18Temperature variability and extremes can have profound impacts on populations and ecological 19 communities. Predicting impacts of thermal variability poses a challenge because it has both 20 direct physiological effects and indirect effects through species interactions. In addition, 21 differences in thermal performance between predators and prey and non-linear averaging of 22 temperature-dependent performance can result in complex and counterintuitive population 23 2 dynamics in response to climate change. Yet the combined consequences of these effects remain 24 underexplored. Here, modeling temperature-dependent predator-prey dynamics, we study how 25 changes in temperature variability affect population size, collapse, and stable coexistence of both 26 predator and prey, relative to under constant environments or warming alone. We find that the 27 effects of temperature variation on interacting species can lead to a diversity of outcomes, from 28 predator collapse to stable coexistence, depending on interaction strengths and differences in 29 species' thermal performance. Temperature variability also alters predictions about population 30 collapse -in some cases allowing predators to persist for longer than predicted when considering 31 warming alone, and in others accelerating collapse. To inform management responses that are 32 robust to future climates with increasing temperature variability and extremes, we need to 33 incorporate the consequences of temperature variation in complex ecosystems. 34 35 a greater risk to species than increases in mean temperature [7,8,11], predicting the importance 47 of temperature variability and extremes for populations, communities, and the ecosystem 48 functions and services they support remains challenging. First, temperature can have both direct 49 and indirect effects that create complex feedbacks and dynamics [12]. Directly, temperature 50 affects species through physiological performance. But temperature can also impact species 51 indirectly, as shown for warming [13,14], by increasing or decreasing important resources or 52 prey species (in turn affecting consumers and predators), changing competitive abilities (altering 53 prey abundance distributions), and altering feeding rates and top-down control (affecting prey) 54 [15][16][17][18]. Second, even without shifts in mean temperatures, temperature variability can alter 55 mean vital rates because of non-linear relationships between temperature and processes including 56 growth, reproduction, and mortality (Fig 1; [19]). As a result, the responses of populations to 57 increasing temperature variability and extremes induced by climate change, especially in a 58 community context, remains a key research frontier in marine population dynamics, community 59 ecology, and fisheries science. 60Directly, temperature variability can impact populations of species in a variety of ways, 61including by altering the rates of fundamental processes that determine population size, 62 extinction risk, and productivity. Increases i...
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