Biology 4070 Presentation #4 PDF

Game theory and other strategy-forming considerations Biology 4070 Presentation #4 Image from Resource: Krebs & Davies, Cornell Lab of Ornithology 1...

Game theory and other strategy-forming considerations Biology 4070 Presentation #4 Image from Resource: Krebs & Davies, Cornell Lab of Ornithology 1 Behavioural Ecology Competition major themes Competition for Resources Within species (Intraspecific) Between species (Interspecific)  Community Ecology Competition for Mates Intrasexual (and intraspecific, of course) Overlay: Interference (direct) Exploitation (indirect) 2 Start with food: Multiple factors, so not just competition Feeding options: Option A – Variable food of 0 or 6 seeds with a probability of 50% each Option B – Fixed food of 3 seeds So, same total amount over long term Yellow-eyed junco Two treatments: 1 degree Celsius 19 degrees Celsius 3  Preference: Variable Preference: Fixed food food (0 or 6 seeds), (3 seeds), because because 3 seeds is not sufficient food is adequate for daily reliable needs Risk averse strategy Risk prone strategy prevails prevails 4 Modelling: Organism’s own state is a factor too Assume: animal needs 8 energy units to survive the night Feeding options: Option A – Variable food of 0 or 2 units with a probability of 50% each Option B – Fixed food of 1 unit So, same total amount, but again, one with uncertainty 5  Six units at twilight with one Seven units at twilight, with one final option to eat final option to eat Preference: Variable food (0 or Preference: Fixed food (1 unit), 2 units), because 1 seed is not because it will certainly reach enough to survive 8 Risk prone strategy prevails Risk averse strategy prevails 50% chance of failure (50% chance of failure in But 100% chance of failure in variable option) fixed option What strategy would likely be employed earlier in the day? 6 Conclusions 1. Foragers will react to variability in food rewards to be obtained, and 2. Foragers will make choices dependent on their own state 7  Observations Small birds in winter can lose 10 or 15% of body mass overnight Usually, even in winter, birds carry less fat than maximum On harshest days, birds carry close to maximum possible fat Weight gain is most rapid in afternoon Black-capped Chickadee 8 Hypothesis? Likely a cost-benefit explanation Hypothesis: Fat is a benefit for surviving cold nights Fat is a cost due to added weight slower foraging vulnerability to predation 9 Circumstantial evidence (Britain) Woods with Sparrow Hawks Winter mass averaged 0.5 g less in ~20 g birds (2 to 3%) Experimental evidence (Britain) Birds presented with model hawks similar mass decline greater decline in high status birds Why? they have priority access to food 10 Empirical evidence: Food storage is an option for some Food storing chickadee Non-food storing chickadee 12  Food storage Risk – other individuals will steal the food Benefit – worth it if it is mostly not stolen 13 Radio-isotopes (from experimenters) invested in food items stored show that the storing individual is the one most likely to harvest the stored food Brodin and Ekman, 1994 14 Review: Decisions Environment (1C vs 19C) Physiological state Variability vs reliability of food Presence of predators Cost-benefit considerations Time of day Option of storing food 15  Competition arrangements What approach should an individual take? It may depend upon others Recall Evolutionarily Stable Strategy (ESS): If all members of a population adopt it, there cannot be an alternative strategy that will displace it 16  Hawk – Dove Game Theory Think of the dichotomy in terms of interaction strategies within a gene pool, not two species. Game Theory: Mathematical models of strategic interactions between individuals. In humans: Operates among In ecology: Designed by “rational agents” Natural Selection 17  Game theory: To be clear… We’re not talking about two species, a heartless raptor and a gentle dove We’re instead talking about two behavioural options that (a) an individual can take and employ at different times, or (b) an individual can take at one point as a then-permanent option An aggressive approach to an encounter with another conspecific A passive approach to an encounter with another conspecific A mix: sometimes passive, sometimes aggressive ESS may not be what would be best for everyone No one can see any better than before… … and no one gets to sit. 19 20 Pay-off Matrix: When a competitive “aggressor” deals with an opponent Metrics: Winner gains resource: B = 50 Loser loses resource: 0 Resistor suffers injury: C = -100 Rules: Hawk vs Hawk: 50% wins, 50% suffers injury Hawk vs Dove: Hawk wins and dove retreats Dove vs Dove: They share the resource Hawks always fight; doves never fight 21  Opponent – Hawk Opponent – Dove Initiator – Hawk What does the initiator get? Initiator – Dove 22  Opponent – Hawk Opponent – Dove Initiator – Hawk ½ B – ½ C = -25 Initiator – Dove 0 23  Opponent – Hawk Opponent – Dove Initiator – Hawk ½ B – ½ C = -25 B = 50 Initiator – Dove 0 ½ B = 25 24  Opponent – Hawk Opponent – Dove Initiator – Hawk ½ B – ½ C = -25 B = 50 Initiator – Dove 0 ½ B = 25 If all are Doves, every Dove in an encounter experiences a plus 25 payoff But a Hawk strategy mutation would succeed and spread, because of its plus 50 payoff. So, the Dove strategy is not an ESS. 25  Opponent – Hawk Opponent – Dove Initiator – Hawk ½ B – ½ C = -25 B = 50 Initiator – Dove 0 ½ B = 25 Will the Hawk strategy then spread throughout? No, because Hawk-Hawk interactions on average are costly → a minus 25 payoff. Then, the Dove strategy would be superior with its yield of 0 (which is neutral, but it survives to forage elsewhere) So, the Hawk strategy is not an ESS either. 26 Generally… … a relatively rare strategy in this competition game is the better strategy Doves prosper when Hawks are common, and Hawks prosper when Doves are common Result: A balance where the pay-off being a Hawk equals the pay- off being a Dove 27  The balance… Let d be the proportion of doves and h be the proportion of hawks d = 1-h Hawk average payoff = -25h + 50(1-h) Dove average payoff = 0h + 25(1-h) 28 Set the averages equal to each other to find the ESS -25h + 50(1-h) = 0h + 25(1-h) -25h + 50 – 50h = 25 -25h 50 – 50h = 25 -50h = -25 h=½ 29 The balance… In this case, h = ½ (and d = ½) More general result: proportion of hawks is B/C proportion of doves is 1 – B/C 30 Either Hawk or Dove? Let’s say B/C is 75% Could be a stable dimorphic state → 25% of individuals are Doves and 75% are Hawks Or, each individual could employ a mixed strategy, where they are hawkish 75% of the time and dovish 25% of the time 31 What’s the average payoff at the ESS? Because individual self-interest can 12.5 supersede the population’s best What if they were all doves? interest. 25 (higher, since the injury costs are removed) Insight: variation may not be noise; it may be a predictable outcome 32 If B > C, then the ESS is… …the Hawk When do we see that fatal fighting is frequent? When life expectancy is short and mating opportunities are few When “the stakes are high” e.g. Bowl and Doily Spiders 33 Reality? Likely to be more than two strategies Likely to be more uncertainty Likely to be other factors Encounters will not be random Assessment of the other… 34 Gouldian Finches  Head colour correlates with dominance Red head individuals ( and ): Behaviourally dominant More testosterone and corticosterone in socially competitive instances = “hawk” strategy Black head individuals ( and ): Behaviourally subordinate = “dove” strategy  Bird sex chromosomes Head colour allele is on the Z chromosome Head colour allele is on the Z chromosome Red males are RR or Rr. Black males are rr. Red females are R. Black females are r. i.e. females are hemizygous Aside: About 1 in 2500 Gouldian finches have yellow-orange heads This is a case of epistasis The effect of one gene is modified by the alleles at another gene Here: the effect of the R/r gene on the Z chromosome is modified by the alleles at a locus of another gene RR or Rr male with yy (a pair of recessive alleles at another gene on an autosome) → yellow-orange head R female with a yy → yellow-orange head rr male or r female with a yy → black head Also, part of this story: They are cavity nesters. Cavities are in limited supply. Red-head individuals tend to outcompete black individuals. This forms the basis of higher reproductive success of “hawks” among individuals that are “doves”. 40  Also: they tend to mate assortatively Assortative mating: Mating pattern where mate choice is based on a) similarity in phenotype (positive assortative mating), or b) dissimilarity in phenotype (negative assortative mating) Example of negative assortative mating in Ontario’s white-throated Sparrows Red-head x Red-head and Black-head x Black-head  r females R females Postzygotic genetic incompatibility One more thing… Reduced broods Enlarged broods So: 1. There are 2 morphs, with red being hawk-like and black being dove-like a) Red-head birds are RR or Rr (males) or R (females) b) Black-head birds are rr (males) or r (females) 2. They tend to mate assortatively (positive) with a) red-head x red-head pairs, and b) black-head x black-head pairs 3. Red-head x black-head pairs have lower reproductive success 4. Nest holes are scarce, with red dominating their control 5. As the red morph becomes more common, fitness drops due to overall levels of aggression, and associated reduced provisioning  How game theory applies Hawks are pairs where the male is RR or Rr (red-head) Have a competitive advantage in contests over nests Breeding success declines as hawks become more common Researchers (Kokko et al paper at slide 36) modelled values for a) Strength of assortative mating b) Competitive advantage of red males in securing nest cavities c) Frequency-dependent decline in breeding success d) Survival e) Habitat structure Population stabilizes quickly Population is close to twice as many black individuals as red. If you remove assortative mating, the red morph goes extinct. Also, frequency-dependent breeding success of hawks is also necessary for the red morph to survive. Why? Competition is zero-sum (there’s a winner and a loser). Provisioning is not (both win). Hawk-dove? The Gouldian Finch example is considerably more complicated Sexual reproduction Sex-linked polymorphism Behavioural differences Population densities Etc. “The morphs of the Gouldian Finch … yield insights into the possibility that selection favours behaviours detrimental for population fitness and species persistence.” ESS does not mean it’s the best for all individuals “Whenever success in zero-sum games (“hawk” behaviour) forms a part of individual fitness…” “…selection may favour underinvestment in traits that population growth relies on” OR: “… selection may favour a steady-state that is not optimal for the population.” Especially true in sexually reproducing species because: Male life histories often feature competition for mates in a zero-sum manner Generally: Competition vs Parenting (in this case, birds) Another twist: heterospecific competition Because they nest in cavities, they also compete with other species This intensifies nest site competition This circumstance favours red-heads, shifting further away from good parenting.