Posts Tagged ‘ maynard smith ’

Evolution of Animal Fighting Behaviour

It is recommended that you read ‘An Introduction to the Evolution of Animal Fighting Behaviour‘ before you read this, as there are some concepts explained in the earlier article which are used without explanation in this article.

Introduction

Success in fighting behaviour is frequency dependent i.e. as the population size increases fighting success decreases. Fighting behaviour amongst a species is often explained in terms of roles, for example we have previously looked at the fairly simplistic Hawk/Dove model which gives animals the role of either hawk or dove.

When determining which strategy will be dominant amongst a population we check it against the ‘standard conditions’ of Maynard Smith. If a strategy is adopted amongst the majority of a population we call it an evolutionarily stable strategy (ESS). An ESS is a strategy which, if adopted by most members of a population, cannot be invaded by a mutant strategy which is initially rare. The standard conditions to determine if a strategy (e.g. strategy I) is an ESS are:

Either:

1 – E (I, I) > E (J, I)

Or

2 – If E (I, I) = E (J, I) then E (I, J) > E (J, J)

E (I, I) is the payoff of strategy I against strategy I. Therefore by the conditions of 1, strategy I is an ESS if the payoff of I vs. I is greater than the payoff J receives from fighting I i.e. E (J, I).

The Hawk/Dove/Retaliator Model

The Hawk/Dove model makes certain assumptions:

  • Animals fight with equal ability
  • Animals fight in pairs
  • Animals can only display, escalate or retreat
  • Encounters are random

Due to the limitations of the Hawk/Dove model an additional strategy was added – retaliator

  • Hawks (H)– Escalate immediately, retreat if injured
  • Doves (D)– Display immediately, retreat if opponent escalates
  • Retaliators (R)– Immediately display, escalate if opponent escalates and retreat if injured

The payoff matrix looks like this:

Vs. > H D R
H (V-C)/2 V (V-C)/2
D 0 V/2 (V/2)x 0.9
R (V-C)/2 (V/2)x 1.1 V/2
  • V = Value of resource.
  • C = Cost paid attempting to gain resource.
  • The reason for the x1.1 is that retaliators do slightly better than doves (10%) as they sometime escalate so their payoff is increased.
  • The reason for the x0.9 is the same as above, but because the doves sometimes lose, their payoff is reduced by 10%.

When V>C: Hawk is not an ESS, doves are unable to invade and therefore retaliator is an ESS.

When V<C: Hawk is not an ESS, doves are unable to invade and therefore retaliator is an ESS.

The War of Attrition

When 2 animals meet in a contest for a resource, the amount of energy they are willing to invest to win that resource are predetermined. The animal will therefore display until this time/energy is up. This value is not modified during the display. In the contest, the animal which wins is therefore the one who invested the most predetermined energy. We can model this:

  • Rate of cost accumulation: c
  • Contest length: T
  • Cost of contest: cT
  • Resource value: V
  • Animal A persistence time: TA
  • Animal B persistence time: TB

In this example TA > TB

Payoff to animal A = V – cTB (Animal A wins the resource V but still has to pay the cost, c for the length of the contest, the length of the contest would therefore be TB as the contest ended when animal B gave in.)

Payoff to animal B = – cTB (Animal B does not win any resource, but must still pay the energy that was used during the contest)

A population does not evolve a constant persistence time, however:

  • If cT < V it is worth persisting longer for a resource as the payoff is greater than the cost.
  • If cT > V then a persistence time of 0 spreads amongst the population as to engage in contest for the resource will mean a loss of energy (even if winning). It is therefore better to not engage and lose nothing.

The length animals choose as their persistence time follows a negative exponential distribution, i.e. many choose short times and a very limited number choose long times. The length of contests will therefore also follow this distribution. The log of the number of contests plotted against the length of the contests will give a straight line.

Examples:

  • Damselfly larvae compete for perching space. Intruders encroaching on perching space will be warned by a ritualised display of the abdomen. The intruder may either leave or contest against the perch space owner. The contests are slow, but their duration follows the negative exponential predicted earlier, however 70-80% of the contests are won by the original occupant and not the 50% you would expect.
  • The fighting of male dungfly over female dungfly (which can be considered a resource) follows the same negative exponential pattern.

The assumption that all contests are fought symmetrically (equal chances of winning) is false, we can assume asymmetry because:

  • Resource Value – Resources are worth more or less to different animals, e.g. a piece of food may be worth more to a hungry animal than a recently fed animal.
  • Resource Holding Power (RHP) – The fighting ability of the animal, this will vary amongst the population, those with a higher RHP will be more likely to win a contest.
  • Uncorrelated Asymmetry – This is any asymmetry which is not correlated to the value of the resource.

Resource Holding Power (RHP):

  • RHP is the fighting ability of an animal, therefore the animal with the greatest RHP is going to keep the resource and the animal with the lower RHP will retreat.
  • Animals must therefore find a way to assess the RHP of others.
  • If RHPs are of similar value, this is when a fight will escalate.
  • For example:
    • The roar contest in red deer helps to determine the RHP. The deer with the lower roaring rate retreats as it is very likely to have a lower RHP. This type of contest is a true signal of RHP (unlike size for example).
    • Croaking in toads when trying to find/compete for a female allows the toads to determine RHP and thus whether or not to attack. Larger males produce deeper croaks and are determined to have a higher RHP.

Bourgeois Strategy

The Bourgeois strategy is a method used to determine the payoff values for competing for resources. It is substituted into the Hawk/Dove model. The Bourgeois strategy is:

  • If it is the owner of a resource, it plays hawk
  • If it is the intruder, it plays dove
  • The assumption is 50% of the time; the Bourgeois is the owner of the resource.

When we put this into a payoff matrix we get the results:

  • If V>C – The hawk strategy is an ESS
  • If V<C – The Bourgeois strategy is an ESS

e.g. The speckled wood butterfly protect areas of sunlight as they are looking for a mate. When an intruder approaches a short spiral fight occurs. The owner of the path of sunlight always wins the spiral fight. If there is confusion over the ownership of the sunlight patch then the spiral fight lasts much longer.

There also exists an Anti-Bourgeois strategy where the intruder always wins the resource for example:

  • In certain spider species, intruders always displace the owner of a web funnel.
  • Seagulls on a flag post always give up the space immediately to invaders.
Advertisements

Introduction to Animal Behaviour Towards Sex

Introduction

It is believed that originally, species reproduced by asexual reproduction. This is where species are able to reproduce through mitosis individually, this means the descendants of the individuals are essentially clones, the only way which variation can occur is through mutations. Asexual reproduction allows for rapid population growth in stable environments (where adaptation through natural selection is not required). Examples of asexual reproducers are many bacteria, plants and fungi.

Sexual reproduction is the converse of this, requiring the gametes of two individuals to fuse together to form the next generation. Because of this, the life cycle of sexually reproductive individuals is typically divided into two phases; a diploid (2n) and haploid phase (n). Gamete production occurs by meiosis (which may introduce variation) where 2n -> n, the fusion of gametes (which also introduces variation) is the reverse, n -> 2n. With sexual reproduction a lot of variation arises each generation, which allows adaptation in changing environments.

The ‘Cost of Sex’

The cost of sex, also known as the cost of producing males is an equation that shows how parthenogenetic individuals (those who produce fertile female eggs asexually) are essentially twice as effective when compared to sexual reproduction. This means asexual individuals are able to quickly reproduce and populate an area, however they lack the variation introduced by sexual reproduction.

Imagine a population that consists of N sexual males and N sexual females (The total population would therefore be 2N). Each sexual female (N) can produce an amount of eggs, K. These eggs have a probability of surviving, S. So in the next generation there will be KSN sexual individuals, this is the number of females, the eggs they produce and the survival of those eggs.

Assuming that within this species there are also parthenogenetic individuals that produce asexually, n, which again produce K eggs with a survivability of S, the next generation of parthenogenetic individuals would consist of KSn. That is the total number of parthenogenetic individuals (n), the eggs they produce (K) and the survival rate of those eggs (S).

To determine the increase in proportion due to parthenogenetic individuals, we must find their proportion within the initial generation and the second generation. We will then be able to see how parthenogenesis compares.

The proportion of parthenogenetic individuals in the first generation was n/(n + 2N), this is the number of parthenogenetic individual divided by the total number of individuals (2N being the number if sexual males and females.)

In the next generation the ration will depend on the number of surviving eggs, which will be:

KSn/(KSn + KSN), this is the number of surviving parthenogenetic eggs, divided by the total number of eggs laid. Because the KS term appears on both the top and bottom, it can be cancelled out to give: n/(n + N)

If we assume that the parthenogenetic form arises as a mutant, we can say that n is very low when compared N. This is because the mutant(s) numbers are so small when compared to the rest of the species population. Because of this relationship we can assume that n + N is so close to the value of N alone, that n + N is roughly equal to N. We can say the same about n + 2N, this is roughly equal to 2N.

By making the above assumptions, the initial proportion on parthenogenetic individuals in the first generation is: n/2N

With the proportion increasing to: n/N in the second generation.

This shows that the proportion of parthenogenetic individuals doubles in one generation, meaning that asexual reproduction has a two-fold advantage over sexual reproduction – this is known as the ‘Cost of Sex’ or the ‘Cost of Producing Males’.

Gamete Production and Parental Investment

Species may exhibit variation in the type of gamete that they produce; for example humans produce two very different types of gametes – the egg which is slow and large compared to sperm which are small, motive and numerous.

Isogamy is believed to have been the first step along the path of sexual reproduction. Isogamy is when both sexes produce similar gametes, making them undistinguishable from one another. Organisms such as algae, fungi and yeast form isogametes.

In contrast to isogamy is anisogamy; this is the production of dissimilar gametes that may differ in size or motility. Both gametes may be motile or neither, however they will always be distinguishable from one another. The anisogamy observed in humans is known as oogamy.

Oogamy is a specialised form of anisogamy, where the female produces significantly larger egg cells, compared to the smaller, more motile spermatozoa. Both gametes are highly specialised towards their role, with the egg containing all the materials required for zygote growth and the sperm containing little more than the male genetic contribution. This does however allow for the sperm to be highly motile and travel the necessary distances required to fertilise the barely motile egg.

Because of this, we often see greater amounts of parental investment from the females of species as they put in nearly all the energy of producing the offspring. Parental investment is defined as, any investment by the parent to an individual offspring that increases the offspring’s chance of surviving (and reproductive success) at the cost of the parent’s ability to invest in other offspring.

Robert Trivers’ theory of parental investment predicts that the sex making the largest investment in lactation, nurturing and protecting offspring will be more discriminating in mating and that the sex that invests less in offspring will compete for access to the higher investing sex. Sex differences in parental effort are important in determining the strength of sexual selection. This is why in many species, the female will be particularly choosy when looking for a male to mate with, as she will be examining the males to see which one will provide the best genes to ensure her offspring’s reproductive success is maximised.

Introduction to Kin Selection

Introduction

Some organisms tend to exhibit strategies that favour the reproductive success of their relatives, even at a cost to their own survival and/or reproduction. The classic example is a eusocial (highly social) insect colony, with sterile females acting as workers to assist their mother in the production of additional offspring. Many evolutionary biologists explain this by the theory of kin selection. Natural selection should eliminate such behaviours; however, there are many cases, such as alarm calling in squirrels, helpers at the nest in scrub jays, and sterile worker castes in honey bees, in which these animals cooperate despite an obvious disadvantage to the donor.

This sacrifice of individual success for the aid of other individuals is known as altruism.

There are thought to be four possible ‘routes’ to altruism – why it might arise, these are:

  • Kin selection – Keeping altruism in the family, possibly shared in the genes. Altruism within a family helps it to proliferate well.
  • Reciprocal altruism – ‘One good turn, deserves another.’ Altruism expressed by an individual is at some point returned. E.g. social grooming in primates, the individual doing the grooming is eventually groomed back.
  • Selfish mutualism – ‘What’s in it for me?’ Altruism which is expressed only because an individual also gains from it. E.g. feeding in house sparrows, they will call for help to break up large pieces of food which they are unable to carry alone thus losing some of the resource but gained more than they would have alone.
  • Group selection – ‘For the good of the group.’ Groups within a population – not necessarily family – which benefit by co-operation.

Kin Selection

John Maynard Smith described Kin Selection in 1964 as “…The evolution of characteristics which favour the survival of close relatives of the affected individual, by processes which do not require any discontinuities in the population breeding structure.”

It goes on the idea that because similar genes are more prevalent within a family (either by kind [species] or by descent [ancestral]), any altruistic genes expressed within the family are more likely to become more prevalent within the entire species.

Kin selection refers to changes in gene frequency across generations that are driven at least in part by interactions between related individuals. Under natural selection, a gene encoding a trait that enhances the fitness of each individual carrying it should increase in frequency within the population; and conversely, a gene that lowers the individual fitness of its carriers should be eliminated. However, a gene that prompts behaviour which enhances the fitness of relatives but lowers that of the individual displaying the behaviour (altruistic genes), may nonetheless increase in frequency, because relatives often carry the same gene; this is the fundamental principle behind the theory of kin selection. According to the theory, the enhanced fitness of relatives can at times more than compensate for the fitness loss incurred by the individuals displaying the behaviour.

Hamilton’s Rule

Whether or not altruism is favoured within a family or species depends on whether or not Hamilton’s rule is met:

Hamilton’s Rule: rB-C>0 or rearranged rB>C

Altruism is favoured when rB>C

  • C – The cost of displaying altruism, any disadvantages to the individuals.
  • B – Benefit to the individual(s) who receive aid.
  • r – The coefficient of relatedness. The probability that 2 individuals contain a gene identical by descent at the same locus. It has a value of 0-1.

Possible r values:

Relationship Coefficient of Relatedness
Identical Twins 1.0
Parent to an offspring 0.5
Siblings 0.5
Half Siblings 0.25
Unrelated individuals 0.0

Hamilton’s rule therefore predicts that we expect closer related individuals to express greater amounts of altruism. For example:

Would a mother warn her child of a predator, thus exposing herself as a target? If doing so has an arbitrary value of 2, but the benefit of saving the child of 5 then using Hamilton’s Rule the following must be true:

r(0.5) x B(5) – C(2) > 0

0.5 x 5 – 2 = 0.5

Thus as the value is greater than zero, altruism in this situation is favoured, would the same be true between half siblings? (r=0.25)

r(0.25) x B(5) – C(2) > 0

0.25 x 5 – 2 = -0.75

Because the result of Hamilton’s rule is less than 0, altruism in the same situation but a half-sibling attempting to warn a half-sibling, is not favoured.