A Model for Brain Life History Evolution

Abstract

Complex cognition and relatively large brains are distributed across various taxa, and many primarily verbal hypotheses exist to explain such diversity. Yet, mathematical approaches formalizing verbal hypotheses would help deepen the understanding of brain and cognition evolution. With this aim, 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 brain's energetic expense is due to production (learning) and maintenance (memory) of energy-extraction skills (or cognitive abilities, knowledge, information, etc.). We also assume that individuals use such skills to extract energy from the environment, and can allocate this energy to grow and maintain the body, including brain and reproductive tissues. The model can be used to ask what fraction of growth energy should be allocated at each age, given natural selection, to growing brain and other tissues under various biological settings. We apply the model to find uninvadable allocation strategies under a baseline setting ("me vs nature"), namely when energy-extraction challenges are environmentally determined and are overcome individually but possibly with maternal help, and use modern-human data to estimate model's parameter values. The resulting uninvadable strategies yield predictions for brain and body mass throughout ontogeny and for the ages at maturity, adulthood, and brain growth arrest. We find that: (1) a me-vs-nature setting is enough to generate adult brain and body mass of ancient human scale and a sequence of childhood, adolescence, and adulthood stages; (2) large brains are favored by intermediately challenging environments, moderately effective skills, and metabolically expensive memory; and (3) adult skill is proportional to brain mass when metabolic costs of memory saturate the brain metabolic rate allocated to skills. Author summaryComplex cognition and relatively large brains occur in a diversity of mammal, bird, and fish species among others, and there is a large number of mostly verbal hypotheses to explain what causes their evolution in certain species but not others. However, these hypotheses have scarcely exploited the power of formulating them in mathematical terms, Funding: This work was funded by Swiss NSF grant PP00P3-146340 to LL http://www.snf.ch/en/ Pages/default.aspx. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests:The authors have declared that no competing interests exist.which has been very useful to understand the evolution of other traits. To address this issue, we formulate a mathematical model that allows incorporating many of those hypotheses and that can be used to obtain predictions for how much and how fast the brain should grow depending on the hypothesis assumed. We apply the model to humans in a setting where each individual must extract energy from the environment alone (e.g., by hunting or coo...

A mathematical framework for evo-devo dynamics

“…Fourth, our equations allow for the study of the evolutionary dynamics of life-history models with dynamic constraints. Lifehistory models with dynamic constraints have previously been restricted to evolutionary equilibria (e.g., González-Forero et al 2017; González-Forero and Gardner 2018). Previous frameworks of evolutionary dynamics of functioned-valued traits allow for the modelling of evolutionary dynamics of traits that vary over age or stage, but such frameworks do not generally consider dynamic constraints (i.e., they consider the evolution of control variables but allow for state variables on a case by case basis at most) (Kirkpatrick and Heckman 1989; Dieckmann et al 2006; Coulson et al 2010; Parvinen et al 2013; Metz et al 2016; Rees and Ellner 2016).…”

Sex allocation conflict and sexual selection throughout the lifespan of eusocial colonies

“…3 First-order condition expressed in terms of optimal control problem In this section, we use optimal control theory in order to solve the marginal value equation (S44) for different scenarios of our model by way of applying Pontryagin's weak maximum principle (e.g., Bryson and Ho, 1975; for broad introductions and Day and Taylor, 2000;González-Forero et al, 2017;Iwasa and Roughgarden, 1984;Perrin, 1992 for previous application to evolutionary biology).…”

Evo-devo dynamics of hominin brain size

“…The fossil record shows a sharp expansion in hominin 4 brain size, tripling over the last four million years 5 from australopithecines to modern humans 1 while some 6 the brain model 37 has found causal, computational evi-35 * mgf3@st-andrews.ac.uk dence that a challenging ecology 7;15;22 and possibly culture 14;19;21 rather than social interactions 6;9;12;16 could have caused hominin brain expansion. In the model, a challenging ecology, where individuals need brainsupported skills to obtain energy, promotes brain expansion 36 . If additionally, learning has weakly, not strongly, diminishing returns, then human-sized brains and bodies can evolve 37 .…”

“…West et al use energy conservation analysis to obtain an equation describing the developmental dynamics of body size depending on param-eters measuring metabolic costs that can be easily estimated from data 38 . The brain model implements West et al's approach to obtain equations describing the developmental dynamics of brain, reproductive, and somatic tissue sizes depending additionally on genotypic traits controlling energy allocation to the production of each tissue at each age 36 . For simplicity, reproductive tissue is defined in the model as preovulatory ovarian follicles which determine fertility given that the model considers only females.…”

“…S5). I call ecological scenario that with such weakly diminishing returns of learning and submultiplicative cooperation but setting the proportion of ecological challenges to one (P 1 = 1), which was previously 36 found to yield the evolution of brain and body sizes of Neanderthal scale at evolutionary equilibrium. The erectus, ergaster, and habilis scenarios use strongly diminishing returns of learning and additive cooperation: specifically, these scenarios use power competence with parameter values given in Regime 2 of Table S2 and with additive cooperation (Eq.…”