Cancer, a leading cause of death globally, is characterized by the uncontrolled growth of abnormal cells evolving due to natural selection. A cancerous tumor is a complex ecosystem of heterogeneous cell populations that, over time, acquire new traits like therapy resistance. Despite progress in experimental methods, measuring genetic and phenotypic processes on time scales relevant to tumor evolution is still challenging. As a result, the mechanisms that lead to tumor heterogeneity, evolution, progression, and response to treatment remain largely unclear. Mathematical models can help address this challenge, allowing us to test hypotheses, predict cellular behavior, and optimize cancer treatment. In this thesis, I investigate the role of genetic and phenotypic heterogeneity in tumor evolution using mathematical models and analysis. Discrete stochastic models are well-suited to study tumor evolution due to the involvement of rare stochastic events and small populations. Here, I introduce evolutionary lattice-gas cellular automata (evo-LGCA), a generalization of classical lattice-gas cellular automata (LGCA). LGCA are discrete mathematical models describing the interactions of moving agents, such as cancer cells, on a regular lattice, with discretized velocities, and in discrete time steps. Agents are indistinguishable and obey an exclusion principle that prevents them from being simultaneously in the same state, causing unwanted behavior. In contrast, in evo-LGCA, agents are distinguishable, have unique properties, and can be in the same state, minimizing model artifacts. This makes evo-LGCA particularly suitable for studying the complexity of tumors. Using this framework, I investigate the interplay of evolutionary dynamics and population growth. In particular, I am interested in the role of the distribution of fitness effects (DFE). The DFE determines the strength and frequency of the effect of mutations. I present an evo-LGCA model for tumor evolution, in which cells can divide, die, move, and mutate given an arbitrary but fixed DFE. From the dynamics of the evo-LGCA model, I derive an integro-partial differential equation, predicting the distribution in fitness space over time. This equation is equivalent to the replicator-mutator equation, establishing a connection to population genetics and evolutionary game theory. Additionally, I derive a generalized version of Fisher’s fundamental theorem of natural selection, a classic theorem stating that a population’s change in mean fitness is proportional to the population’s variance in fitness. However, it neglects the effect of mutations and the dynamics of higher moments, such as the variance. My generalization is a hierarchy of equations for the time evolution of all moments of the fitness distribution, depending on the DFE. Through simulations of the evo-LGCA model, I show that continuum approximations are suitable in regimes of frequent mutations with weak effects on fitness and large, well-mixed populations. I further establish that the fastest-growing cells spearhead spreading populations, accelerating the expansion speed. Next, I examine the evolutionary dynamics within small, clinically undetectable tumors. Cancer cells quickly accumulate weakly disadvantageous passenger mutations, whereas beneficial driver mutations are rare but have a significant effect. Previous studies have shown that this leads to competition between passenger and driver mutations, affecting population fitness. Populations below a critical population size accumulate deleterious mutations too quickly, leading to extinction. I highlight how small cancer cell populations can bypass potential extinction through swift invasion of their microenvironment. This invasion can be seen as an adaptation to counteract the accumulation of disadvantageous mutations. Lastly, I examine the complex relationship between evolution and phenotypic plasticity, focusing on the phenotypic change between proliferative and migratory phenotypes relevant to tumors like glioblastoma, a deadly brain tumor. Contrary to previous studies, I propose that evolution acts on the cellular decision-making process in response to the environment rather than on phenotypic traits like cell motility. I study this hypothesis with an evo-LGCA model that tracks individual cells’ phenotypic and genetic states. I assume cells change between migratory and proliferative states controlled by inherited and mutation-driven genotypes and the cells’ microenvironment in the form of cell density. Cells at the tumor edge evolve to favor migration over proliferation and vice versa in the tumor bulk. Notably, this phenotypic heterogeneity can be realized by two distinct regulations of the phenotypic switch. I predict the outcome of the evolutionary process with a mathematical analysis, revealing a dependence on microenvironmental parameters. The emerging synthetic tumors display varying levels of heterogeneity, which I show are predictors of the cancer’s recurrence time after treatment. Interestingly, higher phenotypic heterogeneity predicts poor treatment outcomes, unlike genetic heterogeneity. In conclusion, this thesis offers a mathematical framework for studying heterogeneous populations. Applying it to tumor evolution, I gained new insights into the relationship between discrete and continuous evolution models and the interplay of population growth and evolutionary dynamics. I also proposed a novel perspective on phenotypic plasticity accounting for cell decision-making, demonstrating the predictive value of phenotypic heterogeneity.:1. Introduction [13] 1.1 Background on Cancer [13] 1.1.1 Definition [13] 1.1.2 Hallmarks of Cancer [13] 1.1.3 Cancer as a Genetic Disease [14] 1.1.4 Tumor Evolution [15] 1.1.5 Tumor Heterogeneity [17] 1.2 Mathematical Models of Tumor Evolution and Heterogeneity [19] 1.2.1 Overview [19] 1.2.2 Deterministic Approaches [20] 1.2.3 Agent-Based Approaches [24] 1.2.4 Hybrid Models [26] 1.2.5 Evolutionary Game Theory [27] 1.3 Research Questions and Dissertation Outline [27] 2. Evolutionary Lattice-Gas Cellular Automata [31] 2.1 Cellular Automaton Basics [31] 2.2 Lattice-Gas Cellular Automata [33] 2.2.1 Origins [33] 2.2.2 Definition [34] 2.2.3 Extensions [39] 2.3 Evolutionary Lattice-Gas Cellular Automata [43] 2.3.1 Concept [43] 2.3.2 State Space [44] 2.3.3 Dynamics [45] 2.4 Discussion [49] 3. Bridging Micro- and Macroscale of Evolutionary Dynamics [51] 3.1 Connecting Discrete and Continuous Models of Evolution [51] 3.2 Model Definition [53] 3.3 Mathematical Analysis [55] 3.3.1 Mean-Field Approximation of Evolutionary Dynamics [55] 3.3.2 A Generalized Fundamental Theorem of Natural Selection [57] 3.3.3 Derivation of Local Replicator-Mutator Equation [61] 3.3.4 Finite-Size Correction [62] 3.3.5 Spatial Growth Dynamics [63] 3.4 Comparison with Agent-Based Simulations [64] 3.4.1 Well-Mixed Populations [64] 3.4.2 Expanding Populations [68] 3.5 Discussion [69] 4. The Interplay of Invasion and Mutational Meltdown [73] 4.1 Muller’s Ratchet in Tumors [73] 4.2 Influence of Invasion on Evolutionary Dynamics [74] 4.3 Model Parameterization [74] 4.4 Tug-of-War between Driver and Passenger Mutations [76] 4.5 Invasion as a Strategy against Mutational Meltdown [79] 4.6 Discussion [80] 5. Evolution under the Go-or-Grow Dichotomy [85] 5.1 Phenotypic Plasticity [85] 5.2 The Role of Cell Decision-Making in Evolutionary Dynamics [86] 5.3 Model Definition [87] 5.4 Emergence of Phenotypic and Genetic Heterogeneity [90] 5.4.1 Migratory Phenotype Favored by Minimal Apoptosis Rates [91] 5.4.2 Emerging Spatial Heterogeneity for Low Switching Threshold [91] 5.4.3 Repulsive Strategy Favored by High Switching Threshold [92] 5.4.4 Prediction of Optimal Go-or-Grow Strategy [92] 5.5 Heterogeneity as a Predictor of Treatment Outcomes [95] 5.6 Discussion [98] 6. Discussion & Outlook [103] A. Mathematical Derivations [107] B. Supplementary Simulations [113] C. Software [119] Bibliography [121]

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Thesis (MScConsEcol (Conservation Ecology and Entomology))--University of Stellenbosch, 2006. / Acacia karroo is widespread in southern Africa and displays remarkable phenotypic plasticity over its geographical range. However, it is currently unknown whether this phenomenon is merely phenotypic variation due to environmental variance or whether such plasticity represents adaptation to different habitats (known as adaptive phenotypic plasticity). Adaptive phenotypic plasticity implies that genotypes differ and that there is local adaptation to the local environment. To shed light on this phenomenon, we used a common-garden experiment to investigate among-population variation in plastic responses to simulated rainfall and browsing in two populations originating from contrasting environments, namely arid Karoo (Leeu Gamka) and subtropical coastal forest (Richards Bay). We also studied genetic variation among populations by means of allozyme markers. The results suggest that the populations investigated are both genetically distinct and phenotypically plastic. In addition, there were high levels of polymorphism within populations and great differences in their range of plastic responses to treatments. Of the two populations investigated, the slow-growing one (Leeu Gamka) was phenotypically more plastic with regard to defence-related traits (longer spines, more tannin) while the fast-growing one (Richards Bay) was phenotypically more plastic regarding growth-related traits (taller, with longer leaves). Patterns of performance revealed that the populations have pure strategies of either growth (forest) or defence (arid). The interactions between populations and environments in some traits indicated genetic differentiation in plastic responses between populations and, consequently, that phenotypic plasticity is locally adaptive and not merely due to environmental differences. The two populations appear to have pure strategies; when environmental conditions were improved by addition of water, the forest population increased investment in growth but not defence, while the arid populations increased defence production but not growth.

Alate morphs can benefit aphid populations by facilitating dispersal from deteriorating food sources and by escaping from natural enemies. Wing development, however, imposes constraints on fecundity. The soybean aphid, Aphis glycines Matsumura (Hemiptera: Aphididae), is an important economic pest in the U.S. and Canada. I conducted a series of laboratory and field experiments to determine the environmental factors inducing wing development in this species, and to determine the effects of asexual alate individual production on an A. glycines population under predation. My results reveal that wing induction in A. glycines occurs in response to interactions between crowding and decreased plant quality cues, and that alate aphid production benefits an aphid population under predation by increasing prevalence at a temporary cost to fecundity. My results contribute to the growing knowledge on the production of asexual alate aphids and provide insight into the biology of A. glycines as an agricultural pest. / May 2017

Cette thèse visait à caractériser l’architecture hydraulique du xylème chez les hybrides de peuplier Populusdeltoides × P. nigra et à juger de ses relations avec le fonctionnement hydrique et carboné de l’arbre en conditions d’irrigation contrastées. A cette fin, huit génotypes se distinguant par leur discrimination isotopique vis-à-vis du carbone 13 ont été cultivés en pépinière. Nos travaux ont permis de mettre en évidence d’importantes variations entre génotypes pour les caractéristiques anatomiques du xylème, l’efficience hydraulique de la tige et de la plante entière ainsi que la résistance à la cavitation. Nos travaux démontrent également que l’anatomie et la résistance à la cavitation du xylème s’ajustent aux conditions hydriques du milieu de façon génotype-dépendante. En condition hydrique non limitante, nous avons mis en évidence un compromis entre l’efficience hydraulique et la résistance à la cavitation ou le potentiel de croissance. Ces deux compromis expliquent la relation positive observée entre la résistance à la cavitationet le potentiel de croissance. En condition hydrique limitante, cette relation n’était toutefois plus observable. Aucune relation n’a pu être identifiée entre les propriétés hydrauliques et l’efficience d’utilisation de l’eau. Ces travaux suggèrent que certaines relations couramment observées à l’échelle inter-spécifique ne sont pas nécessairement applicables à des échelles d’étude plus réduites. Ce travail ouvre des perspectives sur le plan fondamental pour l’identification du déterminisme moléculaire à l’origine de la plasticité structurale observée et sur le plan appliqué, pour la création variétale. / This work aimed at characterizing xylem hydraulic architecture and at describing its relationships with whole plant water and carbon relations among Populus deltoides × P. nigra hybrids under contrasting water regimes. Eight genotypes differing in carbon isotope discrimination were grown in the field in a common garden test. Significant variations were observed between genotypes for all xylem anatomical characteristics, stem or whole-plant hydraulic efficiency and xylem resistance to cavitation. Drought-induced acclimation was observed for xylem structural features and xylem resistance to cavitation, but in a genotype-dependant manner. Under optimal irrigation, a trade-off was observed between hydraulic efficiency and xylem resistance to cavitation or growth performance. These two trade-offs translated into an uncommon positive relationship between xylem resistance to cavitation and growth performance. Under water deficit,this relationship broke down. No relationship could be detected between xylem hydraulics and water-use efficiency estimates. Our results suggest in part that several common relationships that are observed at the between-species level may not necessarily hold true at narrower scales. Further, this work opens up prospects both for identifying the molecular basis of xylem structural acclimation and for breeding strategies.

Le changement climatique rapide auquel nous assistons actuellement est déjà en train de modifier le cycle de vie d’un grand nombre d’organismes. Des études basées sur des modèles d’enveloppe bioclimatique apportent des réponses mais ces prédictions de nouvelles aires de répartition ne tiennent pas compte d’une part de l’adaptation rapide des espèces (plasticité phénotypique et diversité génétique non neutre), et d’autre part des interactions interspécifiques ou de la dynamique des populations. Ce travail de recherche est centré sur les mécanismes permettant la persistance des individus dans un environnement changeant.Nous avons travaillé dans les Pyrénées françaises sur deux espèces à large répartition européenne (chêne sessile et hêtre commun) sur un gradient altitudinal de 1500 m de dénivelé correspondant en moyenne à 8°C d’amplitude thermique. Ce gradient a été répété dans deux vallées parallèles, distantes de 30 km. Basée sur l’étude de traits fonctionnels, nous avons caractérisé les variations altitudinales de traits morphologiques et physiologiques de ces caractères dans des conditions naturelles. Les capacités écophysiologiques apparaissent plus élevée pour le chêne et pour les populations de haute altitude, suggérant une adaptation locale à un environnement stressant. Dans une étude préliminaire, nous avons établi qu’il était nécessaire d’intégrer les variations de pression partielle de dioxyde de carbone et non se concentration dans les mesures d’échanges gazeux. Tous les traits fonctionnels mesurés en populations naturelles varient avec l’altitude. Ainsi la taille des feuilles diminue avec l’altitude tandis que les autres traits augmentent, avec des valeurs de 1.3 à 3.9 fois supérieures entre le haut et le bas du gradient tous traits confondus. Nous avons ensuite cherché à déterminer l’origine de ces variations phénotypiques. Une expérimentation en test de provenance a ainsi permis de déterminer les traits dont la variation in situ était en partie sous contrôle génétique. Les résultats de notre étude montrent que le gradient altitudinal a induit une différenciation génétique au niveau de la croissance, de la phénologie et de traits fonctionnels foliaires pour ces espèces, malgré la proximité des populations étudiées dans leur milieu naturel. Néanmoins, les capacités photosynthétiques pour le hêtre et la surface spécifique foliaire pour le chêne ne montre aucune différentiation génétique, ainsi que la densité stomatique pour les deux espèces. D’autre part, l’expérimentation de transplantations réciproques le long du gradient, a mis en évidence une forte plasticité phénotypique pour les deux espèces, ce qui suggère que les populations peuvent dans une certaine mesure répondre immédiatement aux variations climatiques rencontrées le long de ce gradient. Cependant, tandis que la température optimale pour la longueur de saison de végétation ne semble pas encore atteinte, les populations pourraient réagir négativement à une élévation de la température en terme de croissance. En conclusion, les mécanismes adaptatifs mis en évidence le long d’un gradient climatique naturel, pourraient permettre aux populations de faire face au changement climatique actuel. / The rapid climate change, which we are currently witnessing, is already modifying the physiology and distribution of species. Predictions of changes in species distributions do not take evolutionary mechanisms and biotic interactions into account. Our main objective was to assess the inherent adaptive capacities of tree populations by i) quantifying the phenotypic variations of functional traits with altitude and ii) studying the extent to which these variations are environmentally driven (phenotypic plasticity) and/or genetically fixed (adaptation). The study took place in the French Pyrenees along an altitudinal gradient range of 1500 m corresponding on average to 8°C of thermal amplitude. We focused on two broadleaved species with a wide European distribution (sessile oak and common beech). This gradient was repeated in two parallel valleys, distant from 30 km. Altitudinal trends were investigated for several morphological, physiological and phenological traits in natural conditions (in situ), in a common garden experiment and in reciprocal transplant experiments (RTEs). The phenotypic variability observed in situ showed significant altitudinal trends for all the studied traits and followed similar patterns for both species. We established that together with temperature, it was also necessary to integrate the variations of atmospheric gas partial pressure along the altitudinal gradient. In the common garden experiment, our results showed that the altitudinal gradient induced genetic differentiations for growth, leaf phenology and several morphological and physiological traits. This experiment made it possible to demonstrate, for both species, a weaker effect of genetic variations than in situ observed variations, suggesting a strong effect of the environment on leaf functional traits. A higher intrapopulation than interpopulation genetic variability was also observed for all traits. Finally, the reciprocal transplant experiments highlighted a high magnitude of phenotypic plasticity whatever the trait and the species.

La variabilité phénotypique a tendance à augmenter lorsque l'environnement est variable dans le temps ou l'espace. Cette thèse traite plus précisément de la variabilité des traits d'histoire de vie dans le cadre de populations fragmentées. En région Méditerranéenne, le Pélodyte ponctué, Pelodytes punctatus, se reproduit à la fois au printemps et en automne, en réponse aux variations temporelles de l'environnement. J'ai cherché à comprendre l'origine et les conséquences évolutives de ces stratégies de reproduction. Les deux périodes de reproduction produisent efficacement des descendants (plus en automne) et les têtards de printemps semblent souffrir de la compétition avec les têtards d'automne. Ces derniers se métamorphosent plus tôt et à une plus grande taille. Ces différences de développement ne s'expliquent pas par des différences génétiques entre des populations saisonnières. Au contraire, elles sont liées à la plasticité phénotypique et répondent à des conditions environnementales drastiquement différentes. Il semble plus favorable de se reproduire en automne. Le maintien des deux stratégies correspond à du bet-hedging ou un simple opportunisme. Par ailleurs, la fragmentation, phénomène croissant lié à l'anthropisation des milieux, diminue la taille des populations et augmente l'hétérogénéité génétique au sein d'une population. Il n'y a cependant pas de consanguinité au sein des populations étudiées mais une forte structuration en familles qui induit des associations allèles/phénotypes.Ce travail éclaire les variations de traits d'histoire de vie du Pélodyte et indique une grande plasticité phénotypique face aux variations de l'environnement. / Phenotypic variability tends to increase in temporally and spatially variable environments. This thesis deals with the variability of life-history traits in fragmented populations. In Mediterranean regions, Parsley frog, Pelodytes punctatus, breeds both in spring and in autumn, in response to temporal variations of its environment. I studied the origin and evolutionary consequences of its breeding strategies.Both breeding periods produce offspring (much more in autumn, though) and spring tadpoles suffer from intraspecific competition with older autumn tadpoles. Autumn laid juveniles are bigger and emerged sooner from the ponds. These developmental differences are not due to genetic differences between seasonal populations. They are explained by phenotypic plasticity in response to drastically different conditions. Even if it seems more favourable to breed in autumn, both strategies are maintained either by bet-hedging or pure opportunism.Besides, fragmentation, which increases with global changes, tends to reduce population effective size and increase genetic heterogeneity within populations. However, no inbreeding was found in the studied populations but a high family structure induced alleles/fitness correlations.Together, these results enlighten the variability of breeding strategies and larval traits in Parsley frog and indicate a high phenotypic plasticity in response to environmental variations.

The work in this thesis deals with the ecology and evolution of adaptive individual variation. Ecologists have long used niche theory to describe the ecology of a species as a whole, treating conspecific individuals as ecological equivalent. During recent years, research about individual variation in diet and morphology has gained interest in adaptive radiations and ecological speciation. Such variation among individual niche use may have important conservation implications as well as ecological and evolutionary implications. However, up to date we know very little about the extension of this phenomenon in natural populations and the mechanisms behind it. The results in this thesis show that the extension of individual diet specialization is widely spread throughout the animal kingdom. The variation in diet is mainly correlated to morphological variation but not always. Furthermore, this variation in diet and morphology among individuals could be both genetically determined and environmentally induced and it mainly comes from trade-offs in foraging efficiency between different prey types. The results from a number of studies of perch also show that individual perch differ in morphology and diet depending on habitat, where littoral perch has a deeper body compared to pelagic perch. This difference in morphology corresponds to functional expectations and is related to foraging efficiency trade-offs between foraging in the littoral and pelagic zone of a lake. The variation in morphology in perch is mainly due to phenotypic plasticity but there are also small genetic differences between the littoral and pelagic perch. Two separate studies show that both predation and competition may be important mechanism for the variation in morphology and diet in perch. In conclusion, the results in this thesis show that individual variation in diet and habitat choice is a common phenomenon with lots of ecological and evolutionary implications. However, there are many mechanisms involved in this phenomenon on which we are just about to start learning more about, and only further research in this area will give us the full insight.