Mathematical and Theoretical Insights into Animal Behaviour

Question 1

Hamilton, W. D. 1964.

Answer 1

Inclusive Fitness Theory
“The social behaviour of a species evolves in such a way that in each distinct behaviour- evoking situation the individual will seem to value his neighbours’ fitness against his own according to the coefficients of relationship appropriate to that situation.”

Question 2

c - ‘cost’ to actor of social behaviour
b - ‘benefit’torecipientofsocialbehaviour
r - genetic relatedness between actor and recipient

Answer 2

Hamilton’s Rule: behaviour favoured if c < br

Question 3

Cannibalism in Tiger Salamanders

Answer 3

Tiger salamanders are more likely to develop into cannibals if they are in groups containing:

(1) many conspecifics
(2) variation in larval size
(3) mostly unrelated individuals

Question 4

Game Theory 1: Sex Ratios

Answer 4

If others are producing sons, it’s better to produce daughters as this will maximise number of grand-offspring.
If the sex ratio is even (1F:1M) it’s better to produce an even ratio of sons and daughters.
= Evolutionarily Stable Strategy (ESS)

Question 5

At an even sex ratio sons and daughters give equal fitness returns. The even sex ratio is an:

Answer 5

Evolutionarily Stable Strategy (ESS)

Question 6

John Maynard-Smith

Answer 6

Pairwise Contests
The Hawk-Dove Game
The Hawk-Dove-Bourgeois Game

Question 7

Pairwise Contest: Hawk-Dove Game

Answer 7

Animals compete for resources in pairs
Hawk: Never shares, always fights
Dove: Will share, never fights, retreats if opponent fights
Payoffs:
Value of resource = v
Cost of fighting to loser = c

Payoff Matrix

                         Opponent 
                                  Hawk      Dove Focal Individual Hawk (v – c)/2    v 
                       Dove    0         v/2

Question 8

Invasion of Rare Strategies

Answer 8

Dove common and Hawk rare - can Hawk invade?

Hawk invades if v > v/2 (i.e. always)

Question 9

Hawk common and Dove rare – can Dove invade?

Answer 9

Dove invades if 0 > (v - c)/2 (i.e. if c > v)

Question 10

1. Hawk can invade a population of Doves if v > v/2

2. Dove can invade a population of Hawks if c > v

Answer 10

If 1 & 2 both true, we get invasion from both ends: a mixed ESS

If only 1 is true then we get a pure ESS of Hawks

Question 11

Hawk-Dove-Bourgeois Game

Answer 11

Animals contest resources in pairs
Hawk: Never shares, always fights
Dove: Will share, never fights, retreats if opponent fights Bourgeois: Plays Hawk when resident and Dove when intruder

Outcome (‘Resident wins’ convention)

Bourgeois always invades Dove
Bourgeois can invade Hawk and resists Hawks if v < c

Question 12

Speckled Wood Butterfly

Answer 12

Ephemeral territories so will not try to take territory from a resident. Bourgeois strategy.

Question 13

Three male mating strategies
1. Large territory holders:
Aggressive, hold a large territory with several females (orange throat)

2. Sneakers:
   Mimic females and enter large territories for sneaky matings (yellow striped throat)
3. Defenders:
   Defend small territory with one female, can detect sneakers (blue throat)

Side-blotched lizards. Rock paper scissors scenario. See the dominance of one morph one year, outcompeted by another the next year and another the year after that etc.

Answer 13

Thus, each strategy has a strength and a weakness and there are strong asymmetries in contests between morphs. Trespassing yellows, with their female mimicry, can fool oranges. However, trespassing yellows are hunted down by blue males and attacked. While oranges with their high testosterone and high stamina can defeat blues, they are susceptible to the charms of yellows. In contrast, contests between like morphs (e.g., blue vs blue, orange vs orange or yellow vs yellow) are usually more symmetrical.

Question 14

Game theory was originally developed in the 1940s by John von Neumann as a tool to understand economic and military (“war games”) behaviour. In the 1970’s John Maynard-Smith and George Price started to apply game theory to animal behaviour.

Answer 14

At more or less the same time other biologists, particularly William Hamilton, also used game theory ideas to investigate optimal sex ratios and group formation. Price died soon after, but Maynard-Smith went on to develop the theory within a biological context. For those of you who are interested in learning more, his book (Maynard Smith, J. 1982. Evolution and the theory of games. Cambridge University Press) is well worth looking at, or see the references to some of his shorter articles (Maynard Smith 1998, 2002).

Question 15

Many animals, including humans, have a genetic mechanism for determining sex (e.g., XY chromosomes) that can easily give an even sex ratio. This is the proximate cause of an even sex ratio but it is not the ultimate cause. Animals with chromosomal sex determination can adjust offspring sex ratio. Seychelles warblers have chromosomal sex determination (WZ; in birds the female is the heterogametic sex). Females adjust the sex ratio of their brood according to territory quality. This shows that, when there is an advantage for adjusting sex ratio, even animals with chromosomal sex determination can do it.

Answer 15

There are other forms of sex determination some of which may make sex ratio adjustment a lot easier for the mother. In Hymenoptera (sawflies, wasps, ants, bees) males are haploid and females diploid. A female can control the sex of her offspring by choosing whether or not to release sperm from the sperm storage organ as the egg is laid. The sperm storage organ is connected to the oviduct via a duct controlled by nerves and muscles. In honeybees there is conflict between the mother queen and her daughter workers over the sex ratio of young queens and males reared. The workers may be able to cause a female-biased sex-allocation ratio by selectively killing male larvae and the queen may be able to resist this by laying few female eggs.