Predicting the fundamental thermal niche of ectotherms

Abstract

Climate warming is predicted to increase mean temperatures and thermal extremes on a global scale. Because their body temperature depends on the environmental temperature, ectotherms bear the full brunt of climate warming. Predicting the impact of climate warming on ectotherm diversity and distributions requires a framework that can translate temperature effects on ectotherm life-history traits into population- and community-level outcomes. Here we present a mechanistic theoretical framework that can predict the fundamental thermal niche and climate envelope of ectotherm species based on how temperature affects the underlying life-history traits. The advantage of this framework is twofold. First, it can translate temperature effects on the phenotypic traits of individual organisms to population-level patterns observed in nature. Second, it can predict thermal niches and climate envelopes based solely on trait response data and, hence, completely independently of any population-level information. We find that the temperature at which the intrinsic growth rate is maximized exceeds the temperature at which abundance is maximized under density-dependent growth. As a result, the temperature at which a species will increase the fastest when rare is lower than the temperature at which it will recover from a perturbation the fastest when abundant. We test model predictions using data from a naturalized-invasive interaction to identify the temperatures at which the invasive can most easily invade the naturalized's habitat and the naturalized is most likely to resist the invasive. The framework is sufficiently mechanistic to yield reliable predictions for individual species and sufficiently broad to apply across a range of ectothermic taxa. This ability to predict the thermal niche before a species encounters a new thermal environment is essential to mitigating some of the major effects of climate change on ectotherm populations around the globe.

Keywords: climate envelope; conditions for population viability; delay differential equation population model; density‐independent abundance; temperature response of abundance; temperature response of life‐history traits.

FIGURE 1

Conceptual diagram of typical ectotherm life cycle and temperature responses of life-history traits for bagrada (red curves) and harlequin bug (blue curves) in absence of density dependence (representing Equations 1–4). Juveniles develop into adults over a temperature-dependent duration $\left(T\right)\left(\tau \left(T\right)=\frac{1}{m_J\left(T\right)}\right)$, and adults produce new juveniles at birth rate $B\left(T\right)$. Mortality, $d_J\left(T\right),d_A\left(T\right)$, can occur at either stage. Panels (a)–(d) depict, respectively, the temperature responses of birth, juvenile mortality, maturation, and adult mortality rates in units per day. Solid circles with error bars depict observed trait responses, and curves depict temperature responses predicted using parameterized response functions (Equations 10–12, Table 1). Density dependence can alter these rates in a fashion that is monotonically increasing or unimodal in response to temperature (Appendix S1: Figure S1).

FIGURE 2

Model predictions for generic ectotherm species. (a) Temperature responses of intrinsic growth rate $r\left(T\right)$ (black curve in all panels) and adult abundance $A_{\mathrm{D}\mathrm{I}}\left(T\right)$ (red curve) calculated from DI model (Equation 1). Note that the $A_{\mathrm{D}\mathrm{I}}\left(T\right)$ axis is in units of Log(adult individuals). (b) Comparison of temperature response of intrinsic growth rate (black curve) with those of steady-state adult abundance calculated from density-dependent (DD) model (Equation 8) for when competition affects adult mortality and temperature response of competition is monotonically increasing (blue) versus unimodal (red). The $A_{\mathrm{D}\mathrm{D}}\left(T\right)$ axis is in units of adult individuals. Dashed vertical lines indicate temperature at which abundance (blue, red) and $r\left(T\right)$ (black) are maximized. (c) Comparison of intrinsic growth rate with recovery time to equilibrium calculated from DD model when density dependence operates on adult mortality. The strength of competition is monotonically increasing, but this does not affect stability (Appendix S1). Parameter values are realistic for warm-adapted species, such as those studied: $b_{T_{\text{opt}}}=2.2,T_{{\mathrm{opt}}_b}=302,s=3.4,T_R=297,d_{J{T}_R}=0.03,A_{d_J}=6260,d_{A{T}_R}=0.048,A_{d_A}=\mathrm{14,600},q_{TR}=q_{T_{\text{opt}}}=0.1,A_q=A_{d_A},T_{{\mathrm{o}\mathrm{p}\mathrm{t}}_q}=T_{{\mathrm{o}\mathrm{p}\mathrm{t}}_b},s_q=s,m_{T_{\mathrm{R}}}=0.015$, and $A_m=\mathrm{11,500}$. Maturation function Equation (13) was used.

FIGURE 3

Temperature-dependent intrinsic growth rate, $r\left(T\right)$, and climate envelope under density-independent (DI), $A_{\mathrm{D}\mathrm{I}}\left(T\right)$, and density-dependent (DD) population growth, $A_{\mathrm{D}\mathrm{D}}\left(T\right)$, for the naturalized harlequin bug (top; blue) and invasive bagrada (bottom; red). Panels (a) and (d) depict the intrinsic growth rate (dark blue curve in [a], dark red curve in [d]) and adult abundance (in units Log[adult individuals]) under DI growth (light blue curve in [a], light red curve in [d]). Panels (b) and (e) compare $r\left(T\right)$ with $A_{\mathrm{D}\mathrm{D}}\left(T\right)$ when competition affects adult mortality via a monotonic temperature response of competition. Units of $A_{\mathrm{D}\mathrm{D}}\left(T\right)$ are adult individuals. Panels (c) and (f) depict $r\left(T\right)$ and the recovery time to equilibrium $t_{\text{recovery}}\left(T\right)$ (in units of time). Parameters: $q_{TR}=0.1$ for both bugs; $A_q=A_{d_A}$ for each respective bug; all other parameters are given in Table 1.

FIGURE 4

Fundamental thermal niches of naturalized harlequin (blue and gray regions) and invasive bagrada bugs (red and gray regions) as predicted from trait response data (Figure 1, Table 1). Niche overlap is shown in gray. Niche metrics are given in Table 2.