Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations

We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e. growth rate) requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.Comment: 13 pages, 5 figure

Comparative study between discrete and continuum models for the evolution of competing phenotype-structured cell populations in dynamical environments

Deterministic continuum models formulated as nonlocal partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In light of these considerations, in this paper we develop a stochastic individual-based model for the coevolution of two competing phenotype-structured cell populations that are exposed to time-varying nutrient levels and undergo spontaneous, heritable phenotypic changes with different probabilities. Here, the evolution of every cell is described by a set of rules that result in a discrete-time branching random walk on the space of phenotypic states, and nutrient levels are governed by a difference equation in which a sink term models nutrient consumption by the cells. We formally show that the deterministic continuum counterpart of this model comprises a system of nonlocal partial differential equations for the cell population density functions coupled with an ordinary differential equation for the nutrient concentration. We compare the individual-based model and its continuum analog, focusing on scenarios whereby the predictions of the two models differ. The results obtained clarify the conditions under which significant differences between the two models can emerge due to bottleneck effects that bring about both lower regularity of the density functions of the two populations and more pronounced demographic stochasticity. In particular, bottleneck effects emerge in the presence of lower probabilities of phenotypic variation and are more apparent when the two populations are characterized by lower fitness initial mean phenotypes and smaller initial levels of phenotypic heterogeneity. The emergence of these effects, and thus the agreement between the two modeling approaches, is also dependent on the initial proportions of the two populations. As an illustrative example, we demonstrate the implications of these results in the context of the mathematical modeling of the early stage of metastatic colonization of distant organs

Heterogeneity and noise in living systems: statistical physics perspectives

Even the most distracted observer could hardly miss noticing the extensive heterogeneity of traits and behaviors displayed by living systems. So great a variability is commonly ascribed to differences at the level of the genome, which originated from the evolution process to adapt the organisms to the different environments they live in. However, phenotypic heterogeneity is found even in genetically identical organisms, from monoclonal cellular populations to human twins. The multitude of microscopic causes that sum up to give such variability is commonly referred to as biological noise, coming both in the form of environmental fluctuations affecting the development of individual organisms (extrinsic noise) and as the unavoidable results of stochasticity at the level of molecular reaction (intrinsic noise). The latter persisting even when genetically identical organisms are kept under nearly identical conditions. For quite a long time, such fluctuations were considered a nuisance that makes experiments just difficult to interpret, needing to enlarge the number of observations to have reliable outcomes, and from the point of view of cells, a disturbance cells need to deal with. In the last two decades, however, experimental progresses allowed to investigate the system at single-cell scale. The emerging view is that noise under some circumstances can have a beneficial role, like promoting survival to adverse environments or enhancing differentiation. Ultimately, evolution tunes the systems so they can take advantage of natural stochastic fluctuations. We will follow noise and fluctuation from the cellular level to the higher level of organization of the cellular population where heterogeneity in the molecular reactions translate in the variability of phenotypes. Biology is very broad though, and noise affects all biological processes. Time restraint and my limited knowledge of biological systems did not allow for an exhaustive discussion of all the aspects in which noise and the subsequent heterogeneity play a role. Instead, we will focus on the regulation of noise. More in details, the first part of the thesis introduces to the impact of noise on gene expression and the regulation mechanisms cells use to control it. The action of large regulatory networks is to coordinate a huge of number molecular interactions to obtain robust system-level outcomes. This capability can emerge even when individual interactions are weak and/or strongly heterogeneous. This is the case of post-transcriptional regulation driven by microRNAs (miRNAs). microRNAs are small non-coding RNA molecules able to regulate gene expression at the post-transcriptional level by repressing target RNA molecules. It has been found that such regulation may lead the system to bimodal distributions in the expression of the target mRNA, usually fingerprint of the presence of two distinct phenotypes. Moreover, the nature of the interaction between miRNAs and their targets gives rise to a complex network of miRNAs interacting with several mRNA targets. Such targets may then cross-regulate each other in an indirect miRNA-mediated manner. This effect, called `competing endogenous RNA (ceRNA) effect', despite being typically weak, has been found to possess remarkable properties in the presence of extrinsic noise, where fluctuations affect all the components of the system. We will discuss crosstalk and illustrate how crosstalk patterns are enhanced by both transcriptional and kinetic heterogeneities and achieve high intensities even for RNAs that are not co-regulated. Moreover, we will see that crosstalk patterns are significantly non-local, i.e. correlate weakly with miRNA-RNA interaction parameters. Since these features appear to be encoded in the network's topology this suggests that such crosstalk is tunable by natural selection. Moving at the cellular level, we focus on the outcomes of gene expression, i.e. the observable phenotypes. Depending on the degree of regulation the cell manages to exert with respect to noise, the distribution of those phenotypes will display a certain extent of heterogeneity. Such cell-to-cell variability is found to have many implications especially for the growth of the whole population. In the second part of the thesis, we discuss some properties of those heterogeneous distributions. First, we focus on the dependence on the initial conditions for the different phases of growth, i.e. the adaptive phase and exponential growth phase. Since cellular populations grow in an exponential fashion, the size and composition of the inoculum shall matter. We discuss this following a novel extensive experimental investigation recently done on cancer cell lines in a controlled environment. Finally, we focus on the effects that a heterogeneous phenotype has on the growth in hostile environments, i.e. environments fluctuating between states in which the growth is favored and others where growth is inhibited. In such a case, if cells can only replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations), an exploration-exploitation trade-off is established, whose specifics depend on the statistics of the environment. The phenotypic distribution corresponding to maximum population fitness requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in periodic two-state environments. Most notably, the key parameter overseeing the trade-off is linked to the amount of regulation cells can exert

Individual variation in behaviour

Wild animals show remarkable phenotypic variation despite natural selection eroding it. Phenotypic variation within populations is intriguing because all individuals are expected to be adapted to the same environmental conditions, and thus, to present similar phenotypic traits. However, when repeatedly measured, individuals have been observed to differ in the average expression of various behaviours across time and contexts. Consistent among-individual variation (called “animal personality”) has been proposed to be adaptively maintained if the fitness costs and benefits of behaviour vary with the environment or other phenotypic traits. Theory postulates that two key adaptive mechanisms could play a role: life-history trade-offs and spatiotemporal variation in selection (or heterogeneous selection). Empirical tests of the role of these mechanisms in the maintenance of individual variation in behaviour remain scarce and findings are ambivalent. My PhD thesis aimed at shedding light on the mechanisms allowing the persistence of animal personalities, thereby advancing our understanding of how animals adapt to variable environments. I investigated the role of life-history trade-offs and heterogeneous selection in the coexistence of alternative personalities in the wild. I also examined potential ecological drivers of heterogeneous selection. I used a passerine bird breeding in the wild in nest boxes (the great tit Parus major) as model. Individuals must trade-off investment among various phenotypic traits because they have limited amount of energy and time to acquire resources, grow and reproduce. The optimal resolution of trade-offs may depend on ecological conditions and/or the phenotypic traits of the individuals. Individuals differing in their behavioural phenotypes may thus resolve trade-offs differently. In Chapter 1, my colleagues and I tested this hypothesis by focusing on the trade-off between current reproduction and reproductive senescence. Specifically, we asked whether behavioural phenotypes differed in patterns of senescence. We found that faster explorers increased and subsequently decreased their reproductive investment with age. This finding suggests that faster explorers reproductively senesced later in life. By contrast, slower explorers laid similar clutch sizes through their lifetime; that is, they did not show reproductive senescence. Different behavioural phenotypes, thus, resolved the trade-off between current reproduction and reproductive senescence differently, which may allow them to coexist. Spatial and temporal variation in the environment may cause natural selection to favour different phenotypes in different environments. Spatial variation in selection may maintain phenotypic variation across environments, whereas temporal variation in selection (or fluctuating selection) may maintain phenotypic variation within environments. Though these processes co-occur and may have counteracting effects on phenotypic variation, both processes have rarely been investigated simultaneously. The relative importance of spatial and temporal variation in selection, and thus, the evolutionary potential of phenotypic traits under heterogeneous selection, remains unexplored. In Chapter 2, I studied heterogeneous selection on behaviour within and among great tit populations. To this aim, I gathered longitudinal data from five West European wild great tit populations breeding in nest boxes. In all these populations, behaviour was assayed with the same experimental design. Selection on behaviour varied primarily spatially. Temporal variation in selection was also important. The existence of phenotypic variation in all populations suggests that temporal variation played a key role in counteracting local adaption promoted by spatial variation. Temporal variation in selection was population-specific, which suggests that local ecological conditions also played a role in the evolution of phenotypic variation. This study thereby demonstrated the importance of considering both large- and small-scale geographical and temporal variation to understand the ecological mechanisms maintaining variation in animal behaviour. Previous studies found that variation in the social environment induced by variation in population density caused selection on behaviour to vary. However, we did not find such evidence in great tit populations. Another ecological factor that varies ubiquitously and that is crucial for survival and reproduction is food availability. Food availability also generally positively correlates with population density. Therefore, the effects of population density on fitness may be indirect through food availability. Variation in food availability may cause selection pressures on behaviour to vary because behavioural phenotypes differ in competitive abilities and foraging tactics. In Chapter 3, I studied whether winter food availability drove heterogeneous selection on activity in a novel environment. I experimentally manipulated food abundance outside the breeding season by providing supplementary food in multiple great tit nest box plots. Against expectations, I did not find evidence for fecundity selection on behaviour to vary with the experimental manipulation of food availability. Food availability may drive variation in fecundity selection but simultaneous changes in breeding density may counteract its action. Food- and density-dependent selection on behaviour need to be estimated simultaneously to disentangle their effects. Interestingly, on average, individuals were more active in high than in low food availability context. Moreover, high food availability context increased behavioural variation among individuals. These findings suggest greater plasticity and/or higher survival, recruitment or immigration rate of more active individuals. Future studies should investigate whether viability rather than fecundity selection vary with food availability. In the different projects of this PhD work, I focused on behaviour scored in different “novel environments”, which are all generally labelled “exploration behaviour”. However, “exploration behaviour” was not assayed with the same experimental design in Chapter 2 compared to Chapter 1 and 3. In Chapter 1 and 3, behaviour was assayed in the field in a portable cage. In Chapter 2, behaviour was assayed in a standardized laboratory room. We assumed that birds expressed the same behaviour in both assays because laboratory- and field-based behaviours have been shown to each correlate with other field-based behaviours. In Chapter 4, I tested this assumption and found that laboratory- and field-based behaviour did not correlate. Both assays may present different contexts to the birds, which elicited the expression of different behaviours. I also showed that the population sampled for the laboratory test was biased toward fast explorers. This study highlights the difficulty assaying behaviour in an unbiased and reproducible manner. It is therefore important to cross-validate behavioural assays before making biological assumptions. Overall, this PhD thesis contributed to understanding the role of adaptive mechanisms in individual variation in behaviour and their ecological drivers. This work showed that behavioural phenotypes contribute differently to population dynamics and should thus be considered in ecological and evolutionary studies. This work also exemplified the importance of long-term and collaborative projects. For a comprehensive understanding of phenotypic variation, the next challenge would be to simultaneously consider multiple traits, ecological factors and species that all interact through eco-evolutionary dynamics. Such integrative studies will embrace the complexity of ecological interactions and allow us to better understand how populations adapt to variable environments

How does chromosomal instability affect the tempo and mode of adaptation?

Tese de mestrado, Biologia Evolutiva e do Desenvolvimento, Universidade de Lisboa, Faculdade de Ciências, 2015A instabilidade genómica ao nível da estrutura cromossómica (instabilidade cromossómica) tem um papel importante na progressão do cancro. Vários estudos sugerem também que a instabilidade cromossómica pode proporcionar saltos gigantescos na paisagem adaptativa durante a adaptação a um novo ambiente. Isto porque o número de passos mutacionais necessários para que daí possam resultar mudanças significativas no fenótipo é menor do que em mutadores ao nível de substituições nucleotídicas simples. A instabilidade cromossómica gera alterações estruturais nos cromossomas (rearranjos cromossómicos) que podem afetar não só as sequências nucleotídicas de genes específicos como também interferir com a ordem de elementos regulatórios no genoma e, consequentemente, alterar padrões de expressão génica. Contudo, há uma considerável escassez na literatura de estudos sobre as dinâmicas evolutivas de mutadores da estrutura cromossómica (organismos com elevada instabilidade cromossómica), que em última análise são necessários para uma melhor compreensão do quanto e em que circunstâncias a elevada evolvabilidade, que é intrínseca destes mutadores, poderá ser benéfica ou deletéria a curto e a longo prazo. Há hipóteses que sugerem que em ambientes constantes, não stressantes, a instabilidade cromossómica paga um custo devido à acumulação de mutações deletérias. No entanto, durante a adaptação a novos ambientes ou em ambientes alternados, estes mutadores da estrutura cromossómica podem contribuir com a variabilidade genética necessária para a adaptação da população. Os efeitos positivos que alguns rearranjos cromossómicos representam para o fitness podem exceder os efeitos pejorativos dos restantes rearranjos resultantes deste tipo de instabilidade. O objetivo deste trabalho é o estudo dos “trade-offs” evolutivos que condicionam a evolução da instabilidade cromossómica. Através de evolução experimental estudámos a adaptação a curto prazo de estirpes instáveis de Schizosaccharomyces pombe em duas condições ambientais: um ambiente constante, não stressante, e um ambiente alternado. Nomeadamente, queríamos determinar se as estirpes instáveis têm uma vantagem adaptativa num contexto de ambiente alternado, em que há mais espaço para adaptação, e se, por outro lado, o balanço entre as mutações deletérias e as mutações benéficas que possam surgir pode constituir um custo para estas estirpes num ambiente constante, em que há menos espaço para adaptação. O fenótipo de instabilidade característico das estirpes que usámos é consequência de um conjunto de mutações construídas no laboratório que afetam o encapsulamento dos telómeros bem como mecanismos de reparação de DNA e que, em conjunto, originam padrões de rearranjos cromossómicos brutos como translocações, inversões, deleções, amplificações e aneuploidia. Para responder às questões a que nos propusémos, realizámos ensaios de competição entre as estirpes instáveis e um clone de referência das estirpes controlo, bem como entre as estirpes controlo e um clone referência das estirpes instáveis. As estirpes controlo foram evoluídas em conjunto com as instáveis durante a evolução experimental e estão marcadas com mCherry, uma proteína flourescente, o que permite que as suas frequências sejam seguidas por um equipamento especializado ao longo de alguns ciclos de crescimento e diferenciadas das frequências das estirpes instáveis, que não têm fluorescência. Estes ensaios permitiram-nos determinar o fitness relativo das duas estirpes como função da alteração das suas frequências relativas ao longo das competições. Desta forma, estimámos o fitness das estirpes no início da evolução experimental e depois da adaptação a curto prazo nas duas condições ambientais (ambiente constante e alternado). Também realizámos experiências para testar se o tamanho populacional das duas estirpes sofreu alterações ao longo da evolução experimental, já que alterações neste parâmetro podem afetar grandemente a eficiência da seleção natural em oposição à ação da deriva genética. O efeito fundador também pode afetar a ação da seleção natural. No início da evolução experimental usámos diferentes clones de cada estirpe para fundar os replicados populacionais e testámos se haviam diferenças no fitness inicial. Procurámos também perceber se mutações que possam ter surgido nos diferentes clones das estirpes instáveis imediatamente após a criação do seu fenótipo de instabilidade condicionaram a sua evolução. Para isso testámos o efeito do clone no fitness final de cada estirpe para as duas condições ambientais. Fizémos também uma estimativa do papel relativo da seleção, história e deriva na distribuição dos valores finais de fitness de cada estirpe. Os dados de fitness permitiram-nos responder a várias perguntas específicas: 1) as estirpes adaptaram-se às condições ambientais a que foram expostas (há diferenças entre o fitness inicial e o fitness após a evolução experimental?); 2) qual foi a dinâmica evolutiva das estirpes (houve convergência para os mesmos valores de fitness ou divergência entre os replicados populacionais de cada estirpe?); 3) há diferenças entre as dinâmicas evolutivas das duas estirpes?; 4) há diferenças entre as dinâmicas evolutivas de cada estirpe na adaptação aos dois tipos de ambiente?. Concluímos que, após a adaptação a curto prazo em ambiente constante, o fitness das estirpes instáveis aumentou e a adaptação foi caracterizada por uma divergência fenotípica reveladora de uma paisagem adaptativa complexa, composta por vários picos locais. Estas observações suportam a hipótese de que a instabilidade cromossómica pode permitir uma exploração mais abrangente da paisagem adaptativa, aumentando as probabilidades de se atingirem picos mais elevados. As estirpes controlo, no entanto, sofreram um decréscimo do fitness durante a adaptação em ambiente constante. Não detectámos nenhum padrão de divergência ou convergência entre os replicados populacionais destas estirpes o que, aliado à observação de que o clone teve um efeito significativo nas suas trajectórias evolutivas, constitui evidência para a incapacidade de grandes populações com taxas moderadas de mutação explorarem paisagens adaptativas muito complexas. Assim, os genótipos fundadores dos replicados populacionais destas estirpes terão determinado a paisagem adaptativa passível de ser explorada no início da experiência de evolução tendo em conta as suas limitações em termos de taxa de mutação. O efeito do clone nos valores de fitness das estirpes controlo foi evidente mesmo no fim da experiência de adaptação. Embora a história não tenha tido um efeito considerável nas distribuições de fitness das estirpes evoluídas em comparação com o efeito da seleção natural, há evidências de que a variabilidade genotípica entre as populações no início da experiência de evolução terá limitado as diferentes populações a vales distintos na paisagem adaptativa. A adaptação de ambas as estirpes em ambiente alternado foi caracterizada por um “trade-off” na capacidade de exploração de fontes de carbono alternativas. Em suma, os nossos resultados indicam que as dinâmicas evolutivas que condicionam a adaptação a curto prazo de mutadores da estrutura cromossómica são altamente complexas e dependentes das condições ambientais.Genomic instability at the level of chromosomal structure (chromosomal instability) plays an important role in cancer progression. It has been suggested by several studies that chromosomal instability could facilitate large leaps in the fitness landscape during adaptation to a novel environment with less mutational steps than single-nucleotide substitution mutators. This is because chromosomal instability generates structural changes in chromosomes (chromosome rearrangements) with the ability to not only affect genetic sequences of particular genes but even interfere with the order of regulatory elements, thus changing gene expression patterns. Studies addressing the evolutionary dynamics of mutators for chromosomal structure are currently lacking in the literature and are utterly necessary to understand the extent to which the higher intrinsic evolvability of these mutators could be beneficial or deleterious. It has been hypothesized that in a constant, non-stressful environment, chromosomal instability is expected to pay a cost due to the accumulation of deleterious mutations. However, during adaptation to a novel environment or under fluctuating environments, mutators of chromosomal structure can provide the genetic variation necessary for the population to adapt and the positive fitness effects contributed by individual rearrangements may exceed the detrimental effects. The aim of this work was to ascertain the evolutionary trade-offs that drive evolution of chromosomal instability. Through an experimental evolution approach, we studied the short-term adaptation of Schizosaccharomyces pombe unstable strains to two environmental conditions: a constant non-stressful environment and a fluctuating environment. The instability phenotype of the strains used in this work is given by a set of mutations in the capping of telomeres and in DNA repair mechanisms that ultimately lead to patterns of gross chromosome rearrangements, including translocations, inversions, deletions, amplifications and aneuploidy. After short-term adaptation to a constant environment, the fitness of mutator strains increased and adaptation was accompanied by phenotypic divergence, revealing a complex fitness landscape with many local peaks. Furthermore, adaptation under a fluctuating environment revealed a trade-off in the ability to exploit alternative carbon sources. Altogether, our results indicate that the short-term evolutionary dynamics of mutators for chromosomal structure is highly complex and dependent on the environmental conditions

Experimental evolution of environment dependent gene regulation.

The effects of environment on evolution can be explored by experimentally controlling the environment experienced by a population. Data can be collected continuously on evolutionary change and related to the experimental environment. Further, the controlled conditions allow theoretical predictions to be tested. This thesis reports on the development of two experimental evolution systems that can be used to investigate the effects of environmental change on the evolution of gene regulation. In both systems the fission yeast Schizosaccharomyces pombe grows under defined selection pressures in two alternating environments. Conditions in both environments are under tight control, with one selecting positively for expression of a target gene, and the other selecting negatively against expression. Alternating growth between the two environments creates a selection pressure for environment dependent regulation of the gene. This is an example of phenotypic plasticity – an environment dependent phenotypic change. Thus, the two systems can be used to investigate phenotypic plasticity and gene regulation, including testing of related theories. The first system targets the expression of the ura4 gene. This gene is necessary for the production of uracil, so an environment lacking uracil selects strongly for expression. The alternate environment contains the compound 5-fluoroorotic acid (FOA) which is metabolised by URA4 into a toxin, thus strongly selecting against expression. The second system targets the expression of an introduced green fluorescent protein (GFP) gene using fluorescence activated cell sorting (FACS). The sorting can alternately select for high and low expressing cells from a population. Environmental conditions between the sorts can be altered to provide a cue for the selection the population will face next, thus allowing evolution of environment dependent expression. Experimental work in developing and testing these systems is presented

Evolutionary origins of invasive populations

What factors shape the evolution of invasive populations? Recent theoretical and empirical studies suggest that an evolutionary history of disturbance might be an important factor. This perspective presents hypotheses regarding the impact of disturbance on the evolution of invasive populations, based on a synthesis of the existing literature. Disturbance might select for life-history traits that are favorable for colonizing novel habitats, such as rapid population growth and persistence. Theoretical results suggest that disturbance in the form of fluctuating environments might select for organismal flexibility, or alternatively, the evolution of evolvability. Rapidly fluctuating environments might favor organismal flexibility, such as broad tolerance or plasticity. Alternatively, longer fluctuations or environmental stress might lead to the evolution of evolvability by acting on features of the mutation matrix. Once genetic variance is generated via mutations, temporally fluctuating selection across generations might promote the accumulation and maintenance of genetic variation. Deeper insights into how disturbance in native habitats affects evolutionary and physiological responses of populations would give us greater capacity to predict the populations that are most likely to tolerate or adapt to novel environments during habitat invasions. Moreover, we would gain fundamental insights into the evolutionary origins of invasive populations

The social evolution of individual differences: Future directions for a comparative science of personality in social behavior

Personality is essential for understanding the evolution of cooperation and conflict in behavior. However, per-sonality science remains disconnected from the field of social evolution, limiting our ability to explain how personality and plasticity shape phenotypic adaptation in social behavior. Researchers also lack an integrative framework for comparing personality in the contextualized and multifaceted behaviors central to social in-teractions among humans and other animals. Here we address these challenges by developing a social evolu-tionary approach to personality, synthesizing theory, methods, and organizing questions in the study of individuality and sociality in behavior. We critically review current measurement practices and introduce social reaction norm models for comparative research on the evolution of personality in social environments. These models demonstrate that social plasticity affects the heritable variance of personality, and that individual dif-ferences in social plasticity can further modify the rate and direction of adaptive social evolution. Future empirical studies of frequency-and density-dependent social selection on personality are crucial for further developing this framework and testing adaptive theory of social niche specialization.Peer reviewe