The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species. We introduce an incompetence parameter into a learning function in a single-population game and analyze its effect on the outcome of the replicator dynamics. Incompetence can change the outcome of the game and its dynamics, indicating its significance within what are inherently imperfect natural systems.

5Environmental conditions shape entire communities by driving microbial interactions. These 6 interactions then find their reflection in the evolutionary outcome of microbial competition. In static, 7 homogeneous environments a robust, or evolutionary stable, outcome in microbial communities is 8 reachable, if it exists. However, introducing heterogeneity and time-dependence in microbial ecology 9 leads to stochastic evolutionary outcomes determined by specific environmental changes. We utilise 10 evolutionary game theory to provide insight into phenotypic competition in dynamic environments. 11 We capture these effects in a perturbed evolutionary game describing microbial interactions at a 12 phenotypic level. We show that under regular periodic environmental fluctuations a stable state that 13 preserves dominant phenotypes is reached. However, rapid environmental shifts, especially in a 14 cyclic interactions, can lead to critical shifts in the evolutionary balance among phenotypes. Our 15 analysis suggests that an understanding of the robustness of the systems current state is necessary to 16 understand when system will shift to the new equilibrium. This can be done by understanding the 17 1 systems overall margin of safety, that is, what level of perturbations it can take before its equilibrium 18 changes. In particular, the extent to which an environmental shift affects the system's behaviour. 19 Introduction 22 Despite the primacy of evolution in biology, there remains the critical gap in our understanding of how 23 environment influences evolution [1]. This is especially relevant for environmental changes from the 24 scale of small groups to global climatic events. However, the timescales for genetic adaptation are often 25 slower than environmental changes, meaning that the important response is in the phenotype. 26Bacteria are ideal model systems for studying phenotypic response due to their rapid reproduction, 27 comparatively simple biology, and suitability for laboratory study. With most bacterial sensory systems 28 limited to molecular uptake, it is impossible for them to anticipate environmental changes. As the most 29 abundant life on earth, bacteria regulate the biosphere while being intimately connected to it. A single 30 bacterial species, unlike animals, may rapidly change its role from abundant to rare, and from dominant-31 aggressive to rare-passive or some mix of the two depending on local habitat [2,3]. This may lead to trait 32 variation in originally genetically identical organisms [4]. Microbial research often focuses on coopera-33 tion or competition among species, extending experimental findings to evolutionary models [5][6][7][8]. The 34 intra-specific interactions are often overlooked. However, it is within species phenotypic variation that 35 shapes genetic drift, which subsequently determines the genome evolution behind inter-specific interac-36 tions. 37For identical genotypes in a static environments reaction to stimuli can be distinct [9]. Stochasticity in 38 gene expre...

All organisms on this planet live in a dynamic environment that undergoes changes. Thus, the ability to adapt becomes a key to survival and the adaptation of species to a changing environment is a long-standing question in biology. Adaptation is a mutation process which improves survival skills and reproductive functions of species, and usually includes two components: genetic adaptation and learning. In this doctoral research, we investigate adaptive learning by combining the concept of incompetence with evolutionary population dynamics. In the sense of evolution, incompetence and training are considered as learning processes with a focus on social interactions of individuals. We introduce incompetence into a learning function in a single-population game and analyse its effect on the outcome of the selection. We show that incompetence can change the result of the competition and "It is a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to." J.R.R. Tolkien, The Lord of the Rings Returning to study after several years of working in industry is a challenging task. This is especially so, when one is far away from their home country. The completion of this task would not be possible without all the support from a number of people. I would like to thank my supervisory team for making this possible. In first place, this would not happen without all the trust and patience of Jerzy Filar, who was a wise supervisor, a professional mentor, an understanding friend and, even sometimes, a caring parent. Also, I would like to thank Vladimir Ejov who invested enormous amount of effort to assist my adaptation to Australia and this project benefited greatly from our discussions. I would like to thank Amie Albrecht, who was a patient and inspiring mentor when I started my PhD and was looking for a direction of research. And last, but not least, I would like to thank James Mitchell who made a very important contribution to the project when it was very much needed: when we started to ask ourselves if this theoretical idea could be applied to any real biological problem. In addition, Phil Howlett, as the leader of the grant which supports this project, offered many useful insights. However, this would also not be possible without Jody McKerral, who is a great friend, a brilliant and inspiring researcher, and a wonderful co-author. It was such a great time collaborating at Flinders University! Moreover, the SMP team at the University of Queensland is also awesome! I would like to thank CARM people, especially Roxanne Jemison and Sabriba Streipert, for their thoughtful advice and willingness to help any time it was needed. I would also like to say "Spasibo" to Yoni Nazarathy for his sense v of humour and stressless support. And a big thank you to Cecilia González-Tokman who was always open to insightful discussions which helped to improve this project. And, of course, my friends and family made this journey possible. My mother was al...

A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving. We consider two cases: completely random mistakes when individuals have no bias towards any strategy and a general form of mistakes. Then, we determine conditions for a strategy to dominate all other strategies. However, given that individuals who adopt a dominating strategy are still prone to behavioural mistakes in the observed behaviour, we may still observe extinct strategies. That is, behavioural mistakes in strategy execution stabilise evolutionary dynamics leading to an evolutionary stable and, potentially, mixed co-existence equilibrium.

Cooperation is a ubiquitous and beneficial behavioural trait despite being prone to exploitation by free-riders. Hence, cooperative populations are prone to invasions by selfish individuals. However, a population consisting of only free-riders typically does not survive. Thus, cooperators and free-riders often coexist in some proportion. An evolutionary version of a Snowdrift Game proved its efficiency in analysing this phenomenon. However, what if the system has already reached its stable state but was perturbed due to a change in environmental conditions? Then, individuals may have to re-learn their effective strategies. To address this, we consider behavioural mistakes in strategic choice execution, which we refer to as incompetence. Parametrising the propensity to make such mistakes allows for a mathematical description of learning. We compare strategies based on their relative strategic advantage relying on both fitness and learning factors. When strategies are learned at distinct rates, allowing learning according to a prescribed order is optimal. Interestingly, the strategy with the lowest strategic advantage should be learnt first if we are to optimise fitness over the learning path. Then, the differences between strategies are balanced out in order to minimise the effect of behavioural uncertainty.