Body size is central to ecology at levels ranging from organismal fecundity to the functioning of communities and ecosystems. Understanding temperature‐induced variations in body size is therefore of fundamental and applied interest, yet thermal responses of body size remain poorly understood. Temperature–size (T–S) responses tend to be negative (e.g. smaller body size at maturity when reared under warmer conditions), which has been termed the temperature–size rule (TSR). Explanations emphasize either physiological mechanisms (e.g. limitation of oxygen or other resources and temperature‐dependent resource allocation) or the adaptive value of either a large body size (e.g. to increase fecundity) or a short development time (e.g. in response to increased mortality in warm conditions). Oxygen limitation could act as a proximate factor, but we suggest it more likely constitutes a selective pressure to reduce body size in the warm: risks of oxygen limitation will be reduced as a consequence of evolution eliminating genotypes more prone to oxygen limitation. Thus, T–S responses can be explained by the ‘Ghost of Oxygen‐limitation Past’, whereby the resulting (evolved) T–S responses safeguard sufficient oxygen provisioning under warmer conditions, reflecting the balance between oxygen supply and demands experienced by ancestors. T–S responses vary considerably across species, but some of this variation is predictable. Body‐size reductions with warming are stronger in aquatic taxa than in terrestrial taxa. We discuss whether larger aquatic taxa may especially face greater risks of oxygen limitation as they grow, which may be manifested at the cellular level, the level of the gills and the whole‐organism level. In contrast to aquatic species, terrestrial ectotherms may be less prone to oxygen limitation and prioritize early maturity over large size, likely because overwintering is more challenging, with concomitant stronger end‐of season time constraints. Mechanisms related to time constraints and oxygen limitation are not mutually exclusive explanations for the TSR. Rather, these and other mechanisms may operate in tandem. But their relative importance may vary depending on the ecology and physiology of the species in question, explaining not only the general tendency of negative T–S responses but also variation in T–S responses among animals differing in mode of respiration (e.g. water breathers versus air breathers), genome size, voltinism and thermally associated behaviour (e.g. heliotherms).

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Ectotherms tend to grow faster, but reach a smaller size when reared under warmer conditions. This temperature‐size rule (TSR) is a widespread phenomenon. Despite the generality of this pattern, no general explanation has been found. We therefore tested the relative importance of two proposed mechanisms for the TSR: (1) a stronger increase in development rate relative to growth rate at higher temperatures, which would cause a smaller size at maturity, and (2) resource limitation placing stronger constraints on growth in large individuals at higher temperatures, which would cause problems with attaining a large size in warm conditions. We raised Daphnia magna at eight temperatures to assess their size at maturity, asymptotic size, and size of their offspring. We used three clonal lines that differed in asymptotic size and growth rate. A resource allocation model was developed and fitted to our empirical data to explore the effect of both mechanisms for the TSR. The genetic lines of D. magna showed different temperature dependence of growth and development rates resulting in different responses for size at maturity. Also, at warm temperatures, growth was constrained in large, but not in small individuals. The resource allocation model could fit these empirical data well. Based on our empirical results and model explorations, the TSR of D. magna at maturity is best explained by a stronger increase in development rate relative to growth rate at high temperature, and the TSR at asymptotic size is best explained by a size‐dependent and temperature‐dependent constraint on growth, although resource limitation could also affect size at maturity. In conclusion, the TSR can take different forms for offspring size, size at maturity, and asymptotic size and each form can arise from its own mechanism, which could be an essential step toward finding a solution to this century‐old puzzle.

Temperature affects the physiology and life-history of ectothermic animals, often increasing metabolic rate and decreasing body size. Oxygen limitation has been put forward as a mechanism to explain thermal responses of body size and the ability to survive stress. However the time-scales involved in growth performance and heat tolerance differ radically. In order to increase our understanding of oxygen and temperature effects on body size and heat tolerance and the time scale involved, we reared Lymnaea stagnalis under six combinations of temperature and oxygen tension from hatching up to an age of 300 days and recorded shell length during this whole period. At the end of this period, we determined scope for growth by measuring food intake rate, assimilation efficiency, respiration rate and ammonium excretion rate at two different temperatures. We also measured the snails' ability to survive heat stress (CTmax), both at normoxia and hypoxia. We found that scope for growth and long term growth performance were much more affected by interactions of chronic oxygen and temperature conditions during rearing than by acute conditions during testing. Furthermore, our study shows that individual variation in growth performance can be traced back to individual differences in rates of food and oxygen consumption. Developmental acclimation also gave rise to differences in CTmax, but these were relatively small and were only expressed when CTmax was tested under hypoxia. The large effects of rearing oxygen conditions on growth and other physiological rates compared to modest effects of test oxygen conditions on CTmax suggest that small effects of hypoxia on the short term (e.g. heat tolerance) may nevertheless have large repercussions on the long term (e.g. growth and reproduction), even in a pulmonate snail that can compensate for hypoxia to some extent by aerial respiration.

Forecasting long-term consequences of global warming requires knowledge on thermal mortality and how heat stress interacts with other environmental stressors on different timescales. Here, we describe a flexible analytical framework to forecast mortality risks by combining laboratory measurements on tolerance and field temperature records. Our framework incorporates physiological acclimation effects, temporal scale differences and the ecological reality of fluctuations in temperature, and other factors such as oxygen. As a proof of concept, we investigated the heat tolerance of amphipods Dikerogammarus villosus and Echinogammarus trichiatus in the river Waal, the Netherlands. These organisms were acclimated to different temperatures and oxygen levels. By integrating experimental data with high-resolution field data, we derived the daily heat mortality probabilities for each species under different oxygen levels, considering current temperatures as well as 1 and 2°C warming scenarios. By expressing heat stress as a mortality probability rather than a upper critical temperature, these can be used to calculate cumulative annual mortality, allowing the scaling up from individuals to populations. Our findings indicate a substantial increase in annual mortality over the coming decades, driven by projected increases in summer temperatures. Thermal acclimation and adequate oxygenation improved heat tolerance and their effects were magnified on longer timescales.Consequently, acclimation effects appear to be more effective than previously recognized and crucial for persistence under current temperatures. However, even in the best-case scenario, mortality of D. villosus is expected to approach 100% by 2100, while E. trichiatus appears to be less vulnerable with mortality increasing to 60%. Similarly, mortality risks vary spatially: In southern, warmer rivers, riverine animals will need to shift from the main channel toward the cooler head waters to avoid thermal mortality. Overall, this framework generates high-resolution forecasts on how rising temperatures, in combination with other environmental stressors such as hypoxia, impact ecological communities.