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Fig S1: Temperature records (from 09/18/2013 to 08/18/2017), recorded in 15-min intervals, from the Lake Superior National Estuarine Research Reserve (Pokegama Bay station [lkspowq], water depth 1-2 m). Note that fathead minnows prefer shallower waters, making the maximum temperatures experienced likely higher than 27-28°C as observed in this plot. Fig S2: Growth trajectories for all fish analyzed in the experiment. Table S1: Model selection results for breakpoint regression analysis of every trait measured vs. temperature. Table S2: Model selection results for breakpoint regression analysis of variance in length-at-age vs. temperature. Table S3: MANOVA results on (a) all of the traits combined, (b) all the length-at-age measurements, (c) all of the morphometric and meristic traits, and (d) all the fluctuating asymmetry (FA) traits. Models = “full”: intercept + temp+fluct+temp*fluct; “no interaction”: intercept + temp+fluct; “no temp”: intercept + fluct; “no fluct”: intercept + temp.

Ecologists have long sought to understand the dynamics of populations and communities by deriving mathematical theory from first principles. Theoretical models often take the form of dynamical equations that comprise the ecological processes (e.g. competition, predation) believed to govern system dynamics. The inverse of this approach—inferring which processes and ecological interactions drive observed dynamics—remains an open problem in ecology. Here, we propose a way to attack this problem using a machine learning method known as symbolic regression, which seeks to discover relationships in time-series data and to express those relationships using dynamical equations. We found that this method could rapidly discover models that explained most of the variance in three classic demographic time series. More importantly, it reverse-engineered the models previously proposed by theoretical ecologists to describe these time series, capturing the core ecological processes these models describe and their functional forms. Our findings suggest a potentially powerful new way to merge theory development and data analysis.