Hamilton’s rule, gradual evolution, and the optimal (feedback) control of phenotypically plastic traits

Avila, Piret; Priklopil, Tadeas; Lehmann, Laurent

doi:10.1016/j.jtbi.2021.110602

Cited by 21 publications

(42 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…4–10) generalises the results of Dawson (1998, p. 148) to overlapping generations and an explicit life-history context. Because takes the standard form of the basic reproductive number, the results of optimal control control and dynamic game theory can be applied to characterise uninvadability. This is useful in particular for reaction norm and developmental evolution and formalising different modes of trait expressions (see Avila et al, 2021). While low mutation rates are presumed to be able to use , these mutation rates are endogenously determined by the uninvadable strategy.…”

Section: Modelmentioning

confidence: 99%

See 1 more Smart Citation

Life history and deleterious mutation rate coevolution

Avila

Lehmann

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The cost of germline maintenance and repair gives rise to a trade-off between lowering the deleterious mutation rate and investing into life-history functions. Life-history and the mutation rate therefore coevolve, but this joint evolutionary process is not well understood. Here, we develop a mathematical model to analyse the long-term evolution of traits affecting life-history and the deleterious mutation rate. First, we show that under certain biologically feasible conditions, the evolutionary stable life-history and mutation rate can be characterised using the basic reproductive number of the least-loaded class. This is the expected lifetime production of offspring without deleterious mutations born to individuals with no deleterious mutations. Second, we analyse two specific biological scenarios: (i) coevolution between reproductive effort and mutation rate and (ii) coevolution between age-at-maturity and mutation rate. These two scenarios suggest two broad results. First, the trade-off between lowering mutation rate vs investing into life-history functions depends strongly on environmental conditions and baseline mutation rate. Second, the trade-offs between different life-history functions can be strongly affected by mutation rate coevolution and higher baseline mutation rates select for faster life histories: (i) higher investment into fecundity at the expense of survival and (ii) earlier age of maturation at smaller sizes.

show abstract

Section: Modelmentioning

confidence: 99%

“…Because takes the standard form of the basic reproductive number, the results of optimal control control and dynamic game theory can be applied to characterise uninvadability. This is useful in particular for reaction norm and developmental evolution and formalising different modes of trait expressions (see Avila et al, 2021).…”

Section: Modelmentioning

confidence: 99%

Life history and deleterious mutation rate coevolution

Avila

Lehmann

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…First, developmental and en- Metz et al, 2016). However, such an approach poses substantial mathematical challenges by requiring derivation of functional derivatives and solution of associated differential equations for costate variables (Parvinen et al, 2013;Metz et al, 2016;Avila et al, 2021). By using discrete age, we have obtained closedform equations that facilitate modelling the evo-devo dynamics.…”

Section: Discussionmentioning

confidence: 99%

“…2a). Avila et al (2021) derive dλ/dy| y=ȳ for a broad class of models for a univariate continuous function-valued control where λ depends on a univariate continuous state variable in a group-structured population (their Eqs. 7,23,24); the resulting equation depends on an unknown univariate costate variable, which at evolutionary equilibrium can be calculated by solving an associated differential equation (their Eq.…”

mentioning

confidence: 99%

A mathematical framework for evo-devo dynamics

González-Forero

Gardner

2021

Preprint

View full text Add to dashboard Cite

Natural selection acts on phenotypes constructed over development, which raises the question of how development affects evolution. Existing mathematical theory has considered either evolutionary dynamics while neglecting developmental dynamics, or developmental dynamics while neglecting evolutionary dynamics by assuming evolutionary equilibrium. We formulate a mathematical framework that integrates explicit developmental dynamics into evolutionary dynamics. We consider two types of traits: genetic traits called control variables and developed traits called state variables. Developed traits are constructed over ontogeny according to a developmental map of ontogenetically prior traits and the social and non-social environment. We obtain general equations describing the evolutionary-developmental (evo-devo) dynamics. These equations can be arranged in a layered structure called the evo-devo process, where five elementary components generate all equations including those describing genetic covariation and the evo-devo dynamics. These equations recover Lande's equation as a special case and describe the evolution of Lande's G-matrix from the evolution of the phenotype, environment, and mutational covariation. This shows that genetic variation is necessarily absent in some directions of phenotype space if at least one trait develops and enough traits are included in the analysis so as to guarantee dynamic sufficiency. Consequently, directional selection alone is generally insufficient to identify evolutionary equilibria. Instead, "total genetic selection" is sufficient to identify evolutionary equilibria if mutational variation exists in all directions of control space and exogenous plastic response vanishes. Developmental and environmental constraints influence the evolutionary equilibria and determine the admissible evolutionary trajectory. These results show that development has major evolutionary effects.

show abstract

“…Such closed loop traits can be thought of as a contingency plans or strategies, since they specify a conditional trait expression rule according to fitness relevant conditions and close the output-input feedback loop between phenotypic expression and individual states. For this mode of trait control too, admixtures between Hamilton’s rule and control theory have been explored (Avila et al, 2021), and the evolution of closed loop traits are often studied using dynamic programming and the spellbounding Hamilton-Jacobi-Bellman equation (e.g., Houston and McNamara, 1999; Mangel et al, 1988; Ewald et al, 2007; Nakamura and Ohtsuki, 2016).…”

Section: Introductionmentioning

confidence: 99%

Hamilton’s rule, the evolution of behavior rules and the wizardry of control theory

Lehmann

2022

Preprint

Self Cite

View full text Add to dashboard Cite

This paper formalizes selection on a quantitative trait affecting the evolution of behavior rules through which individuals act and react with their surroundings. Combining Hamilton's marginal rule for selection on scalar traits and concepts from optimal control theory, a necessary first-order conditions for the evolutionary stability of the trait in group-structured population are derived. The model, which is of intermediate level of complexity, fills a gap between the formalization of selection on evolving traits that are directly conceived as actions (no phenotypic plasticity) and selection on evolving traits that are conceived as strategies or function valued actions (complete phenotypic plasticity). By conceptualizing individuals as open deterministic dynamical systems expressing incomplete phenotypic plasticity, the model captures selection on a large class of phenotypic expression mechanisms, including the evolution of learning and preferences under life-history trade-offs. As an illustration of the results, a first-order condition for the evolutionary stability of behavior response rules from the social evolution literature is re-derived, strenghthened, and generalized. All results of the paper also generalize directly to selection on mutildimenstional quantitative traits affecting behavior rule evolution, thereby covering neural and gene network evolution.

show abstract

Hamilton’s rule, gradual evolution, and the optimal (feedback) control of phenotypically plastic traits

Cited by 21 publications

References 73 publications

Life history and deleterious mutation rate coevolution

Life history and deleterious mutation rate coevolution

A mathematical framework for evo-devo dynamics

Hamilton’s rule, the evolution of behavior rules and the wizardry of control theory

Contact Info

Product

Resources

About