Environmental memory alters the fitness effects of adaptive mutations in fluctuating environments.

Evolution in a static laboratory environment often proceeds via large-effect beneficial mutations that may become maladaptive in other environments. Conversely, natural settings require populations to endure environmental fluctuations. A sensible assumption is that the fitness of a lineage in a fluctuating environment is the time average of its fitness over the sequence of static conditions it encounters. However, transitions between conditions may pose entirely new challenges, which could cause deviations from this time average. To test this, we tracked hundreds of thousands of barcoded yeast lineages evolving in static and fluctuating conditions and subsequently isolated 900 mutants for pooled fitness assays in 15 environments. Here we find that fitness in fluctuating environments indeed often deviates from the time average, leading to fitness non-additivity. Moreover, closer examination reveals that fitness in one component of a fluctuating environment is often strongly influenced by the previous component. We show that this environmental memory is especially common for mutants with high variance in fitness across tested environments. We use a simple mathematical model and whole-genome sequencing to propose mechanisms underlying this effect, including lag time evolution and sensing mutations. Our results show that environmental fluctuations impact fitness and suggest that variance in static environments can explain these impacts.

Enumeration of Rooted Binary Unlabeled Galled Trees.

Rooted binary galled trees generalize rooted binary trees to allow a restricted class of cycles, known as galls. We build upon the Wedderburn-Etherington enumeration of rooted binary unlabeled trees with n leaves to enumerate rooted binary unlabeled galled trees with n leaves, also enumerating rooted binary unlabeled galled trees with n leaves and g galls, 0 ⩽ g ⩽ ⌊ n - 1 2 ⌋ . The enumerations rely on a recursive decomposition that considers subtrees descended from the nodes of a gall, adopting a restriction on galls that amounts to considering only the rooted binary normal unlabeled galled trees in our enumeration. We write an implicit expression for the generating function encoding the numbers of trees for all n. We show that the number of rooted binary unlabeled galled trees grows with 0.0779 ( 4 . 8230 n ) n - 3 2 , exceeding the growth 0.3188 ( 2 . 4833 n ) n - 3 2 of the number of rooted binary unlabeled trees without galls. However, the growth of the number of galled trees with only one gall has the same exponential order 2.4833 as the number with no galls, exceeding it only in the subexponential term, 0.3910 n 1 2 compared to 0.3188 n - 3 2 . For a fixed number of leaves n, the number of galls g that produces the largest number of rooted binary unlabeled galled trees lies intermediate between the minimum of g = 0 and the maximum of g = ⌊ n - 1 2 ⌋ . We discuss implications in mathematical phylogenetics.

Strong environmental memory revealed by experimental evolution in static and fluctuating environments.

Evolution in a static environment, such as a laboratory setting with constant and uniform conditions, often proceeds via large-effect beneficial mutations that may become maladaptive in other environments. Conversely, natural settings require populations to endure environmental fluctuations. A sensible assumption is that the fitness of a lineage in a fluctuating environment is the time-average of its fitness over the sequence of static conditions it encounters. However, transitions between conditions may pose entirely new challenges, which could cause deviations from this time-average. To test this, we tracked hundreds of thousands of barcoded yeast lineages evolving in static and fluctuating conditions and subsequently isolated 900 mutants for pooled fitness assays in 15 environments. We find that fitness in fluctuating environments indeed often deviates from the expectation based on static components, leading to fitness non-additivity. Moreover, closer examination reveals that fitness in one component of a fluctuating environment is often strongly influenced by the previous component. We show that this environmental memory is especially common for mutants with high variance in fitness across tested environments, even if the components of the focal fluctuating environment are excluded from this variance. We employ a simple mathematical model and whole-genome sequencing to propose mechanisms underlying this effect, including lag time evolution and sensing mutations. Our results demonstrate that environmental fluctuations have large impacts on fitness and suggest that variance in static environments can explain these impacts.

All galls are divided into three or more parts: recursive enumeration of labeled histories for galled trees.

OBJECTIVE: In mathematical phylogenetics, a labeled rooted binary tree topology can possess any of a number of labeled histories, each of which represents a possible temporal ordering of its coalescences. Labeled histories appear frequently in calculations that describe the combinatorics of phylogenetic trees. Here, we generalize the concept of labeled histories from rooted phylogenetic trees to rooted phylogenetic networks, specifically for the class of rooted phylogenetic networks known as rooted galled trees. RESULTS: Extending a recursive algorithm for enumerating the labeled histories of a labeled tree topology, we present a method to enumerate the labeled histories associated with a labeled rooted galled tree. The method relies on a recursive decomposition by which each gall in a galled tree possesses three or more descendant subtrees. We exhaustively provide the numbers of labeled histories for all small galled trees, finding that each gall reduces the number of labeled histories relative to a specified galled tree that does not contain it. CONCLUSION: The results expand the set of structures for which labeled histories can be enumerated, extending a well-known calculation for phylogenetic trees to a class of phylogenetic networks.