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The file contains the supplementary tables and figures for the study.

sites_information.csv is the location, codename,land type of study sites. CCH_east_open_*_2018_2019.csv are the daily Tmax/Tmin/DTR in the open field from 2018to 2019. CCH_east_forest_*_2018_2019.csv are the daily Tmax/Tmin/DTR in the understory from 2018to 2019.

Assessing the impact of environmental fluctuations on species coexistence is critical for understanding biodiversity loss and the ecological impacts of climate change. Yet, determining how properties like the intensity, frequency or duration of environmental fluctuations influence species coexistence remains challenging, presumably because previous studies have focused on indefinite coexistence. Here, we model the impact of environmental fluctuations at different temporal scales on species coexistence over a finite time period by employing the concepts of time windowed averaging and performance curves to incorporate temporal niche differences within a stochastic Lotka–Volterra model. We discover that short- and long-term environmental variability has contrasting effects on transient species coexistence, such that short-term variation favours species coexistence, whereas long-term variation promotes competitive exclusion. This dichotomy occurs because small samples (e.g. environmental changes over long time periods) are more likely to show large deviations from the expected mean and are more difficult to predict than large samples (e.g. environmental changes over short time periods), as described in the central limit theorem. Consequently, we show the complex set of relationships among environmental fluctuations and species coexistence found in previous studies can all be synthesized within a general framework by explicitly considering both long- and short-term environmental variation.

Results of game theoretic model of dominance hierarchies and social conflict and cooperation as environmental quality varies.

Many aspects of behaviour depend on recognition, but accurate recognition is difficult because the traits used for recognition often overlap. For example, brood parasitic birds mimic host eggs, so it is challenging for hosts to discriminate between their own eggs and parasitic eggs. Complex signals that occur in multiple sensory modalities or involve multiple signal components are thought to facilitate accurate recognition. However, we lack models that explore the effect of complex signals on the evolution of recognition systems. Here, we use individual-based models with a genetic algorithm to test how complex signals influence recognition thresholds, signaller phenotypes and receiver responses. The model has three main results. First, complex signals lead to more accurate recognition than simple signals. Second, when two signals provide different amounts of information, receivers will rely on the more informative signal to make recognition decisions and may ignore the less informative signal. As a result, the particular traits used for recognition change over evolutionary time as sender and receiver phenotypes evolve. Third, complex signals are more likely to evolve when recognition errors are high cost than when errors are low cost. Overall, redundant, complex signals are an evolutionarily stable mechanism to reduce recognition errors.This article is part of the theme issue ‘Signal detection theory in recognition systems: from evolving models to experimental tests’.