Temperature variability alters the stability and thresholds for collapse of interacting species

Abstract

Temperature variability and extremes can have profound impacts on populations and ecological communities. Predicting impacts of thermal variability poses a challenge, because it has both direct physiological effects and indirect effects through species interactions. In addition, differences in thermal performance between predators and prey and nonlinear averaging of temperature-dependent performance can result in complex and counterintuitive population dynamics in response to climate change. Yet the combined consequences of these effects remain underexplored. Here, modelling temperature-dependent predator-prey dynamics, we study how changes in temperature variability affect population size, collapse and stable coexistence of both predator and prey, relative to under constant environments or warming alone. We find that the effects of temperature variation on interacting species can lead to a diversity of outcomes, from predator collapse to stable coexistence, depending on interaction strengths and differences in species' thermal performance. Temperature variability also alters predictions about population collapse-in some cases allowing predators to persist for longer than predicted when considering warming alone, and in others accelerating collapse. To inform management responses that are robust to future climates with increasing temperature variability and extremes, we need to incorporate the consequences of temperature variation in complex ecosystems. This article is part of the theme issue 'Integrative research perspectives on marine conservation'.

Keywords: climate extremes; climate variability; predator–prey interactions; stability; temperature variability; thermal performance curves.

Figure 1.

Nonlinear responses to temperature. A conceptual figure of how variable temperatures affect demographic rates, e.g. intrinsic per capita growth rate r(T) or attack rate a(T), following thermal performance curves (TPCs). Each individual of a species has a temperature optimum T* at which its performance is maximized, which may be offset from the mean environmental temperature $\overline{T}$. When temperature varies, average demographic rates $\overline{r(T)}$ and $\overline{a(T)}$ may be higher or lower than demographic rates at the mean temperature $(r(\overline{T})\hspace{0.17em}\text{and}\hspace{0.17em}a(\overline{T}))$ due to Jensen's inequality. For example, average rates are likely to be smaller for species adapted to their average ecosystem temperature, i.e. $T^{\ast }\approx \overline{T\hspace{0.17em}}$. If the range of temperatures encompasses both convex and concave regions of the TPC, the net effect is indeterminate but generally non-zero. In experiments, we vary (1) the amplitude of temperature variability (T_max − T_min), and (2) how far the TPCs are offset from the environmental mean temperature ($T_r^{\ast }-\overline{T}$ and $T_a^{\ast }-\overline{T}$). We restrict offsets to be equal in magnitude but have opposite sign, reporting results in terms of the predator's TPC offset $(T_r^{\ast }-\overline{T})$.

Figure 2.

Stable predator collapse or predator–prey coexistence depends on both the offset in the predator and prey TPCs and amplitude of temperature variability. Effects of offset in the predator and prey TPCs (x-axis) and amplitude of temperature variability (y-axis) on predator population abundance (colours) and the type of equilibrium that arises: predator collapse or predator–prey coexistence, and whether the latter is stable or unstable (e.g. cycles or oscillatory behavior). Base scenario parameters (a) are mortality m = 0.2, carrying capacity K = 20, conversion efficiency c = 0.3, maximum attack rate a = 0.3 and handling time h = 0.3, whereas species interactions are modified in (b,c) by lowering conversion efficiency c = 0.1 (b) or increasing attack rate a = 0.5 (c). TPC parameters are in electronic supplementary material, table S1.

Figure 3.

The net and direct effects of temperature variability on predator population. Net effects (blue, positive; pink, negative) of temperature variability on long-run population levels for the predator, as a function of how far the prey TPC is offset relative to the mean temperature (x-axis) and the amplitude of temperature variability (y-axis). The pixel outlines indicate whether net effects have the same sign (black outline) or not (light grey outline) as when only considering the effects of temperature variability on the predator, ignoring the temperature-dependence of its prey (direct effects). For example, pink-filled and black-outlined regions indicate parameterizations where considering only temperature effects on the predator would suggest a positive effect of temperature variability for the predator population when the true net effect is negative, due to species interactions. Parameters as in figure 2a with TPC parameters in electronic supplementary material, table S1; see figure S4 for results from additional parameterizations.

Figure 4.

Interacting effects of warming and temperature variability. Population trajectories for the prey (a,c) and predator (b,d) under scenarios of warming (increasing mean temperatures) with no variability (red), constant temperature variability with constant mean temperatures (blue), increases in mean temperatures with constant variability (purple), and increases in both mean temperatures and temperature variability (orange). Variability on top of warming can either delay (b) or accelerate (d) predator collapse. (a,b) Reflect model parameters as in figure 2a with T_max−T_min = 8°C; (c,d) reflect model parameters as in figure 2b with T_max−T_min = 2°C. TPC parameters are in electronic supplementary material, table S1 with zero offset.