Biology subjects

Laurent Lehmann

Publications and source records attributed to Laurent Lehmann.

5 recordsLinked to original sources

bioRxiv2016

A Model for Brain Life History Evolution

Mathematical modeling of brain evolution is scarce, possibly due in part to the difficulty of describing how brain relates to fitness. Yet such modeling is needed to formalize verbal arguments and deepen our understanding of brain evolution. To address this issue, we combine elements of life history and metabolic theories to formulate a metabolically explicit mathematical model for brain life history evolution. We assume that some of the brains energetic expense is due to production (learning) and maintenance (memory) of skills (or cognitive abilities, knowledge, information, etc.). We also assume that individuals use skills to extract energy from the environment, and can allocate this energy to grow and maintain the body, including brain and reproductive tissues. Our model can be used to ask what fraction of growth energy should be allocated to the growth of brain and other tissues at each age under various biological settings as a result of natural selection. We apply the model to find uninvadable allocation strategies under a \"me-against-nature\" setting, namely when overcoming environmentally determined energy-extraction challenges does not involve any interactions with other individuals (possibly except caregivers), and using parameter values for modern humans. The uninvadable strategies yield predictions for brain and body mass throughout ontogeny, as well as for the ages at maturity, adulthood, and brain growth arrest. We find that (1) a me-against-nature setting is enough to generate adult brain and body mass of ancient human scale, (2) large brains are favored by intermediately challenging environments, moderately effective skills, and metabolically expensive memory, and (3) adult skill number is proportional to brain mass when metabolic costs of memory saturate the brain metabolic rate allocated to skills. Overall, our model is a step towards a quantitative theory of brain life history evolution yielding testable quantitative predictions as ecological, demographic, and social factors vary.\n\nAuthor SummaryUnderstanding what promotes the evolution of a given feature is often helped by mathematical modeling. However, mathematical modeling of brain evolution has remained scarce, possibly because of difficulties describing mathematically how the brain relates to reproductive success, which is the currency of evolution. Here we combine elements of two research fields that have previously been successful at detailing how a feature impacts reproductive success (life history theory) and at predicting the individuals body mass throughout its life without the need to describe in detail the inner workings of the body (metabolic theory). We apply the model to a setting where individuals must extract energy from the environment without interacting with other individuals except caregivers (\"me-against-nature\") and parameterize the model with data from humans. In this setting, the model can correctly predict a variety of human features, including large brain sizes. Our model can be used to obtain testable quantitative predictions in terms of brain mass throughout an individuals life from assumed hypotheses promoting brain evolution, such as harsh environments or plentiful social interactions.

Evolutionary Biology↗

bioRxiv2016

Evolutionary stability of jointly evolving traits in subdivided populations

The evolutionary stability of quantitative traits depends on whether a population can resist invasion by any mutant. While uninvadability is well understood in well-mixed populations, it is much less so in subdivided populations when multiple traits evolve jointly. Here, we investigate whether a spatially subdivided population at a monomorphic equilibrium for multiple traits can withstand invasion by any mutant, or is subject to diversifying selection. Our model also explores the among traits correlations arising from diversifying selection and how they depend on relatedness due to limited dispersal. We find that selection favours a positive (negative) correlation between two traits, when the selective effects of one trait on relatedness is positively (negatively) correlated to the indirect fitness effects of the other trait. We study the evolution of traits for which this matters: dispersal that decreases relatedness, and helping that has positive indirect fitness effects. We find that when dispersal cost is low and the benefits of helping accelerate faster than its costs, selection leads to the coexistence of mobile defectors and sessile helpers. Otherwise, the population evolves to a monomorphic state with intermediate helping and dispersal. Overall, our results highlight the importance of population subdivision for evolutionary stability and correlations among traits.

Evolutionary Biology↗

bioRxiv2016

Invasion fitness, inclusive fitness, and reproductive numbers in heterogeneous populations

How should fitness be measured to determine which phenotype or \"strategy\" is uninvadable when evolution occurs in subdivided populations subject to local demographic and environmental heterogeneity? Several invasion fitness measures, such as basic reproductive number, lifetime dispersal success of a local lineage, or inclusive fitness have been proposed to address this question, but the relationships between them and their generality remains unclear. Here, we ascertain uninvadability (all mutant strategies always go extinct) in terms of the growth rate of a mutant allele arising as a single copy in a population. We show from this growth rate that uninvadability is equivalently characterized by at least three conceptually distinct invasion fitness measures: (i) lineage fitness, giving the average personal fitness of a randomly sampled mutant lineage member; (ii) inclusive fitness, giving a reproductive value weighted average of the direct fitness cost and relatedness weighted indirect fitness benefits accruing to a randomly sampled mutant lineage member; and (iii) three types of reproductive numbers, giving lifetime success of a local lineage. Our analysis connects approaches that have been deemed different, generalizes the exact version of inclusive fitness to class-structured populations, and provides a biological interpretation of selection on a mutant allele under arbitrary strength of selection.

Preprint↗

bioRxiv2015

Environmental complexity favors the evolution of learning

Learning is a fundamental biological adaptation that is widespread throughout the animal kingdom. According to previous research, two conditions are necessary for learning to be adaptive: between-generation environmental variability and within-generation environmental predictability. In this paper, we show that between-generation variability is not necessary, and that instrumental learning can provide a selective advantage in complex environments, where an individual is exposed to a large number of different challenges during its lifespan. We construct an evolutionary model where individuals have a memory with limited storage capacity, and an evolving trait determines the fraction of that memory that should be allocated to innate responses to the environment versus learning these responses. The evolutionarily stable level of learning depends critically on the environmental process, but generally increases with environmental complexity. Overall, our work sheds light on the importance of global structural properties of the environment in shaping the evolution of learning.

Evolutionary Biology↗

bioRxiv2014

Evolutionary dynamics of collective action in spatially structured populations

Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of relatedness as a solution to collective action problems in biology and the fact that most social interactions unavoidably occur between relatives, incorporating relatedness into these models has so far proved elusive. We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. As an application, we use our mathematical framework to investigate the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: \"public goods\" (both providers and shirkers can use the good, e.g., alarm calls), \"club goods\" (only providers can use the good, e.g., participation in collective hunting), and \"charity goods\" (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness relaxes the collective action problems associated to the provision of these goods in different ways depending on the kind of good (public, club, or charity) and on its economies of scale (constant, diminishing, or increasing returns to scale). Our findings highlight the importance of explicitly accounting for relatedness, the kind of good, and economies of scale in theoretical and empirical studies of collective action.

Evolutionary Biology↗