the population growth rate with respect to a climate vari- able, evaluated at the current value of that variable. The difference in the rate of population growth between the future and current climates could then be approximated by multiplying the change in each climate variable by its climate sensitivity, and summing the products over all climate variables, a procedure akin to a so-called “life table response experiment” or LTRE [10, cf. 11]. Inherent in the LTRE approach is the assumption that the population growth rate changes linearly in response to a change in a climate variable. Even if the linear assumption were true, populations could differ in their sensitivities to climate variables (i.e., differ in the slope of the relationship between population growth and climate), due to life history differ- ences among populations [12, 13]. Differences in (linear) sensitivities could contribute to among-population differences in climate change impacts. For example, low climate sensitivity may buffer some populations from changes in a given climate variable, while high sensitivity

may amplify the impact of changes in the same climate variable in other populations. However, it is well known that the population growth rate is a non-linear function of the underlying vital rates [10, 14], and thus changes in climate variables may, if large enough, drive a change in the population growth rate that is substantially different than the linear approximation. In this case, the climate sensitivity may either underestimate (if population growth is an accelerating function of the climate variable; Fig 1A) or overestimate (if popula- tion growth is a decelerating function of the climate variable; Fig 1B) the true population response to climate change (hereafter, “climate responsiveness”, measured as the change in the population growth rate divided by the actual change in climate). Among-population differ- ences in climate responsiveness will shape the responses to different magnitudes of climate change across a species’ range. Thus, to gauge the consequences of climate change on popula- tions across species’ geographic ranges accurately, we must account for the true pattern of pop- ulation growth responses to climate in different populations. PLOS ONE Nonlinear responses of population growth rate to climate change PLOS ONE | https://doi.org/10.1371/journal.pone.0247290 March 3, 2021 2 / 20 analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.