Theories and Models of the Evolution of Altruism Unification vs. Unique Explanations Jeffrey A. Fletcher Systems Science Graduate Program Portland State University 1
Outline • Intro • Example of unification effort o Hamilton’s rule applied to Reciprocal Altruism (including mutualisms) • Example of framework emphasizing role of assortment o Interaction Environments • Examine claim that only Inclusive Fitness explains “true” altruism o Implications for doing Science with Models 2
The Problem • How can natural selection favor individuals that carry helping traits, over those that carry selfish ones? 3
Main Theories for the Evolution of Altruism • Multilevel (Group) Selection o Altruist dominated groups do better; altruists within groups do worse o Δ Q = Δ Q B + Δ Q W • Inclusive Fitness/Kin Selection o Gene self interest, Hamilton's rule ( Δ Q > 0 if rb > c ) o w inclusive = w direct + w indirect • Reciprocal Altruism o Conditional behaviour, Iterated Prisoner's Dilemma (PD), emphasis on non-relatives, mutualism o Indirect reciprocity, strong reciprocity, reciprocity on graphs • Others o By-product mutualism, conflict mediators, policing, social markets 4
Reciprocal Altruism Model • Interactions modeled as a Prisoner’s Dilemma Game (PD) • Iterated conditional behaviours o Genotype (G) no longer determines Phenotype (P) • Axelrod’s Tournaments (late 1970s on) o Tit-For-Tat (TFT) • Anatol Rapoport • Evolutionary experiments o Random interactions o offspring proportional to cumulative payoffs 5
Simple Iterated PD Model T F TFT T ALLD TFT A TFT L L TFT D ALLD ALLD TFT A L L D T F T T T F TFT ALLD TFT TFT TFT ALLD ALLD TFT ALLD ALLD ALLD TFT ALLD offspring pick pairs other (O) replace at random C D parents contributes b contributes w 0 + b – c w 0 – c C 4 0 ALLD actor sacrifices c TFT T F T w 0 + b w 0 (A) D TFT D L L A offspring 5 1 A L L D TFT sacrifices 0 proportional to cumulative payoff Play PD i times 6
Axelrod and Hamilton (1981) • Distinguished two mechanisms – Inclusive Fitness for relatives – Reciprocal Altruism for non-relatives • Why didn’t Hamilton apply Hamilton’s rule? • Two obstacles for unification 1. Phenotype/Genotype differences 2. PD used is non-additive 7
Additive PD other (O) C D actor's fitness contributes 0 (utility) contributes b w 0 + b – c w 0 – c C 4 0 actor sacrifices c w 0 + b w 0 (A) D 5 1 sacrifices 0 • w 0 = 1; b = 4; c = 1 8
Non-additive PD other (O) C D actor's fitness contributes b (utility) contributes 0 w 0 + b – c w 0 – c C + d sacrifices c 3 0 actor w 0 + b w 0 (A) D 5 1 sacrifices 0 • w 0 = 1; b = 4; c = 1; d = -1 (diminishing returns) 9
Queller's Generalization • To solve problem 1 ( G / P difference) o Use phenotypes (behaviours), not just genotypes, in Hamilton’s rule o Hamilton (1975) Queller (1985) cov( G , G ) cov( G , P ) r = r = A O A O var ( G ) cov( G , P ) t A A A • To solve problem 2 (non-additivity) – Use an additional term to account for deviations from additivity (Queller 1985) cov( G , P ) cov( G , P P ) + > A O A A O b d c cov( G , P ) cov( G , P ) A A A A 10
Numerical Simulations of Iterated PD varying Q , i, and b ( c = 1) 0.1 Δ Q 0 Q = 0.2; i = 2 Q = 0.15; i = 2 Q = 0.15; i = 4 Q = 0.15; i = 15 Q = 0.1; i = 2 -0.1 1 3 5 7 9 11 13 15 b - Fletcher & Zwick, 2006. The American Naturalist 11
A Simple Mutualism Model • Interactions are heterospecific and pair-wise • Each species has two types o ALLD type o a cooperative type (e.g. TFT) • b, c, d, and the cooperative strategy can all vary between species 12
A Simple Mutualism Model b 1 d 2 c 1 c 2 2 1 d 1 b 2 cov( G , P ) cov( , ) G P r = r = 2 1 1 2 2 1 cov( , ) G P cov( G , P ) 2 2 1 1 > > r b c r b c HR 1 : HR 2 : 1 2 1 2 1 2 – Fletcher & Zwick, 2006. The American Naturalist 13
HR 1 HR 1 HR 1 HR 2 HR 2 HR 2 1 1 1 Q1 Q 1 0.8 0.8 0.8 Q2 Q 2 0.6 0.6 0.6 Q Q Q 0.4 0.4 0.4 0.2 0.2 0.2 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 generations generations generations 1 2 1 2 1 2 1.5 5 4 4 2 2.2 b b b 2.0 0.1 1 1 1 0.1 c c c 2 2 1 1 1 1 w 0 w 0 w 0 0 0 0 0 0 1.3 d d d TFT TFT TF2T Pavlov ALLC TFT Str Str Str 4 80 100 i i i – Fletcher & Zwick, 2006. The American Naturalist 14
There is no general theory of mutualism that approaches the explanatory power that ‘Hamilton’s Rule’ appears to hold for the understanding of within-species interactions. o Herre et al. 1999, TREE 14:49-53 15
Back to Basics of Selection • Queller’s version emphasizes direct fitness; no G O term—genotype of Other irrelevant! cov( G , P ) cov( G , P P ) + > A O A A O b d c cov( G , P ) cov( G , P ) A A A A • More intuitive form + > cov( G , P ) b cov( G , P P ) d cov( G , P ) c A O A A O A A • An even simpler form + − > cov( G , P b P P d P c ) 0 A O A O A cov( G A , net fitnessbenefitsto A ) > 0 16
Outline • Intro • Example of unification effort o Hamilton’s rule applied to Reciprocal Altruism (including mutualisms) • Example of framework emphasizing role of assortment o Interaction Environments • Examine claim that only Inclusive Fitness explains “true” altruism o Implications for doing Science with Models 17
Simple Public Goods Game • Two types of behaviors o Cooperate (C) and Defect (D) • C and D behaviors have simple genetic basis • Interaction environments of N individuals; split benefits evenly • C behavior contributes b , at cost c • b > c (non-zero-sum-ness) • D behavior contributes nothing and imposes no cost 18
Partition Single Interaction Environment Phenotype Payoff received Payoff received from the behavior of others Total direct from own in interaction environment (excluding self) payoff (within behavior group ) b − Cooperate (C) ( − kb − k 1 ) b c [ k -1 cooperators, N - k defectors] c N N N Defect (D) kb kb 0 [ k cooperators, N - k -1 defectors] N N • Within any interaction environment, defectors (D) do better than cooperators (C) • But C can be selected for when we consider a whole system of interaction environments • This is the basic dilemma of altruism – Fletcher & Doebeli, 2009. Proceedings B 19
Average Interaction Environment • A “mean field” approach to social interactions • Let e C and e D be average interaction environments of C and D individuals, respectively • Measure e C and e D as the number of C behaviors among interaction partners (here N -1) • Compare e C with e D – Fletcher & Doebeli, 2009. Proceedings B 20
Partition Average Interaction Environment Phenotype Average payoff Average payoff received from others’ Average total received behaviors in average interaction payoff from own environment (excluding self) behavior b − e C b ⎛ ⎞ Cooperate (C) e C b b + − c ⎜ ⎟ c N ⎝ ⎠ N N N e D b e D b Defect (D) 0 N N • The condition for C genotype to increase: average net payoff to C is greater than average net payoff to D ⎛ ⎞ e b b e b + − > ⎜ ⎟ C D c ⎝ ⎠ N N N • This is true of any trait! – Fletcher & Doebeli, 2009. Proceedings B 21
Interaction Structures cN ⎛ ⎞ e b b e b − > − + − > e e 1 ⎜ ⎟ C D c C D b ⎝ ⎠ N N N • Random Binomial Distribution: e C = e D o Dividing line between weak ( b / N > c ) and strong altruism ( b / N < c ) • Over Dispersion: every environment has one C o e C = 0 ; e D = 1 (C decreases even if weak: b / N > c ) • Extreme Assortment: only C with C; D with D o e C = N -1; e D = 0 (C increase if b > c >0) – Fletcher & Doebeli, 2009. Proceedings B 22
Outline • Intro • Example of unification effort o Hamilton’s rule applied to Reciprocal Altruism (including mutualisms) • Example of framework emphasizing role of assortment o Interaction Environments • Examine claim that only Inclusive Fitness explains “true” altruism o Implications for doing Science with Models 23
Claim (Hypothesis) • “True” altruism only evolves via inclusive fitness (kin selection) • "Direct benefits explain mutually beneficial cooperation, whereas indirect benefits explain altruistic cooperation” o West et al. 2007, JEB . 24
Direct Fitness Concept Inclusive Fitness Concept r 1 – r r b b c c A A A S • w direct (A) = w baseline – c + rb • w indirect (A) = rb • w inclusive (A) = w direct (A) + w indirect (A) • w inclusive (A) = w baseline – c + rb • Hamilton’s rule: rb – c > 0 25
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