Order invariance of fitness makes evolution predictable despite strong history-dependent effects

Environmental change is ubiquitous in nature, yet understanding its effect on the predictability of evolution remains a challenge. Previous work in microbes has shown that growth and fitness in a particular environment can depend strongly on the environments encountered previously. If such history-dependent effects are large, then any sequence of environments must be thought of as unique, and even a modest number of environments could generate a combinatorially large number of evolutionary paths. This would make evolution in changing environments difficult to predict. Here, we use cycles of three environments, which is the smallest number of environments which allow for comparisons of different environmental orderings – X →Y →Z →X vs X →Z →Y →X – to empirically test how environmental order affects the fitness of S. cerevisiae mutants. We measured the fitness of ∼900 adaptive mutants in distinct three-environment cycles, and find large history-dependent effects which cause fitness in individual environmental components to differ drastically across the two directions of the cycle. However, these effects tend to compensate for each other, resulting in similar overall fitness across the whole cycle. This is true even when we specifically conduct experimental evolution in both directions of the same three-environment cycle. Of the ∼450 mutants we isolated, only a small number of strains showed higher fitness in the direction in which they evolved. By splitting the contribution of each environment on fitness into its effect on the current and next component, we show that the invariance of overall fitness to environment order emerges because the effect of an environment on the next component is largely independent of the identity of the subsequent component, and can be captured by an additive model. Despite this general pattern of compensation, we do find instances of non-additivity, some of which are partly due to history-dependent effects lasting beyond two growth components. Overall, these results suggest that despite large history-dependent effects, fitness across a sequence of environments can be surprisingly predictable.