Posts Tagged ‘ animal behaviour ’

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.

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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.