Mark Broom

Human and non-human animals often form highly structured social systems in which individuals interact preferentially within specific groups, shaped by habitat structure, movement patterns, or social preferences. We consider a model that captures the interplay between social structure and emerging behaviour. Individuals are probabilistically distributed across the nodes of a spatial network representing interaction sites such as resource patches, territorial areas, or social hubs. Individuals present at the same node interact through a multiplayer game, so group structure is not imposed but instead emerges from movement under spatial constraints. As a benchmark, we analyse the completely mixed population, a null model in which individuals are indistinguishable, analogous to the classical well-mixed assumption, and further have no preference for particular network nodes. We derive exact expressions for fundamental properties of this population under arbitrary payoff functions, including the group size distribution, fitness functions, and fixation probabilities. We consider five multiplayer social dilemmas capturing the tension between individual and collective interests, such as those arising in public goods production, collective defence, and communal resource use. For these dilemmas, we derive analytical conditions for the evolution of cooperation in completely mixed populations. Using these as a reference, we reassess the effects of community structure. We show that asymptotically isolated communities expand the parameter range favouring cooperation, particularly under low population density. Finally, we explore intermediate regimes between completely mixed populations and isolated community structure, demonstrating that this expansion of the cooperative region remains robust even under higher levels of mixing between adjacent communities.

Microbes often generate by-products that inhibit own or consortial growth. Such imposing constraints can be alleviated by symbiotic partnerships where the partner consumes the limiting factor resulting in mutually beneficial cooperation. Theories of mitochondrial origin envisage such metabolic syntrophy of partners as the initial interaction, often coupled with mechanistic membrane gymnastics to trap the alphaproteobacterial symbiont to ensure vertical inheritance and as a prerequisite or vestibule of endosymbiosis. Yet we do not know how this happened. Here, using a mathematical model, we investigate how such metabolic self-inhibition enables and facilitates the evolution of compact physical integration between syntrophic partners. We show that when one species produces a metabolite that is self-inhibitory, selection favors increasingly tight spatial association of a detoxifying partner to mitigate local accumulation of the self-limiting product. Under a broad parameter range, this process drives the emergence of surface-associated configurations promoting morphological adaptations such as membrane protrusions or invaginations that increase inter-partner contact area. Our results prove that such costly host membrane contortions can evolve as a means to improve benefits of inhibition reduction by protective syntrophic ectosymbionts. Additionally, a unilateral syntrophic interaction between parties is sufficient for the transition; a mutualistic (or bilateral) one is not necessary. Our model establishes a direct evolutionary link between metabolic coupling and physical integration, suggesting that the need to alleviate (self-generated) inhibition can be a primary driver of ectosymbiotic attachment and its transition toward more intimate associations. Our findings provide a general theoretical framework for understanding how microbial consortia evolve structural complexity from initially loose metabolic interactions, with implications for the origins of stable symbioses and the early steps toward cellular integration.

A comparative examination of breast cancer survival between two data sets from the Kurdistan area of Iraq and a corresponding data set from Germany is the aim of this paper. Using breast cancer data from the Kurdistan area of Iraq, both censored and unfiltered, we developed a methodology in a previous publication (2016) for predicting survival probabilities and hazard functions in a health context when a significant fraction of participants are lost to the research. This study follows earlier research (2023) where we had to use unique estimation methods to address the two Iraqi datasets' filtering problems. In particular, the data from Nanakaly hospital in the city of Erbil and Hewa hospitals in the city of Sulamani involved problems with hidden censoring affecting the survival time, leading to significant biases in survival curves generated using standard methods, and we had developed new Markov chain-based methods for generating survival curves providing adjusted Kaplan Meier analyses. Due to the availability of a reliable survival function, we chose to work with a German data set from the W. Sauerbrei Institute for Medical Biometry and Informatics, University of Freiburg—Germany. Our data analysis leads us to the conclusion that younger German women had a higher breast cancer survival rate than patients from the Kurdistan Region of Iraq.

The Ultimatum Game is conventionally formulated in the context of two players. Nonetheless, real-life scenarios often entail community interactions among numerous individuals. To address this, we introduce an extended version of the Ultimatum Game, called the Multi-Proposer-Multi-Responder Ultimatum Game. In this model, multiple responders and proposers simultaneously interact in a one-shot game, introducing competition both within proposers and within responders. We derive subgame-perfect Nash equilibria for all scenarios and explore how these non-trivial values might provide insight into proposal and rejection behaviour experimentally observed in the context of one vs. one Ultimatum Game. Additionally, by considering the asymptotic numbers of players, we propose two potential estimates for a “fair” threshold: either 31.8% or 36.8% of the pie (share) for the responder.

We present a game-theoretic model of a polymorphic cancer cell population where the treatment-induced resistance is a quantitative evolving trait. When stabilization of the tumor burden is possible, we expand the model into a Stackelberg evolutionary game, where the physician is the leader and the cancer cells are followers. The physician chooses a treatment dose to maximize an objective function that is a proxy of the patient’s quality of life. In response, the cancer cells evolve a resistance level that maximizes their proliferation and survival. Assuming that cancer is in its ecological equilibrium, we compare the outcomes of three different treatment strategies: giving the maximum tolerable dose throughout, corresponding to the standard of care for most metastatic cancers, an ecologically enlightened therapy, where the physician anticipates the short-run, ecological response of cancer cells to their treatment, but not the evolution of resistance to treatment, and an evolutionarily enlightened therapy, where the physician anticipates both ecological and evolutionary consequences of the treatment. Of the three therapeutic strategies, the evolutionarily enlightened therapy leads to the highest values of the objective function, the lowest treatment dose, and the lowest treatment-induced resistance. Conversely, in our model, the maximum tolerable dose leads to the worst values of the objective function, the highest treatment dose, and the highest treatment-induced resistance.

Community organisation permeates both social and biological complex systems. To study its interplay with behaviour emergence, we model mobile structured populations with multiplayer interactions. We derive general analytical methods for evolutionary dynamics under high home fidelity when populations self-organise into networks of asymptotically isolated communities. In this limit, community organisation dominates over the network structure and emerging behaviour is independent of network topology. We obtain the rules of multiplayer cooperation in networks of communities for different types of social dilemmas. The success of cooperation is a result of the benefits shared among communal cooperators outperforming the benefits reaped by defectors in mixed communities. Under weak selection, cooperation can evolve and be stable for any size (Q) and number (M) of communities if the reward-to-cost ratio (V/K) of public goods is higher than a critical value. Community organisation is a solid mechanism for sustaining the evolution of cooperation under public goods dilemmas, particularly when populations are organised into a higher number of smaller communities. Contrary to public goods dilemmas relating to production, the multiplayer Hawk-Dove (HD) dilemma is a commons dilemma focusing on the fair consumption of preexisting resources. This game yields mixed results but tends to favour cooperation under larger communities, highlighting that the two types of social dilemmas might lead to solid differences in the behaviour adopted under community structure.

Using a two-player common pool resource game, we investigated the influence of multiple factors on cooperation: (1) probability of future rounds, (2) visibility of other participants, (3) biophilia, (4) future discounting, and (5) life history. In each round, participants simultaneously and independently (without conferring) decided how much of the common pool to consume. Participants (n = 116) were informed that the shared resource would be fully replenished in the next round—but only if—both players together consumed ≤ 50% of the common pool in the current round. Additionally, participants were told the probability (0–100%) of further rounds of play with the same player (this probability was not real; it was purely to manipulate the player’s expectations). To assess the effect of the probability of future rounds, we developed a mathematical model to predict the threshold that would permit a Nash Equilibrium of Conditional Cooperation (CC). To manipulate visibility, half the pairs were tested in the same room (seen condition) and half in separate rooms (unseen condition). To measure biophilia, the “Nature Relatedness” (NR) scale was used. To measure future discounting, the “consideration of future consequences” (CFC) scale was used. To measure life history, the participant’s UK postcode was obtained (indicating possible residence in a deprived neighbourhood). Participants in our study were not paid. In our results, there was a significant effect showing more cooperation in the visible than not visible condition, but no significant effects of NR, CFC, nor postcodes (but NR was significant in interaction with visibility). For predictability of future rounds, we found a number of significant effects using different tests. A notable result was that there was significantly more CC when the probability of future rounds was ≥ 69% (congruent with one of our model predictions).