Eco-phenotypic physiologies:a new kind of modelingfor unifying evolution, ecology andcultural transmissionF. Panebianco and E. SerrelliLisbon, 28 May 2013
MotivationWe propose a mathematical framework of formalrelations general enough to be applicable inbiology (ecology and evolutionary biology)cultural transmission (economics)We are interested in modeling some biological conceptswe will call “eco-phenotypic concepts”Development, plasticity, reaction norm, phenotypicheritability, epigenetics, and niche construction.
PhysiologyConsider a population composed at each time of Ntagents and a set of resources RtA Physiology is an algorithm that deﬁnes the resourcemanagement behavior of the agent.the resources needed by the agent for the basicsurvival ˜Mithe efﬁciency is the resource extraction αithe efﬁciency of their use βithe agent’s resource intake target Git¯Pit = ( ˜Mit, αi, βi, Git) (1)
EnvironmentAll the elements of the world and of the population thatare not part of the agent.the resources Rt that are available to the population.The number of agents Ntthe vector of all the other agents’ physiologies ¯P−it¯Eit = (Rt, Nt, ¯P−it ) (2)
Resource extraction∑iRit ≤ Rtown resource intake target Git,others’ resource intake targets G−itthe vector of all extraction efﬁciencies ¯α¯Rit = (Rt, Git, G−it , ¯α) (3)Notice that if Rit < ˜Mit then the agent dies.
Matching Function and Reproductioneach male with physiology i, that extracted Rit is matchedwith a female of physiology j that extracted Rjtγijt the share of Rit that an agent of physiology i in a ijmatching devotes to own subsistence and (1 − γijt ) theshare devoted for offspring production.Nijt+1(Rit, Rjt, γijt , γjit ) (4)
Niche construction and ResourceRegenerationRt+1 = (Rt − ∑iRit)(1 + λ)if individuals resource extraction and physiologies areniche constructing then λt( ¯Rt) so thatRt+1 = (Rt − ∑iRit)(1 + λt( ¯Rt)) (5)
Reaction Norms and the New Generation’sPhysiology (I)Reaction norm: dictates how to use or not use informationfrom the environment and from parental physiologies ascues to form a new physiology.The reaction norm Xit+1 accepts as inputsthe resources the new generation faces Rt+1the parental physiologies Pit and Pjtthe physiologies agents in new generation meetduring their formation process ¯PtPit+1 = Xit+1(Rt, Pit, Pjt, ¯Pt) (6)
Reaction Norms and the New Generation’sPhysiology (II)Pit+1 = Xit+1(Rt, Pit, Pjt, ¯Pt)with probability pijt the new individual born frommatching ij takes i’s reaction norm Xit+1 = Xitwith probability 1 − pijt the new individual born frommatching ij takes j’s reaction norm Xit+1 = Xjt.
Summing up the frameworkPhysiology: ¯Pit = ( ˜Mit, αi, βi, Git)Environment: ¯Eit = (Rt, Nt, ¯P−it )Resource Extraction: ¯Rit = (Rt, Git, G−it , ¯α)Matching and Reproduction: Nijt+1(Rit, Rjt, γijt , γjit )Niche construction and resource generation:Rt+1 = (Rt − ∑i Rit)(1 + λt( ¯Rt))Reaction Norms and new physiology:Pit+1 = Xit+1(Rt, Pit, Pjt, ¯Pt)
Next StepsFixing one reaction norm, studying how the shape ofthe different elements impact the dynamics of thepopulationCompare the patterns of different reaction norms(adaptive and forward looking reaction norms)Make reaction norms compete (plasticity in mostsuccessful population, necessary feature for areaction norm to survive, ...)