Archive for the ‘ Animal Behaviour & Sociobiology ’ Category

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.
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Animal Communication

Introduction

Communication is the process of transferring information from one animal to another; there are typically three types of roles involved with communication. These are:

  • Signaller – Initiates the communication, the signaller must benefit from making the signal
  • Receiver – Receives the signals sent by the signaller, these signals are often of benefit to the receiver as well
  • Eavesdropper – Takes advantage of the signals generated by the signaller

There are also different forms of communication two of which are:

  • Cooperative signalling – Signalling that benefits both parties involved, e.g. a birding singing to attract a mate
  • Non-cooperative signalling – Only one party benefits, e.g. the ‘broken wing display’ by birds (The bird pretends to have a broken wing to make it appear an easy target, thus distracting the predator from its young).

Types of Communication

Examples of communication types:

Type of Communication Example Species Function
Pheromones Moth Pheromones are short chain hydrocarbons which are easily diffused and are detected by vomeronasal organs. Pheromones and their receptors are species specific and so undetectable by predators. It only takes one molecule of pheromone to elicit a response – unlike smell.
Stridulation Grasshopper Stridulation is the rubbing together of body parts to produce a sound. Stridulation is used when auditory signals are of more benefit than pheromones (e.g. in long grass pheromones are diffused and harder to detect). Different species produce different sounds and calls via stridulation.
Bioluminescence Fireflies A specialised pigment – luciferin releases energy in the form of light by oxidised by the enzyme luciferinase. The light produced is aposematic, this warns predators that they are distasteful. Different species produce different patterns of light.
Alarm Calls Birds – Bird song Similar amongst all species, alarm calls alert other members of the group that a predator is nearby. Alarm calls are generated in a way that makes it difficult to pinpoint the exact source.

Bird Song

Bird song differs between habits, differing mainly by frequency. The birds have adapted to produce a song which is designed to travel as far as possible given the habitat.

In open areas, with wind, a higher frequency and rapid songs are best as they allow the message to travel far without being disrupted by the wind.

In more closed habitats such as woodland, purer tones are used. This helps to prevent degradation of the song by obstructions e.g. trees.

Dance Language of Honeybees

The primary use of the honeybee dance language is to communicate the location of food sources to colony mates. The dance involves 2 components:

  1. A straight run whilst waggling the abdomen
  2. Return back to starting point and repeat but in reverse

This dance conveys information about distance from a food source as well as its direction. The angle of the waggle tells the colony mates the angle of the flower from the sun. The direction of the straight run shows the direction of the flower and the distance of the straight run is related to the distance to the flower. The bees also buzz during the ‘dance’ which also helps to convey the message.

The honey bees are still able to communicate the whereabouts of a food source, even without the sun. On a cloudy day they use their ability to detect polarised light and relate this to the direction of the food source.

The honey bees are able to roughly estimate the distance to the flower by measuring the rate of optic flow. They can roughly estimate their speed by using objects in the distance at and how quickly they pass by, from this they can estimate distance as they know roughly how long they have been travelling.

Experiments have been conducted to show that the dance is an important tool for honey bees. One such experiment measured this by measuring the reproductive success of the honey bees under two conditions:

  1. Diffuse light (non-directional) which lead to the bees giving a disorientated dance
  2. Orientated light (natural e.g. sun) which allowed the bees to give dances as normal

The bees with the orientated light source had much better reproductive success. The dance becomes very important during winter when food sources run low.

Intrasexual Selection

Introduction

Intrasexual selection is when members of the same sex (within a species) compete with each other in order to gain opportunities to mate with others, e.g. the male against male competition for females. Because intrasexual selection often involves fighting, species or individuals well adapt for intrasexual selection will have developed better armourments (weapons) than their competition.

On the other hand, there is intersexual selection. Often known as female choice, it is the process where the female choses the male based on certain ornaments e.g. a peacock’s tail. The ornament is not usually beneficial to the male (e.g. bright colours make it an attractive target for predators) but the female prefers the larger ornaments as it signals the male’s is able  to cope with the hindrance – and therefore a better genetic make-up which will be passed on to her offspring. The reason the females choose is to prevent wasting invested time and energy on offspring which are of poor genetic merit.

Competition

There are two main types of competition over females, scramble and contest competition.

  • Scramble: Typically whoever gets to the female first. An example with dung flies; brightly coloured male dung flies are attracted to a dung pat. Shortly after females will arrive at the dung pat. These females are quickly grabbed by the males. Very shortly after female arrival rate decreases and the number of both males and females around the pat decreases

In a similar scenario, male damselflies also grab females as soon as they arrive. However male body size also contributes to reproductive success. Larger males live for longer and hence have more possible days or reproductive ability but smaller males have a higher daily mating rate as they are more agile and able to grab the females faster. It is therefore beneficial for reproduction to be of intermediate size.

  • Contest: Contest competition is a more typical form of competition where the male with the best fighting technique, largest body size or the largest weapons will win the female. Although not always guaranteed to win, they have a much higher chance than inferior males. This has however; inevitably lead to the production of larger male offspring by reproductive selection – as the larger males are more likely to reproduce and pass on their genes.
  • Alternative Mating Techniques: Smaller males would therefore seem to be at a disadvantage during contest competitions. Fortunately there are species where the smaller males have developed alternative mating tactics to ensure reproductive success. For example:
  • Red deer – Smaller males with small antlers are much less likely to win in a contest competition. Instead they wait near a female deer and when the large male intending to copulate with her engages in a contest with a competitor, the smaller deer sneaks in and copulates with the female.
  • Sunfish – Males defend their territory and wait for females to come and lay their eggs. When a female arrives at the nest she will lay her eggs as the male fertilises them. However subordinate males may quickly dart in-between the male and female. The subordinate male mimics the female as not to alarm the dominant male and both males deposit sperm, this gives the subordinate male a chance to fertilise the eggs of the female.
  • Coho Salmon – There are two forms of male Coho salmon, the larger males known as Hooknoses and the smaller males known as Jacks. Females and Hooknoses spend 3 years at sea before returning to reproduce; Jacks spend only 2 years, meaning a larger proportion return – a lower mortality rate. As is typical with other species, the larger males compete for females by fighting, whilst the smaller males sneak to mate with the females. When comparing Jacks to Hooknoses, both have the same level of reproductive fitness (resulting in a mixed evolutionarily stable strategy).

Sperm Competition

Once a male has mated with a female, it is still possible for the sperm of another male to fertilise the female. Some species have therefore developed methods to prevent this. The basic methods are pre/post copulation guarding. Prior to copulation the male will guard the female until she is sexually receptive and after copulation the male will guard the female until she has laid her eggs.

There is also the basic sperm competition, where the sperm ‘compete’ against the sperm of other males within the female reproductive tract. Two examples of more dedicated sperm competition are:

  • Scrapers – Males who compete by this method use bodily structures to remove the sperm of other males from the female reproductive tract
  • Mating Plugs – Males which use the mating plug method, copulate with a female and when they disengage a ‘plug’ is left within the female. This plug prevents further males from mating with the female.

Intersexual Selection

Introduction

Intersexual selection, often known as female choice, is the process where the female choses the male based on certain ornaments e.g. a peacock’s tail. The ornament is not usually beneficial to the male (e.g. bright colours make it an attractive target for predators) but the female prefers the larger ornaments as it signals the male’s is able  to cope with the hindrance – and therefore a better genetic make-up which will be passed on to her offspring. The reason the females choose is to prevent wasting invested time and energy on offspring which are of poor genetic merit. A study which monitored female choice in peacocks, found that 19 out of 22 times the female mated with the male which had the largest tail.

Fisher’s Runaway Process

Fisher’s runaway process is a method which explains the reasoning for selection and development of male ornaments.

  • Males have a gene which determines the ornament trait e.g. tail length
  • Females have a gene which makes them find the male ornament appealing
  • Initially females will base their choice on what is best for their offspring. For example the utilitarian optimum is the optimum tail length for flight in birds; females will therefore select males who have a tail length closest to this.
  • Continuing with the example, the female will produce male offspring that have a longer tail length and closer to the optimum for flight.
  • The male offspring are more likely to be selected and reproduce, meaning even more offspring produced with longer tails.
  • Natural variation and selection for the largest tail length will eventually lead to males that have tail lengths exceeding the optimum, yet the females continue to prefer the males with the longer tails.
  • A trade-off is produced; a longer than optimum tail length leads to decreased flight ability but increased reproduction success.
  • The two traits eventually reach equilibrium, as males with too long a tail are unable to survive.

Zahavi’s Handicap Principle

Zahavi’s Handicap Principle says that although exaggerated ornaments are selected for by females, it does not actually benefit the female directly (however, you could argue that it helps to spread her genes because her offspring have the exaggerated feature, which in turn leads them to greater reproductive success). The exaggerated features are not beneficial for the male; they act as a disability e.g. the large tail that prevents flight, bright colours which alert predators or larger ornaments which make escape difficult.

The reason the female still chooses the male with the disabling trait, is because it shows that despite the disability, the male is still able to survive. This in turn must mean that the male has good genes, which is why the female choses him.

A distinction is often made between indicator genes, which indicate that beneficial genes will be passed to the offspring (‘good genes’) for example a colourful plumage, and genes which will simply make the male offspring sexually favoured when searching for a mate (‘pure Fisherian’).

The Hamilton & Zuk Hypothesis

This hypothesis states that female swill be more likely to choose healthy male, i.e. those with a resistance to parasites.

This is often seen in birds, a way to determine whether the male is healthy or not is to observe the colour of its plumage. The more colourful the male, the better its resistance against parasites and the more likely it is to be sexually selected by the female (as she will want to pass on those parasitic resistant genes to her offspring). This is because a bird burdened with a parasite will be unable to meet the metabolic rate required to produce a colourful plumage whilst trying to remove the parasite.

However, this is not apparent in all birds only those where parasitic burden is likely to occur. Birds where incidence of parasitism is low do not tend to display bright colours as there is no need for the female to base her mate choice on parasitic burden. If parasite presence is high amongst a species, then that species is more likely to display bright colours as a way to show they are not burdened with the parasite – thus increasing their reproductive success.

An example of this has been shown with sticklebacks. The males display a bright red colour on their stomach; females choose males with the brightest stomach. To prove this was the case, scientists bathed the experiment tank with green light to remove the red colouring from the stomach. The result was random female choice. Then some of the males were infected with a parasite, they proceeded to lose colour an when females were given the choice of which mate they chose the more colourful, non-infected males.

Intersexual Role Reversal

Intersexual selection is not always a female’s choice however. There are examples where males are the ones who invest more time in the upbringing of offspring. There are some species of bird where the females lay their eggs in many nests leaving the males to raise the offspring.

A more specific example is that of bush crickets. Bush crickets only feed on the pollen of one specific plant, early in the season this plant is numerous and pollen is high. However later in the season, the plant number decreases and therefore so does the pollen. The mating process of bush crickets sees the males transfer a sack of sperm during mating, when the female is ready to lay her eggs she is able to eat a protein rich sack from her own body to give her enough energy.

Early in the season when pollen is high males outnumber females so intersexual selection acts as normal. However later in the season when pollen begins to run low, the females are able to consume their protein rich sack to ensure they have enough energy. Males do not have a structure similar to this and so decline in number. This leads to females outnumbering males, and the occurrence of a sexual role reversal – therefore males are now the ones able to choose which females they mate with.

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.

Introduction to the Evolution of Animal Fighting Behaviour

Introduction

Animal fighting behaviour can be introduced using the simple models discussed here; one of these is the ‘Hawk/Dove’ model by Maynard Smith. From this model, we can construct payoff matrixes which can then be used to determine evolutionarily stable strategies (defined below).

Evolutionarily stable strategy – An evolutionary stable strategy or ESS is a strategy which, if adopted by most members of the population, cannot be invaded by a mutant strategy which is initially rare.

Maynard Smith’s Model

The evolution of ritualised behaviour has evolved for the benefit of individuals. Simply, we can imagine that a ritualised behaviour has evolved to allow an animal to avoid participating in conflict, when it is aware that the opposition is more capable. By avoiding conflict, the animal does not have to pay a ‘cost’ of injury. This is looked at in the Maynard Smith Hawk/Dove model.

There are many examples, such as the domestic dog will roll on to its back making itself vulnerable to the opposition, signifying that it does not want to participate in the conflict and the opposition may take the resource for which the conflict arose

Another example is the roaring behaviour of the Red Deer. Typically a roaring contest (another type of ritualised behaviour) will mark the start of a conflict; this allows each Red Deer to gauge the prowess of one another, from which they can decide whether or not to elevate the aggression.

The payoff of conflict is frequency dependent i.e. if there are very few dominant aggressive males, they will obtain a large majority of the resources as the other males are highly likely to show submissive behaviour and flee.

The payoff of conflict can be broken down into two simple values:

  • V – The value of the resource (This could be food, females etc.)
  • C – The cost of the conflict (Injury), however if the animal retreats, no cost is therefore paid

From this we can build the Hawk/Dove Model.

Building the Hawk/Dove Model

The hawk/dove model is a simplistic model concerning the possibilities and outcomes of conflict. By simplifying the animal’s behaviour, we can break down their responses to conflict into 3 choices, either:

  • The animal displays ritualised behaviour (E.g. the roaring contest of the Red Deer)
  • The animal retreats
  • Or the animal elevates the conflict and engages in a fight

Using these three possible outcomes, 2 strategies are built, the Hawk strategy and the Dove strategy. Animals can be related to either the dove strategy or the hawk strategy.

The Hawk strategy consists of the following behaviour:

  • The hawk will engage in conflict immediately and only retreat if it becomes injured

The Dove strategy consists of the following behaviour:

  • The dove will display immediately and only retreat should its opponent escalate the conflict

By winning in a conflict, the animal will gain the resource V, by losing the animal will have to pay the cost C. Some possible scenarios are listed below (Hawk – H, Dove – D)

  • H vs. H – Both will escalate the conflict meaning one gets injured and retreats. This means there is a 50% chance of winning resource V and a 50% chance of paying cost C. (This is assuming both individuals are equally matched and of the same fitness – see assumptions section below). In mathematical terms, E (the energy gain from the conflict, or payoff) of the conflict between two hawks is E(H,H). We can equate this to the value and cost, so:
  • E(H,H) = (V-C)/2
  • H vs. D – The hawk immediately escalates the fight and so the dove retreats. This means the hawk always gets the resource V and the dove always gets nothing – but does not pay a cost as it retreats. So:
  • E(H,D) = V, E(D,H) = 0
  • D vs. D – Both immediately display but as both are of equal fitness (see assumptions below) they must either share the resource or one randomly wins the resource, either way they receive the equivalent of half the resource. So:
  • E(D,D) = V/2

Assumptions

The Hawk/Dove model retains its simplicity due to some assumptions, these are:

  • All individuals are of the same Darwinian fitness, making them evenly matched.
  • The V gained and C paid are the same for all individuals e.g. the cost of an injury costs the same amount of energy in all ‘dove’ individuals.
  • All interactions are completely at random.

Payoff Matrixes

Payoff matrixes are grids which determine whether an ESS is in place, by inputting the values of V and C we can see whether or not hawks, doves or a mixture of both give an ESS.

From previous knowledge (above) we know the following information:

Vs. > H D
H (V-C)/2 V
D 0 V/2

To determine which strategy is an ESS depends on whether or not V<C or V>C, which would depend on the situation. Each has been equated below:

V>C

If V>C e.g. V=4, C=2, we would get the following information (by substituting the values into the table above):

Vs. > H D
H 1 4
D 0 2

What this shows us is that, because in column 1, H vs. H = 1 and D vs. H = 0, Doves are unable to invade a hawk population – This means that the Hawk Strategy when V>C is an ESS. We back this up by looking at column 2 and seeing D vs. D = 2 and H vs. D = 4. This means Hawks are able to invade doves, so doves therefore cannot be an ESS.

V<C

If V<C e.g. V=2, C=4, is there a difference when compared to V>C? Again by substituting the values into the table above, the following information is obtained:

Vs. > H D
H -1 2
D 0 1

Column 1 – D vs. H = 0, H vs. H = -1. This means that Doves are able to invade hawks, does this mean hawk is not an ESS?

Column 2 – D vs. D = 1, H vs. D = 2. This means that Hawks can invade doves.

As both strategies are able to invade one another, when V<C, a mixed ESS arises.

Determining Proportions in a Mixes ESS

In a mixed ESS, we are able to determine the proportion of each strategy by using a simple equation, p=V/C. The equation is derived initially from a more complex equation however:

W=Fitness, W(H) = Fitness of hawks, W(D) = Fitness of doves, W0 = basic fitness p = proportion

We assume that W(H) = W(D)

  • W(H) = W0 + p[(V-C)/2] + pV
  • Where p[(V-C)/2] is the proportion of occasions that we see H vs. H
  • Where pV is the proportion of occasions we see H vs. D
  • W(D) = W0 + p0 + p[V/2]
  • Where p0 is the proportion of occasions we see D vs. H
  • Where p[V/2] is the proportion of occasions we see D vs. D

Because we assume that W(H)=W(D) we can equate these equations to one another, therefore:

  • W0 + p[(V-C)/2] + pV =  W0 + p0 + p[V/2]
  • p[(V-C)/2] + pV = p[V/2]
  • p=V/C

So when simplified we get p = V/C which means the proportion of a strategy in the mixed ESS depends entirely on the value of the resource and cost of injury. Using the values we saw in the V<C example above (V=2, C=4) we get p(H)=2/4. This equates to 0.5 or 50%, therefore the proportion of hawks in this mixed ESS is 50%.

What we can conclude from this is that behavioural variation in a population is suited to evolve that way, especially when V<C. Also that it is frequency dependent. Also as the cost of injury increases, more contests for resources within the species will be settled by ritualised displays.