Changes in body size with age do not follow the temperature-size rule

The temperature size-rule is often described as a reduction in ectothermic body size with warming. This coincides with the expectation that faster growth under warming would lead to larger sizes early in life but smaller sizes later in life. Here, we use > 99,000 observations of weight-at-age of four commercially-important fishes over 25 years to ask whether changes in size and growth can be explained by temperature. We also examine whether oxygen, a key part of a proposed mechanism behind the temperature size-rule, explains patterns of weight-at-age better than temperature. Changes in weight-at-age over time were more related to temperature than oxygen but the effect of temperature on weight was small and did not vary by age, counter to the temperature size-rule. Importantly, these results were sensitive to how the relationship between weight-at-age and temperature was modeled. While the functional form (linear or polynomial) mattered little, how space was included in the model led to different conclusions regarding how temperature affects size and growth. Assuming that spatial and spatiotemporal random effects - those that account for the higher degree of similarity between observations collected closer in space and time - are shared across ages led to different results compared to allowing these effects to vary by age. Models with shared effects suggested weight for younger ages had positive relationships with temperature and negative relationships for older ages. However, these models provided spurious support for the temperature size-rule as they had less statistical support than models that allowed spatial effects to vary by age. Overall, our work highlights that relationships among size, growth, temperature, and oxygen may not be as straightforward as theory suggests and illustrates that modeling decisions can have a large effect on tests of ecological theory, and more broadly, our ability to understand biological responses to climate change.