Stochastic eco-evolutionary model of a prey-predator community

Evolutionary Adaptation of an RNA Bacteriophage to Repeated Freezing and Thawing Cycles

Bacteriophage fitness is determined by factors influencing both their replication within bacteria and their ability to maintain infectivity between infections. The latter becomes particularly crucial under adverse environmental conditions or when host density is low. In such scenarios, the damage experienced by viral particles could lead to the loss of infectivity, which might be mitigated if the virus undergoes evolutionary optimization through replication. In this study, we conducted an evolution experiment involving bacteriophage Qβ, wherein it underwent 30 serial transfers, each involving a cycle of freezing and thawing followed by replication of the surviving viruses. Our findings show that Qβ was capable of enhancing its resistance to this selective pressure through various adaptive pathways that did not impair the virus replicative capacity. Notably, these adaptations predominantly involved mutations located within genes encoding capsid proteins. The adapted populations exhibited higher resistance levels than individual viruses isolated from them, and the latter surpassed those observed in single mutants generated via site-directed mutagenesis. This suggests potential interactions among mutants and mutations. In conclusion, our study highlights the significant role of extracellular selective pressures in driving the evolution of phages, influencing both the genetic composition of their populations and their phenotypic properties.

The impact of dormancy on evolutionary branching

In this paper, we investigate the consequences of dormancy in the 'rare mutation' and 'large population' regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second 'small mutations' limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the 'speed of adaptation' of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.

Variation in environmental stochasticity dramatically affects viability and extinction time in a predator-prey system with high prey group cohesion

Understanding how tipping points arise is critical for population protection and ecosystem robustness. This work evaluates the impact of environmental stochasticity on the emergence of tipping points in a predator-prey system subject to the Allee effect and Holling type IV functional response, modeling an environment in which the prey has high group cohesion. We analyze the relationship between stochasticity and the probability and time that predator and prey populations in our model tip between different steady states. We evaluate the safety from extinction of different population values for each species, and accordingly assign extinction warning levels to these population values. Our analysis suggests that the effects of environmental stochasticity on tipping phenomena are scenario-dependent but follow a few interpretable trends. The probability of tipping towards a steady state in which one or both species go extinct generally monotonically increased with noise intensity, while the probability of tipping towards a more favorable steady state (in which more species were viable) usually peaked at intermediate noise intensity. For tipping between two equilibria where a given species was at risk of extinction in one equilibrium but not the other, noise affecting that species had greater impact on tipping probability than noise affecting the other species. Noise in the predator population facilitated quicker tipping to extinction equilibria, whereas prey noise instead often slowed down extinction. Changes in warning level for initial population values due to noise were most apparent near attraction basin boundaries, but noise of sufficient magnitude (especially in the predator population) could alter risk even far away from these boundaries. Our model provides critical theoretical insights for the conservation of population diversity: management criteria and early warning signals can be developed based on our results to keep populations away from destructive critical thresholds.

Stochasticity directs adaptive evolution toward nonequilibrium evolutionary attractors

Stochastic processes such as genetic drift may hinder adaptation, but the effect of such stochasticity on evolution via its effect on ecological dynamics is poorly understood. Here we evaluate patterns of adaptation in a population subject to variation in demographic stochasticity. We show that stochasticity can alter population dynamics and lead to evolutionary outcomes that are not predicted by classic eco-evolutionary modeling approaches. We also show, however, that these outcomes are governed by nonequilibrium evolutionary attractors-these are maxima in lifetime reproductive success when stochasticity keeps the ecological system away from the deterministic equilibrium. These NEEAs alter the path of evolution but are not visible through the equilibrium lens that underlies much evolutionary theory. Our results reveal that considering population processes during transient periods can greatly improve our understanding of the path and pace of evolution.

Virus-immune dynamics determined by prey-predator interaction network and epistasis in viral fitness landscape

Population dynamics and evolutionary genetics underly the structure of ecosystems, changing on the same timescale for interacting species with rapid turnover, such as virus (e.g. HIV) and immune response. Thus, an important problem in mathematical modeling is to connect ecology, evolution and genetics, which often have been treated separately. Here, extending analysis of multiple virus and immune response populations in a resource-prey (consumer)-predator model from Browne and Smith (2018), we show that long term dynamics of viral mutants evolving resistance at distinct epitopes (viral proteins targeted by immune responses) are governed by epistasis in the virus fitness landscape. In particular, the stability of persistent equilibrium virus-immune (prey-predator) network structures, such as nested and one-to-one, and bifurcations are determined by a collection of circuits defined by combinations of viral fitnesses that are minimally additive within a hypercube of binary sequences representing all possible viral epitope sequences ordered according to immunodominance hierarchy. Numerical solutions of our ordinary differential equation system, along with an extended stochastic version including random mutation, demonstrate how pairwise or multiplicative epistatic interactions shape viral evolution against concurrent immune responses and convergence to the multi-variant steady state predicted by theoretical results. Furthermore, simulations illustrate how periodic infusions of subdominant immune responses can induce a bifurcation in the persistent viral strains, offering superior host outcome over an alternative strategy of immunotherapy with strongest immune response.

Importance of interindividual interactions in eco-evolutionary population dynamics: The rise of demo-genetic agent-based models

The study of eco-evolutionary dynamics, that is of the intertwinning between ecological and evolutionary processes when they occur at comparable time scales, is of growing interest in the current context of global change. However, many eco-evolutionary studies overlook the role of interindividual interactions, which are hard to predict and yet central to selective values. Here, we aimed at putting forward models that simulate interindividual interactions in an eco-evolutionary framework: the demo-genetic agent-based models (DG-ABMs). Being demo-genetic, DG-ABMs consider the feedback loop between ecological and evolutionary processes. Being agent-based, DG-ABMs follow populations of interacting individuals with sets of traits that vary among the individuals. We argue that the ability of DG-ABMs to take into account the genetic heterogeneity-that affects individual decisions/traits related to local and instantaneous conditions-differentiates them from analytical models, another type of model largely used by evolutionary biologists to investigate eco-evolutionary feedback loops. Based on the review of studies employing DG-ABMs and explicitly or implicitly accounting for competitive, cooperative or reproductive interactions, we illustrate that DG-ABMs are particularly relevant for the exploration of fundamental, yet pressing, questions in evolutionary ecology across various levels of organization. By jointly modelling the effects of management practices and other eco-evolutionary processes on interindividual interactions and population dynamics, DG-ABMs are also effective prospective and decision support tools to evaluate the short- and long-term evolutionary costs and benefits of management strategies and to assess potential trade-offs. Finally, we provide a list of the recent practical advances of the ABM community that should facilitate the development of DG-ABMs.

Parameter estimation and treatment optimization in a stochastic model for immunotherapy of cancer

Adoptive Cell Transfer therapy of cancer is currently in full development and mathematical modeling is playing a critical role in this area. We study a stochastic model developed by Baar et al. (2015) for modeling immunotherapy against melanoma skin cancer. First, we estimate the parameters of the deterministic limit of the model based on biological data of tumor growth in mice. A Nonlinear Mixed Effects Model is estimated by the Stochastic Approximation Expectation Maximization algorithm. With the estimated parameters, we return to the stochastic model and calculate the probability of complete T cells exhaustion. We show that for some relevant parameter values, an early relapse is due to stochastic fluctuations (complete T cells exhaustion) with a non negligible probability. Then, focusing on the relapse related to the T cell exhaustion, we propose to optimize the treatment plan (treatment doses and restimulation times) by minimizing the T cell exhaustion probability in the parameter estimation ranges.

A stochastic model for immunotherapy of cancer

We propose an extension of a standard stochastic individual-based model in population dynamics which broadens the range of biological applications. Our primary motivation is modelling of immunotherapy of malignant tumours. In this context the different actors, T-cells, cytokines or cancer cells, are modelled as single particles (individuals) in the stochastic system. The main expansions of the model are distinguishing cancer cells by phenotype and genotype, including environment-dependent phenotypic plasticity that does not affect the genotype, taking into account the effects of therapy and introducing a competition term which lowers the reproduction rate of an individual in addition to the usual term that increases its death rate. We illustrate the new setup by using it to model various phenomena arising in immunotherapy. Our aim is twofold: on the one hand, we show that the interplay of genetic mutations and phenotypic switches on different timescales as well as the occurrence of metastability phenomena raise new mathematical challenges. On the other hand, we argue why understanding purely stochastic events (which cannot be obtained with deterministic models) may help to understand the resistance of tumours to therapeutic approaches and may have non-trivial consequences on tumour treatment protocols. This is supported through numerical simulations.