Populations facing adverse environments, novel pathogens or invasive competitors may be destined to extinction if they are unable to adapt rapidly. Quantitative predictions of the probability of survival through adaptation, evolutionary rescue, have been previously developed for one of the most natural and well-studied mappings from an organism\'s traits to its fitness, Fisher\'s geometric model (FGM). While FGM assumes that all possible trait values are accessible via mutation, in many applications only a finite set of rescue mutations will be available, such as mutations conferring resistance to a parasite, predator or toxin. We predict the probability of evolutionary rescue, via de novo mutation, when this underlying genetic structure is included. We find that rescue probability is always reduced when its genetic basis is taken into account. Unlike other known features of the genotypic FGM, however, the probability of rescue increases monotonically with the number of available mutations and approaches the behaviour of the classical FGM as the number of available mutations approaches infinity.

What causes evolution to be repeatable is a fundamental question in evolutionary biology. Pleiotropy, i.e. the effect of an allele on multiple traits, is thought to enhance repeatability by constraining the number of available beneficial mutations. Additionally, pleiotropy may promote repeatability by allowing large fitness benefits of single mutations via adaptive combinations of phenotypic effects. Yet, this latter evolutionary potential may be reaped solely by specific types of mutations able to realize optimal combinations of phenotypic effects while avoiding the costs of pleiotropy. Here, we address the interaction of gene pleiotropy and mutation type on evolutionary repeatability in a meta-analysis of experimental evolution studies with Escherichia coli. We hypothesize that single nucleotide polymorphisms (SNPs) are principally able to yield large fitness benefits by targeting highly pleiotropic genes, whereas indels and structural variants (SVs) provide smaller benefits and are restricted to genes with lower pleiotropy. By using gene connectivity as proxy for pleiotropy, we show that non-disruptive SNPs in highly pleiotropic genes yield the largest fitness benefits, since they contribute more to parallel evolution, especially in large populations, than inactivating SNPs, indels and SVs. Our findings underscore the importance of considering genetic architecture together with mutation type for understanding evolutionary repeatability. This article is part of the theme issue \'Interdisciplinary approaches to predicting evolutionary biology\'.

Most marine organisms have complex life histories, where the individual stages of a life cycle are often morphologically and ecologically distinct. Nevertheless, life-history stages share a single genome and are linked phenotypically (by \"carry-over effects\"). These commonalities across the life history couple the evolutionary dynamics of different stages and provide an arena for evolutionary constraints. The degree to which genetic and phenotypic links among stages hamper adaptation in any one stage remains unclear and yet adaptation is essential if marine organisms will adapt to future climates. Here, we use an extension of Fisher\'s geometric model to explore how both carry-over effects and genetic links among life-history stages affect the emergence of pleiotropic trade-offs between fitness components of different stages. We subsequently explore the evolutionary trajectories of adaptation of each stage to its optimum using a simple model of stage-specific viability selection with nonoverlapping generations. We show that fitness trade-offs between stages are likely to be common and that such trade-offs naturally emerge through either divergent selection or mutation. We also find that evolutionary conflicts among stages should escalate during adaptation, but carry-over effects can ameliorate this conflict. Carry-over effects also tip the evolutionary balance in favor of better survival in earlier life-history stages at the expense of poorer survival in later stages. This effect arises in our discrete-generation framework and is, therefore, unrelated to age-related declines in the efficacy of selection that arise in models with overlapping generations. Our results imply a vast scope for conflicting selection between life-history stages, with pervasive evolutionary constraints emerging from initially modest selection differences between stages. Organisms with complex life histories should also be more constrained in their capacity to adapt to global change than those with simple life histories.

Conflicts of interest abound not only in human affairs but also in the biological realm. Evolutionary conflict occurs over multiple scales of biological organization, from genetic outlawry within genomes, to sibling rivalry within nuclear families, to collective-action disputes within societies. However, achieving a general understanding of the dynamics and consequences of evolutionary conflict remains an outstanding challenge. Here, we show that a development of R. A. Fisher\'s classic \'geometric model\' of adaptation yields novel and surprising insights into the dynamics of evolutionary conflict and resulting maladaptation, including the discoveries that: (i) conflict can drive evolving traits arbitrarily far away from all parties\' optima and, indeed, if all mutations are equally likely then contested traits are more often than not driven outwith the zone of actual conflict (hyper-maladaptation); (ii) evolutionary conflicts drive persistent maladaptation of orthogonal, non-contested traits (para-maladaptation); and (iii) modular design greatly ameliorates conflict-driven maladaptation, thereby facilitating major transitions in individuality.

When divergent populations interbreed, their alleles are brought together in hybrids. In the initial F1 cross, most divergent loci are heterozygous. Therefore, F1 fitness can be influenced by dominance effects that could not have been selected to function well together. We present a systematic study of these F1 dominance effects by introducing variable phenotypic dominance into Fisher\'s geometric model. We show that dominance often reduces hybrid fitness, which can generate optimal outbreeding followed by a steady decline in F1 fitness, as is often observed. We also show that \"lucky\" beneficial effects sometimes arise by chance, which might be important when hybrids can access novel environments. We then show that dominance can lead to violations of Haldane\'s Rule (reduced fitness of the heterogametic F1) but strengthens Darwin\'s Corollary (F1 fitness differences between cross directions). Taken together, results show that the effects of dominance on hybrid fitness can be surprisingly difficult to isolate, because they often resemble the effects of uniparental inheritance or expression. Nevertheless, we identify a pattern of environment-dependent heterosis that only dominance can explain, and for which there is some suggestive evidence. Our results also show how existing data set upper bounds on the size of dominance effects. These bounds could explain why additive models often provide good predictions for later-generation recombinant hybrids, even when dominance qualitatively changes outcomes for the F1.

Little is empirically known about the contribution of mutations to fitness in natural environments. However, Fisher\'s Geometric Model (FGM) provides a conceptual foundation to consider the influence of the environment on mutational effects. To quantify mutational properties in the field, we established eight sets of MA lines (7-10 generations) derived from eight founders collected from natural populations of Arabidopsis thaliana from French and Swedish sites, representing the range margins of the species in Europe. We reciprocally planted the MA lines and their founders at French and Swedish sites, allowing us to test predictions of FGM under naturally occurring environmental conditions. The performance of the MA lines relative to each other and to their respective founders confirmed some and contradicted other predictions of the FGM: the contribution of mutation to fitness variance increased when the genotype was in an environment where its fitness was low, that is, in the away environment, but mutations were more likely to be beneficial when the genotype was in its home environment. Consequently, environmental context plays a large role in the contribution of mutations to the evolutionary process and local adaptation does not guarantee that a genotype is at or close to its optimum.

When divergent populations form hybrids, hybrid fitness can vary with genome composition, current environmental conditions, and the divergence history of the populations. We develop analytical predictions for hybrid fitness, which incorporate all three factors. The predictions are based on Fisher\'s geometric model, and apply to a wide range of population genetic parameter regimes and divergence conditions, including allopatry and parapatry, local adaptation, and drift. Results show that hybrid fitness can be decomposed into intrinsic effects of admixture and heterozygosity, and extrinsic effects of the (local) adaptedness of the parental lines. Effect sizes are determined by a handful of geometric distances, which have a simple biological interpretation. These distances also reflect the mode and amount of divergence, such that there is convergence toward a characteristic pattern of intrinsic isolation. We next connect our results to the quantitative genetics of line crosses in variable or patchy environments. This means that the geometrical distances can be estimated from cross data, and provides a simple interpretation of the \"composite effects.\" Finally, we develop extensions to the model, involving selectively induced disequilibria, and variable phenotypic dominance. The geometry of fitness landscapes provides a unifying framework for understanding speciation, and wider patterns of hybrid fitness.

The formation of new species via the accumulation of incompatible genetic changes is thought to result either from ecologically based divergent natural selection or the order by which mutations happen to arise, leading to different evolutionary trajectories even under similar selection pressures. There is growing evidence in support of both ecological speciation and mutation-order speciation, but how different environmental scenarios affect the rate of species formation remains underexplored. We use a simple model of optimizing selection on multiple traits (\"Fisher\'s geometric model\") to determine the conditions that generate genetic incompatibilities in a changing environment. We find that incompatibilities are likely to accumulate in isolated populations adapting to different environments, consistent with ecological speciation. Incompatibilities also arise when isolated populations face a similar novel environment; these cases of mutation-order speciation are particularly likely when the environment changes rapidly and favors the accumulation of large-effect mutations. In addition, we find that homoploid hybrid speciation is likely to occur either when new environments arise in between the parental environments or when parental populations have accumulated large-effect mutations following a period of rapid adaptation. Our results indicate that periods of rapid environmental change are particularly conducive to speciation, especially mutation-order or hybrid speciation.

Evolutionary conflict and arms races are important drivers of evolution in nature. During arms races, new abilities in one party select for counterabilities in the second party. This process can repeat and lead to successive fixations of novel mutations, without a long-term increase in fitness. Models of co-evolution rarely address successive fixations, and one of the main models that use successive fixations-Fisher\'s geometric model-does not address co-evolution. We address this gap by expanding Fisher\'s geometric model to the evolution of joint phenotypes that are affected by two parties, such as probability of infection of a host by a pathogen. The model confirms important intuitions and offers some new insights. Conflict can lead to long-term Sisyphean arms races, where parties continue to climb toward their fitness peaks, but are dragged back down by their opponents. This results in far more adaptive evolution compared to the standard geometric model. It also results in fixation of mutations of larger effect, with the important implication that the common modeling assumption of small mutations will apply less often under conflict. Even in comparison with random abiotic change of the same magnitude, evolution under conflict results in greater distances from the optimum, lower fitness, and more fixations, but surprisingly, not larger fixed mutations. We also show how asymmetries in selection strength, mutation size, and mutation input allow one party to win over another. However, winning abilities come with diminishing returns, helping to keep weaker parties in the game.

Populations may genetically adapt to severe stress that would otherwise cause their extirpation. Recent theoretical work, combining stochastic demography with Fisher\'s geometric model of adaptation, has shown how evolutionary rescue becomes unlikely beyond some critical intensity of stress. Increasing mutation rates may however allow adaptation to more intense stress, raising concerns about the effectiveness of treatments against pathogens. This previous work assumes that populations are rescued by the rise of a single resistance mutation. However, even in asexual organisms, rescue can also stem from the accumulation of multiple mutations in a single genome. Here, we extend previous work to study the rescue process in an asexual population where the mutation rate is sufficiently high so that such events may be common. We predict both the ultimate extinction probability of the population and the distribution of extinction times. We compare the accuracy of different approximations covering a large range of mutation rates. Moderate increase in mutation rates favors evolutionary rescue. However, larger increase leads to extinction by the accumulation of a large mutation load, a process called lethal mutagenesis. We discuss how these results could help design \"evolution-proof\" antipathogen treatments that even highly mutable strains could not overcome.