What To Say To God To Convince Him to Allow You to Enter Heaven

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Two nights ago, three strangers stopped me while I was on my way home. It was a Friday night and I was tired, overworked and stressed. The week had been trying, what with tests and experiments that didn't work. 

"Hello, hi, can we ask you 5 simple questions?" They saw the wariness on my face and added, "please? Just five questions?"

The three of them - 2 aunties, 1 uncle, all middle-aged - looked suspiciously like insurance agents. They reminded me of people who loiter about the train stations, asking by-passers to sign up for credit cards or mobile broadband plans.

"Okay." I relented. I'm almost one-quarter-century years old and I still have difficulties saying 'no'.

"So, what's your name?" My answer was brief.

"What're you studying?" Science.

"What's your greatest worry?"

This survey was becoming interesting, judging from this question. What's my greatest worry? Hmm, what is it?

World peace? Recently, America proposed to bomb Syria for chemically attacking its citizens. Russia, naturally, objected to a US-led military invasion. Maybe something closer to home? The South China Sea disputes between China and Japan/ Korea/ Vietnam/ Malaysia/ Philipines/ Brunei aren't resolved yet. This could lead to regional instability.

I gave serious thought to answering 'world peace'. They'd probably think that I'm teasing them.

"Graduating," I said. After all, this is a safer answer and I've no wish to prolong the conversation. I'm in my final year of studies and worrying about graduation is a legitimate concern.   

"Wow, which university are you studying in?"

"NUS."

"Okay, could we know what's your religious belief?"

"Erm, I've none."

"Do you mean you're a freethinker?"

"I suppose so."

One of them quickly ticked a checkbox on their Life Questionnaire. "Now, for the last question. Suppose that you're to die and reach the gates of heaven, what do you think you'd say to God to convince him to allow you to enter?"

I paused. "I don't know what I'd say. I haven't considered this question before."

They offered suggestions. "Perhaps you would say that you're a good person who deserves to be in heaven? That you might be imperfect but you've tried my best? You deserve a second chance?"

"Honestly, I don't even know if I believe there's a god, or gods, or God."

"Erm," they paused. Apparently, my answer didn't fit any MCQ answer. 

"Thanks." I left, even more tired and discomforted than before answering this street-side questionnaire.

Their last question is, perhaps, the greatest fear of people without faith. What to say to God to gain entry to heaven. Almost akin to what to say to teachers if one is late for school, or to the policemen when caught speeding. Every answer would sound like an excuse, a desperate plea. 

It reminds these people - they without faith - that the world beyond is a great unknown. There is no one to trust and nowhere to look forward to.

There may be no higher purpose in life other than to eat, sleep, shit, pee and procreate. Life may simply be a random game of luck and numbers. A genetic lottery deciding where we were born and how we were raised.

Human beings, little macro-organisms with their existential angst, have always been trying to impute meanings on the meaningless. At times, their attempts may be successful. And at times, not so.

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Donating A Bag of Blood

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It's strange, how the metallic needle pierces into the inside of the elbow, stealing blood from a throbbing vein.

It can be seen, going in, how sharp and glinting, but can't be felt. The effects of anaesthesia, the influence of chemicals. It's as though my sense of sight is disagreeing with that of touch.

As my blood spirals through the plastic tube, into a plastic bag, I marvel at the modernity of this process. The artificial creation of such cheap and readily available plastics that carry blood from a faceless somebody to another faceless somebody.

To whom, will this bag of blood go?

And why am I donating blood? To help people.

But is it just to help people? Perhaps I simply don't treasure myself enough, to be sufficiently self-centric to run away from an impending needle, the way other friends would.

It's the sixth time I'm donating blood and it's the sixth time I'm donating alone. I've learnt not to ask people to donate alongside. Those herds of friends, happily squealing, coming together, giving blood on adjacent beds, what is it that they have that I'm so profoundly envious of?

The crimson tube, resting against my arm, is warm.

At least, the viruses and bacteria living in my red fluids will find a new home.

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Lecture 15: Evolution of Communication

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APS209 Animal Behaviour

The Evolution of Communication

Aims

1. Present examples of honest communication in animals.
2. Describe the logic in how natural selection can favour honest communication.
3. Present a detailed account of the logic behind begging as an honest signal of need in chicks.

Objectives

1. Learn specific examples.
2. Understand why honest communication is an evolutionary puzzle.
3. Understand the logic behind how cost or common interest can make a signal honest.

We humans communicate all the time. Is this communication honest? Consider two situations. In the first, one person is selling a car to another and is telling the potential buyer about it. In the second, a pilot and navigator are flying an aircraft. In the first situation there is considerable incentive for dishonesty in communication. The vendor may not tell the truth about the car and the buyer may disguise his interest. But in the second situation there is no incentive for dishonesty concerning communication needed to keep the aircraft operating properly. Honest communication is also favoured in the waggle dance communication between nestmate honeybees, or between cells and organs in your body. In both cases there is nothing to benefit from making a dishonest signal. The communicating parties benefit equally from any advantage to plane, colony or body. Communication can still be honest or reliable, however, even if the interests of the different communicating parties are not identical. Consider the car sale. If the vendor tells obvious lies about the car the potential buyer will be put off, so there is incentive in being reasonably honest. (Society may also impose laws preventing sellers from dishonestly describing their goods, but that is another matter.)
            Ravens who have found an animal carcass in the Maine woods sometimes call others to the feast by yelling. Yelling is a deliberate and honest signal that food is available. How can natural selection favour one animal making a signal that attracts a competitor to food? It seems that yelling is not always favoured. If a resident raven finds a carcass on its territory it does not yell and may be able to have it all to itself, or to share it with its mate. But if a non-resident bird finds a carcass it yells to attract other non-residents. The attracted birds are too many to be driven off by the territory owners.
            Nestling birds often beg loudly. Parents often give more food to chicks that beg more. Why do they do this? If chicks that beg the loudest are also the hungriest then it makes sense for the parents to feed them more because a piece of food given to a hungry chick will normally increase its survival more that when given to a well-fed chick. By doing this, parents have more surviving offspring. But if parents give more food to chicks that beg more, what stops well-fed chicks from also begging as loudly as hungry chicks? There should be no physiological reason why they could not make as much noise. The puzzle can be resolved when we realise that begging also has a cost. Not only the energy of making the calls but also the attraction of predators. (And remember inclusive fitness. It is not just your own death, but that of your relatives, which is costly to cause.) The same amount of noise made by two chicks, one hungry and one well fed, would presumably be equally harmful in attracting predators. But the benefit of the begging would be greater to the hungry chick. Thus the optimum begging intensity would be greater for a hungrier chick. Paradoxically, it is the cost of making the signal that can keep begging an honest signal of need. (Question—if begging had zero cost what would be the evolutionary consequences of this for chicks and parents in terms of begging intensity and parental response?)
            By using simple figures, the cost-benefit logic underlying this argument can easily be seen. We can also see that if the cost of begging is reduced then the optimum begging intensity rises. One way that the cost can be reduced is via extra-pair parentage. This lowers the relatedness among chicks and so lowers the cost of nest predation to a begging chick, which would value the lives of the other chicks in the nest less. Data support this prediction. Chicks beg more loudly in species in which extra-pair parentage is higher.
            A similar cost-benefit argument can be made for male displays to attract females. Some displays, such as the peacock’s tail, are so elaborate that they actually handicap the male. If the handicap is more costly to make for a low-quality male than for a high-quality male, then the optimum size of the display (handicap) will correlate with male quality. In other words, male display can be a revealing signal of male quality when the display is costly.
            Some signals are honest because they are uncheatable. This is referred to as an index by Maynard-Smith and Harper (2003). For example, larger males may be able to make louder or deeper calls than small males. In many animals, from red deer to toads, deep male calls can deter rivals because a deep call will normally mean that a large male is making them. It is difficult to cheat on body size, although animals can cheat to some extent by inflating their abdomen, puffing out their chest, or making their hair stand on end. In doing this they are trying to look as large as possible, because large size is correlated with fighting ability in males and fecundity in females. In some spiders contests are decided by body size. A resident spider in a web can gauge the weight of an intruder by its effect on the web. Body weight is a reliable indicator of size.

            The book Animal Signals (Maynard Smith & Harper 2003) mainly addresses the question of honesty in communication. It categorises three basic ways that a signal can be honest or reliable.

common interest       e.g. communication within your body, bee dance, pilot & navigator
handicap/cost            e.g. costly chick begging, male displays that are handicaps.
index of quality         e.g. uncheatable indices of size such as the roar of a male red deer

Finally, it is worth remembering that communication can be subject to deception and conflict. The bolas spider attracts male moths by producing the pheromone made by female moths to attract males. Some predatory female fireflies mimic the flashing signal used by females of other species to attract males. These are known as “fire fly femme fatales”. Why do the males allow themselves to be attracted to a predator? Presumably, the predators are rather rare in relation to the legitimate signallers. On average, a male increases his fitness by responding to the signal, even if a small proportion of the signals are deceptive and lead the amorous male to his doom, rather than to a receptive female.

References
See Chapter 9 in Alcock’s Animal Behavior (2009).

See also: Maynard Smith, J., Harper, D. 2003. Animal Signals. Oxford University Press

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Lecture 14: Brood Paratism

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APS209 Animal Behaviour

Brood Parasites

Aims

1. To present the concept of a coevolutionary arms race between brood parasites and their hosts.

2. To describe the biology of cuckoos and experimental tests of the function of behaviour
3. To examine whether the host-parasite arms race is ongoing or in evolutionary equilibrium.

 

Objectives

1. To understand the principles underlying coevolutionary arms races
2. To understand how adaptations and counter-adaptations may be tested in field experiments
3. To understand the importance of studying mechanisms in the study of behaviour

Brood parasites
Brood parasites effectively parasitise the parental care of their hosts. Such parasitism may occur among members of the same species (intra-specific brood parasitism, which is a fairly widespread behaviour among birds) or different species (inter-specific brood parasitism). About 1% of all bird species are obligate brood parasites.

Coevolutionary ‘arms race’
Parasites and their hosts (and equally, predators and prey) are expected to be in a coevolutionary arms race whereby host defences select for adaptations in the parasite, which in turn result in counter-adaptations from the hosts, and so on. Such arms races may reach a stable evolutionary equilibrium of adaptation and counter-adaptation, or may remain evolutionarily dynamic with continuous adaptive change occurring, of which we can observe only a snapshot.

Common cuckoos Cuculus canorus and their hosts
The common cuckoo has about 10 regular host species in the UK. Various features of female egg-laying behaviour have been shown, by experiments, to be adaptive responses to host egg-rejection defences. Among these adaptations is the production of eggs that mimic the host eggs. Thus each female will specialise on a particular host species, with those specialising on a particular host being referred to as a ‘gens’ (plural ‘gentes’), as in ‘reed warbler gens’, ‘meadow pipit gens’, etc.

Hosts have also evolved in response to parasitism, exhibiting a range of egg rejection abilities. Suitable hosts are more discriminating than unsuitable hosts. Furthermore, in places where cuckoos and hosts are sympatric, hosts are more discriminatory than when hosts are not parasitized.

Continuing arms race or evolutionary equilibrium?
Variation among species in egg rejection ability suggest that hosts and their parasites are in a continuing arms race. However, it may not always pay to be a rejector if the costs of parasitism are low, or if the costs of rejection are high. Alternatively, the ability of a host to discriminate may depend on the rejection mechanism.

Reading: see Chapter 12 in John Alcock’s Animal Behavior (2009: pp. 379-419); also Nick Davies’ book: Cuckoos, cowbirds and other cheats (2000; T & AD Poyser, London).
Davies NB & Brooke ML (1988) Cuckoo versus reed warblers: adaptations and counter-adaptations. Animal Behaviour 36: 262-284.
Davies NB & Brooke ML (1988) An experimental study of coevolution between the cuckoo, Cuculus canorus, and its hosts I Host egg discrimination. J. Animal Ecology 58: 207-224.


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Lecture 13: Eusociality

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APS209 Animal Behaviour

Social Insects - Eusociality

Aims

1. To define eusociality and describe its distribution among insects

2. To explain the role of ecological and genetic predispositions in the evolution of eusociality, with particular reference to haplodiploidy
3. To examine sources and outcome of conflicts over reproduction within social insect colonies

 

Objectives

1. To understand the likely evolutionary routes to eusociality
2. To understand the consequences of haplodiploidy for genetic relatedness within colonies
3. To understand potential sources of conflict among queens and workers in social insects

Eusociality – Eusociality describes social systems where there is cooperative brood care, generational overlap, and, critically, sterile castes. Eusociality has evolved independently many times in the Hymenoptera (ants – 9500 spp, bees – 1000 spp. and wasps – 800 spp), and also in Isoptera (termites – 2000 spp.) and Homoptera (aphids). Eusocial species have a dominant ecological presence in most parts of the world, and have evolved remarkable specialisations associated with their social way of life.

Evolution of eusociality – There are two hypotheses for the evolution of eusociality from solitary ancestral forms

     Staying at home: from a solitary parasitoid that guards its nest against parasites, it is proposed that young stayed at home to help their mother defend and build the protective nest. As nests become more elaborate, the benefit of staying and helping raise siblings could outweigh the benefit of independent breeding. Remember that full siblings are as closely related as offspring in diploid organisms, and from the mother’s perspective, offspring are more closely related than grand-offspring.

     Sharing a nest: in many wasps, nests are founded by a group of cooperating females, very often sisters. In primitively social wasps, all females reproduce, but in others one ‘queen’ dominates reproduction, setting the scene for the evolution of workers. The ecological factors leading to shared nesting are probably similar to those described above: predation/parasitism and nest-building costs. Again, relatedness will ensure that non-reproductive females would benefit from the queen’s reproduction.

Contemporary subsocial halictine bees follow the ‘stay-at-home’ model, while parasocial Polistes and stenogastrine wasps follow the ‘share-a-nest’ model.

E.g. Naked mole rats
1 dominant queens and many subservient non-reproductive helpers. When queen dies, females fight over succession.

Haplodiploidy
The Hymenoptera exhibit haplodiploidy: males develop from unfertilized eggs and are haploid; females develop from normally fertilized eggs and are diploid. Males form gametes without meiosis, so all his sperm are identical, while females form gametes through meiosis, as is usual in sexually reproducing organisms. This has important consequences for relatedness among individuals in the colony.

To calculate relatedness, draw a pedigree linking two individuals through their recent common ancestors. Draw arrows along the pathways and indicate alongside each pathway the probability that a copy of a gene will be shared. Remember that two individuals may differ in their perspective on mutual relatedness. See lecture slides on MOLE for other examples.

Relatedness among close relatives in a haplodiploid species.

               mother             father               sister                brother             daughter          son
Female     0.5                   0.5                   0.75                 0.25                 0.5                   0.5
Male         1                      0                      0.5                   0.5                   1                      0

In hymenoptera, workers are always female. In diploid termites they may be either sex. In eusocial aphids, colony members are clonal (genetically identical). Haplodiploidy results in interesting conflicts among colony members over reproductive options.

Conflicts over sex ratio
Queens are equally related to sons and daughters and so should invest equally in reproductive sons and daughters (1:1 ratio of investment). Workers are more closely related to sisters (0.75) than brothers (0.25) and so prefer to invest more in sisters (3:1 ratio of investment). Workers are more closely related to fellow workers and future queens than to own offspring.

A comparison across 21 ant species by Trivers and Hare (1976, Science 191: 249-263) suggested that workers win this conflict. But, preferred sex ratio of each party will also be influenced by:

(a)  Local Mate Competition - if sons compete with each other for matings it should pay to produce fewer of them, e.g. fig wasps

(b)  Queen mating frequency – if a female mates with multiple males, workers will be less closely related to each other, on average.


References

See Chapter 13 in Alcock’s Animal Behavior (2009). See also Chapter 13 in J.R. Krebs & N.B. Davies Introduction to Behavioural Ecology, 3rd edition (1993).

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Lecture 12: Cooperative Breeding

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APS209 Animal Behaviour

Cooperative Breeding

Aims

1. To present the two-stage ecological constraints model for the evolution of cooperative breeding

2. To explain the role of ecological and demographic factors in constraining reproduction
3. To examine the potential direct and indirect sources of inclusive fitness for helpers

 

Objectives

1. To understand the principles underlying the ecological constraints hypothesis
2. To understand how predictions of the ecological constraints hypothesis have been tested
3. To understand the alternative routes to fitness for helpers

Cooperative breeding - Some individuals forego personal reproduction and spend all or part of their lives helping others to breed. The great majority of cooperative systems are kin-based and these breeding systems are therefore likely to provide examples of kin-selected behaviour. The social organisation of cooperative breeders varies widely, with a continuum of social organisation encompassing: 'helpers-at-the-nest'  where breeding pairs are aided by one or more helpers,  usually offspring of previous broods, and 'plural breeders' where communal nests have several breeders of one or both sexes.

Evolution of cooperative breeding - The ecological constraints hypothesis (aka the habitat saturation hypothesis) envisages the evolution of cooperative breeding as a 2-stage process:
     Stage 1. Ecological factors (no suitable breeding territories available) and/or demographic factors (no breeding partners available) constrain independent breeding causing grown young to delay dispersal and 'stay at home' on their natal territory. Observational evidence provides some support, but the best evidence comes from removal experiments: e.g. superb fairy wren Pruett-Jones & Lewis 1990, Nature 348:541-542). However, reproductive constraints are widespread, comparative studies have been inconclusive, and other factors may be important, e.g. phylogeny.
     Stage 2. Fitness benefits of helping exceed those of not helping, so young who have delayed dispersal help relatives to raise later broods.

What are the fitness benefits of helping?
            (a) Direct fitness - fitness component resulting from personal reproduction.
-       increased survival of helpers through group benefits – ‘group augmentation’, e.g. reduce predation risks, share resources
-       increased probability of future breeding, e.g. territory or mate acquisition/ inheritance
-       increased experience of parental care ('skills' hypothesis)
-       direct reproduction

     (b) Indirect fitness - fitness component from increased production of non-descendant kin.
-       increased reproductive success of relatives (genetic benefits through raising siblings which share 50% of genes)
-       increased survival of related breeders through reduced reproductive costs
                
The relative importance of indirect or direct fitness benefits in the evolution of helping behaviour is still debated

References

See Chapter 13 in Alcock’s Animal Behavior (2009). See also more detailed accounts in Cockburn A (1998) Evolution of helping behaviour in cooperatively breeding birds, Annual Review of Ecology & Systematics 29: 141-177. Emlen S.T. (1991). Evolution of cooperative breeding in birds and mammals; in J.R. Krebs & N.B. Davies (eds), Behavioural Ecology, 3rd edition.

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Lecture 11: Mating Systems

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APS209 Animal Behaviour - Mating systems

Aims

1. To present the concept of mating systems and the relative reproductive potential of the two sexes.

2. To illustrate the role of ecology and paternal care in determining mating systems
3. To demonstrate the prevalence of sexual conflict in mating system evolution.

 

Objectives

1. To understand a general model of mating system evolution
2. To understand the role of ecology and parental care in mating system evolution
3. To understand the basis for sexual conflict over emergent mating system and its outcome.

Mating systems
Includes description of: copulation behaviour, social organization, parental care system, and pattern of competition for mates. Results in monogamy, polygyny, polyandry, and promiscuity, but social mating system does not always reflect genetic mating system (e.g. extra-pair paternity in monogamous birds). There are consistent taxonomic differences in mating systems

Male and female reproductive potential and a general model
Male reproduction is limited principally by access to mates, while females reproduction is limited by access to resources. Therefore, we can construct a general model:

Ecology, e.g. resources,         ->         Female dispersion     ->      Male dispersion
predation, etc

Males may compete directly to monopolise females or they may try to monopolise the resources that females need for survival and reproduction.

Ecology and mating systems
The general model for the evolution of mating systems predicts that mating systems should reflect female dispersion and resource distribution. This model is supported by a comparative study of mammals by Clutton-Brock (1989, Proceedings of the Royal Society of London, Series B 236: 339-372). Mating systems from monogamy to lekking can be explained using just three female parameters: group size, range size and breeding synchrony.

Mating systems with male parental care
When males care for offspring, they become an important resource for female and his reproductive potential is reduced. The identity of the competing sex depends on relative reproductive rate (see Clutton-Brock & Vincent 1991 Nature 351: 58-60)

Most birds are socially monogamous with biparental care. However, monogamy is usually facultative rather than obligate. When one sex deserts, it is usually male because they have greater opportunity for desertion (internal fertilization), and more to gain (higher reproductive rate). In many cases monogamy results from limited opportunity for polygamy, due to competition among males and/or females.

Sexual conflict over mating systems
Males usually prefer polygyny and females may prefer polyandry over monogamy if they get better resources or good genes. Therefore, in many species, monogamy occurs not because both sexes do best but because of conflict within and between the sexes. For example, males compete for females and may be unable to defend >1 at a time. Alternatively, females may enforce monogamy on males.


Reading: see Chapter 11 in John Alcock’s Animal Behavior (2009: pp. 379-419); also Nick Davies’ chapter on Mating Systems in Krebs JR & Davies NB (eds) Behavioural Ecology 3rd edn, Blackwell.

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Lecture 8,9 and 10: Mathematical and Theoretical Insights in Animal Behaviour

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APS209 Animal Behaviour

Mathematical and theoretical insights in animal behaviour
 Aims

1. To introduce the use of simple mathematics in the study of animal behaviour.

2. To show how to combine mathematics with biology.

Objectives

1. Understand the use of figures and equations to express mathematical ideas in biology.
2. Understand how to combine mathematics with biology.
3. Lose fear of a mathematical approach in biology by being able to follow some simple models.

This lecture on mathematical and theoretical insights will introduce you to the use of maths in biology in the context of important questions in animal behaviour. No mathematical background beyond GCSE is necessary. The material will cover two topics. 1. Inclusive fitness theory; 2. Game theory.

To maximize the number of copies of genes in the next generation, an individual can:
1)    Produce as many offspring itself
2)    Help to raise siblings/ offspring of siblings

1. Inclusive fitness theory
The slides provide the information to understand this section. We first consider Hamilton’s rule (Inclusive Fitness Theory) in the context of cannibalism by tiger salamanders, following up on the research by David Pfennig (see Alcock pp 95-96) showing that salamanders are less likely to be cannibalistic when in a tank with siblings versus unrelated individuals. We can consider cannibalism to be a social action (i.e., directed at members of the same species in your environment) and determine how variation in relatedness between individuals, and the cost and benefit of the action to actor and recipient influence whether natural selection will favour carrying out that action or not.
            Hamilton’s Rule states that a social action is favoured by natural selection if c < b.r, where c is the cost to the actor (reduced fitness) and b the benefit to the recipient (increased fitness), and r is their genetic relatedness. For example, giving food to another animal will have a survival cost to the actor and so will only be favoured by natural selection if the receiving individual is kin (r positive). Note however, that costs and benefits can be negative. Stealing food is also a social action. Who should actors steal from? In this case the “cost” is negative, and the “benefit” is also negative. Hamilton’s rule is more likely to be satisfied (i.e., stealing is favoured by natural selection) if actors steal from non-kin (r = 0).

2. Game Theory: Introduction and sex ratio

Human sports come in two main kinds. In one type, it is you against the clock or some physical challenge. For example, climbing a mountain or running 100m in the shortest possible time. In the other type, you are playing directly against an opponent. For example, in tennis the best place to put the ball is where your opponent isn’t. In tennis you have to adjust your game according to the opponent’s behaviour. Similar things happen with animals. Many of the challenges facing animals do not depend upon what other animals are doing: a bird migrating alone across the sea, for example. But many of the challenges faced by animals are more like a game of tennis. The best place for a male to find a female may be where there are few other competing males. The best place to find food may be where there are few other foragers. Thus, the fitness benefits of behaviours often depend upon what others are doing.
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. At more of 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).
On receiving the Kyoto Prize for evolutionary biology in 2001, Maynard Smith commented “I have devoted most of my life to trying to apply mathematical reasoning, for example, Game theory, to biology. Trivial as it may seem, mathematics is of great use in biological studies. This is because verbal models can be interpreted in different ways, depending on who the reader is. Any theory to explain the complicated activities of organisms must always be simple. I felt the greatest happiness in finding that my theory, which I had elaborated after the most tenacious thinking, proved to be correct as some animal turned out to be doing something odd that the theory predicted.” [www.inamori-f.or.jp]. Using game theory in biology can be very mathematical. But it can also have zero or very little mathematics. In these lectures on game theory we will stick to the latter. As Maynard Smith (2002) notes, any theory investigating something as complex as animal behaviour must be simple.

Sex ratio

It is perhaps surprising to think of a sex ratio as a behavioural strategy. But consider a female who can choose the sex of her offspring. Should she choose males or females or both? If most parents are producing daughters then it is best to produce sons, because on average a son will produce more sets of grand-offspring for his mother. If most parents are producing sons, then it is better to have daughters. But when half of the offspring in the population are sons and half are daughters, then offspring of either sex give a mother the same number of grand-offspring. In other words an equal sex ratio is an ESS (evolutionary stable strategy). It cannot be “invaded” by a better strategy. An equal sex ratio is a “Nash equilibrium” (after the Princeton scientist who devised it in his PhD research and for which he was awarded the Nobel prize for Economics many years later. In a Nash equilibrium, the optimum strategy is its own best reply.) That is, the best reply in a population where every female is producing equal numbers of sons and daughters is to do the same yourself.
            A little simple maths will make things clear (see also the slides). Assume that every female has n surviving offspring. Each daughter, therefore, results in n grand-offspring. How many grand-offspring will a son provide? If there are equal numbers of males and females in the population, then each son, on average, will have one mate. So each son will also provide n grand-offspring. But imagine that there are twice as many females as males in the population. Each son will now mate with two females, on average. So each son provides 2n grand-offspring. This shows that if the sex ratio in the population is female biased, then a female having sons will have greater fitness (grand-offspring) that a female having daughters. Likewise, if the sex ratio is male biased, a female having daughters will have higher fitness than a female having sons. In this way, selection tends to cause an even sex ratio.
            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. 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.

3. Game Theory: Hawk-Dove and Hawk-Dove-Bourgeois games and cyclical dynamics.
In the sex ratio game, the contestants (mothers choosing sex of offspring) were all playing each other, which is known as playing the field, as matings take place panmictically. However, many contests may take place between paired opponents, (pairwise contests). For example, if two individuals are contesting ownership of a resource, which forms the next series of examples.
Animals often fight over resources such as food or females. But not all do. Often, one animal quickly backs off. For example, in the speckled wood butterfly, a resident male always wins an encounter with a non-resident over the possession of a sun patch, a location where mating can occur. Traditionally, it was considered that such non-aggressive contests were for the good of the species. But game theory analyses have shown that non-aggressive contests can be explained via their benefits to the individual. Sometimes it is selfishly better to be less aggressive.
Consider a resource with a fitness value of v to whoever controls it. The resource might be a feeding or mating location. We will consider that animals compete for discrete resources in pairs and can have just two behavioural strategies: Hawk and Dove.

Focal
individual

What happens in a pairwise contest over the resource

Opponent
Fitness payoff to focal individual
Hawk
Always fights. Always wins if opponent is Dove, and without paying the fighting cost. Wins half the time if opponent is Hawk but pays fighting cost half the time if it loses.
Dove
Hawk
v
(v - c)/2    on average
Dove
Never fights. Shares resource if opponent is Dove, but always loses resource if opponent is Hawk. Never pays the fighting cost.
Dove
Hawk
v/2
0

Hawk always wins when paired to a Dove. So it would seem that the Dove strategy should be replaced by the Hawk strategy if both occur in the population. But Hawk pays a fighting cost, c, when it pairs up with another Hawk. Dove does not pay this cost because it never fights. Could this make Dove a winning strategy?
Consider a population of Doves with a lone Hawk. (We say that the rare strategy is “invading”.) The Hawk can only pair with a Dove so the rare Hawk’s payoff is always v. The payoff of most Doves, who pair with other Doves, is v/2. This shows that Hawk can invade Dove because the rare Hawk has a higher payoff than do Doves.
Now consider a population of Hawks with a lone Dove. The Dove can only pair with a Hawk so the rare Dove’s payoff is 0. The payoff of most Hawks is (v-c)/2. This is < 0 when c > v. So Dove can invade Hawk if c > v. That is, when there is a high fighting cost (greater than half the value of the resource being fought over). In essence, the resource is not worth the fight because there can only be one winner (hence the benefit is v/2 not v).
In general, there are two conditions of cost and benefit that determine the best strategy to use.
c > v      Dove can invade Hawk. We already know that Hawk can invade Dove (because we assume that v > 0, that is the resource has some positive value for survival or reproduction), so this means that each strategy can invade a pure population of the other. What we end up with is a “mixed ESS” (Evolutionarily Stable Strategy) in which both strategies are present in the population. The exact proportions depend on the values of c and v. At the mixed ESS the fitness of individuals playing each strategy will be equal. Hawks pass on as many copies of their genes as Doves.
c < v      Dove cannot invade Hawk. As we know that Hawk can invade Dove this means that Hawk forms a “pure ESS”. The Dove strategy cannot persist. If it occurs in a population, and a rare mutant Hawk occurs, then Hawk will replace it (referred to as go to fixation).
The Hawk–Dove game is not meant to be a realistic model of any real animal population. But it gives some important insights. It shows that a non-fighting strategy can persist even when fighters occur, and that a population can have animals playing two different strategies, each having equal fitness. The two strategies do not have to be genetically determined, and in a mixed ESS each individual could play both strategies. For example, if the mixed ESS was 40% Doves, then this could come about by 40% always being Doves and 60% Hawks, or via each individual playing both strategies at different times such that, across all contests, 40% of the plays were Dove. 
            The payoffs to the different strategies are often put into a payoff matrix. In the matrix below (don’t be put off by the word matrix—it just means a table), the payoffs relevant to a population with a rare Dove are in column 1 (i.e., Dove can only pair with Hawk). The payoffs relevant to a population with a rare Hawk are in column 2 (i.e., Hawk can only pair with Dove). For example, cover up column 2 with your finger. This means that the only possible opponent is a Hawk (i.e., everyone is a Hawk except for one Dove, who cannot have itself as an opponent). The payoff to the rare Dove is 0 and to the Hawks is (v-c)/2. This shows the condition under which Dove can invade is 0 > v-c, which is the same as c > v (i.e., cost is greater than victory) Now cover up column 1. This means that the only possible opponent is a Dove (i.e., everyone is a Dove except for one Hawk, who cannot have itself as an opponent). The payoff to the rare Hawk is v and to the Doves is v/2. As v > 0 (i.e., the resource is worth something) this shows that the Hawk can invade a population of Doves.

Payoff Matrix for the Hawk-Dove Game. The payoff is the change in fitness of a focal individual who is playing either Hawk or Dove when paired to an opponent who is playing either Hawk or Dove.

Focal Individual’s Strategy                  Opponent’s Strategy
                                                            Hawk (col. 1)  Dove (col. 2)  

            Hawk                                       (v-c)/2             v
            Dove                                       0                      v/2
                                                                                                           

Further strategies
Are Hawk and Dove the only possible strategies? No, they are not. Maynard Smith (2002) discusses some additional strategies, such as ‘Retaliator’ (plays Dove initially but fights back if opponent fights), ‘Prober-Retaliator’ (occasionally fights but backs down if opponent fights), ‘Bully’ (always start by fighting but back down if opponent fights) and ‘Bourgeois’ (see below).

Hawk-Dove-Bourgeois and the speckled wood butterfly (Alcock pages 278-279).       Note: For the exam, you do not have to understand the maths behind the H-D-B game but you do have to understand the maths behind the H-D game.

Maynard-Smith considered various other strategies and the one that seemed the most successful in many situations of pairwise contests is Bourgeois, which is better than both Hawk and Dove and can form a pure ESS. That is, everyone plays Bourgeois. Bourgeois also seems to be quite common in nature. A good example of theory leading the way.
            In some animal contests, the strategy of an animal depends upon whether it is a resident or not. Thus, male speckled wood butterflies can be either Hawks or Doves. They play Hawk when they are the resident/owner of a sun patch, but play Dove if they are the non-resident/intruder. Normally, when an intruder enters the patch of another male butterfly, the resident flies up and chases him away. The resident always wins after a short spiral flight. The intruder does not contest. However, it is possible to have two residents. For example, by experimentally moving one resident to the sun patch of another resident so that both think that they are the resident. When they see each other, they both play Hawk and this results in an “escalated” contest—a long spiral chase into the tree tops. (The speckled wood is a common butterfly and it is easy to see these behaviours.) So it seems that a butterfly plays Hawk when resident and Dove when non-resident. This particular strategy has been called Bourgeois, in reference to property owning people and their determination to hang on to their house. It would perhaps have been more immediately obvious if the strategy name Owner had been used instead of Bourgeois. How can we build upon our analysis of the Hawk-Dove game to include Bourgeois? First, the basics…

Focal
individual

What happens in a pairwise contest over the resource

Opponent
Fitness payoff to focal individual
Hawk
Always fights. Always wins if opponent is Dove, and without paying the fighting cost. Wins half the time if opponent is Hawk but pays fighting cost
Dove
Hawk
Bourgeois
v               (as above)
(v-c)/2      (as above)
(3/4)vc/4  (note 5)
Dove
Never fights. Shares resource if opponent is Dove, but always loses resource if opponent is Hawk. Never pays the fighting cost.
Dove
Hawk
Bourgeois
v//2           (as above)
0               (as above)
v/4            (note 4)
Bourgeois
Plays Hawk when resident and Dove when non-resident
Dove
Hawk
Bourgeois
(3/4)v       (note 3)
(v-c)/4      (note 2)
v/2            (note 1)

Note 1 Assume that when two Bourgeois meet, one is the resident and one the non-resident so there is no fighting. On average, individuals are resident half of the time so the average payoff is (v + 0)/2 = v/2.
Note 2 When Bourgeois is resident it plays Hawk to an intruding Hawk and gets a payoff of (v-c)/2. When Bourgeois is non-resident it plays Dove when intruding on a Hawk and gets a payoff of 0. On average individuals are resident half of the time so the average payoff is ((v-c)/2 + 0)/2 = (v-c)/4.
Note 3 When Bourgeois is resident it plays Hawk to an intruding Dove and gets a payoff of v. When Bourgeois is non-resident it plays Dove when intruding on a Dove and gets a payoff of v/2. On average individuals are resident half of the time so the average payoff is (v + v/2)/2 = (3/4)v.
Note 4 When Dove plays Bourgeois it gets a payoff of v/2 when it is resident and Bourgeois is intruder, because both play Dove.   When Dove is non-resident it has a payoff of 0 when intruding on Bourgeois, who plays Hawk. On average, Dove individuals are resident half of the time so the average payoff is (0 + v/2)/2 = v/4.
Note 5 When Hawk plays Bourgeois it gets a payoff of v when resident and Bourgeois is intruder, because Bourgeois plays Dove. When Hawk is non-resident it has a payoff of (v-c)/2 when intruding on Bourgeois, who plays Hawk. On average, Bourgeois individuals are resident half of the time so the average payoff is (v + (v-c)/2)/2 = (3/4)vc/4.

Payoff Matrix for the Hawk-Dove-Bourgeois Game. The Payoff is the change in fitness of a focal individual who is playing either Hawk, Dove or Bourgeois when paired to an opponent who is playing either Hawk, Dove or Bourgeois.  

Focal Individual’s Strategy                                          Opponent’s Strategy
                                                            Hawk (col 1)   Dove (col 2)    Bourgeois (col 3)                    

            Hawk                                       (v-c)/2             v                      (3/4)v c/4
            Dove                                       0                      v/2                   v/4
            Bourgeois                                (v-c)/4             (3/4)v               v/2
                                                                                                                                                           

From the matrix above we can determine whether the Bourgeois strategy is an ESS, that is whether it gives a higher payoff than playing either Hawk or Dove. The first question is, can Bourgeois invade a population of Doves? From Column 2 we can see that the payoff to Bourgeois from playing against Dove, (3/4)v, is greater than the payoff to Dove when playing Dove, v/2. Thus Bourgeois can invade Dove. The second question is, can Bourgeois invade a population of Hawks? From Column 1 we can see that the payoff to Bourgeois from playing against Hawk is (v-c)/4 whereas the payoff to Hawk from playing against Hawk is (v-c)/2. The payoff to Bourgeois is greater than that to Hawk if v < c. Thus, Bourgeois can invade Hawk if v < c. Finally, if everyone plays Bourgeois, can this be invaded by Hawk or Dove? Column 3 shows that the payoff to Hawk, Dove and Bourgeois when playing Bourgeois are (3/4)v – c/2, v/4, v/2, respectively. Clearly, Dove is always worse off than Bourgeois, as v > 0, and Hawk is worse off than Bourgeois if v < c. The final condition is also the same as the condition that allowed Bourgeois to invade Hawk. In summary, Bourgeois can always invade Dove and is resistant to invasion by Dove, and can invade Hawk and is resistant to invasion by Hawk if v < c.
            This “Resident wins” situation is called a conventional settlement. In other words, who wins is decided by convention. It is logically possible to have the opposite convention, non-resident wins, being the ESS. There are a few examples of this. It is also possible that who wins is decided by some asymmetry in resource holding power, such as “Bigger wins”. In the case of the speckled wood it seems that there is also some asymmetry in resource holding power as the resident, who has been sunning himself, may have higher body temperature.

Further insights from game theory

The above examples will provide you with a start to understanding the use of mathematics in the study of animal behaviour. Game theory has also made numerous other insights. For example, some games may have cyclical dynamics, with one strategy invading another, then being invaded by a third strategy which in turn is invaded by the first strategy. This is similar to the children’s game Rock, Scissors, Paper. Rock beats scissors, paper beats rock, and scissors beats paper. Amazingly enough, cyclical dynamics has been found in the reproductive behaviour of lizards, Uta stansburiana (Sinervo, B. Lively, C. M. 1996. Lizards play rock-scissors-paper. Nature 380: 240-243). Maynard Smith (1998 p. 130-131) describes the situation in the following way. “Male...lizards have one of three mating strategies. Orange-throated males establish large territories, within which live several females. A population of such males can be invaded by males with yellow throats: these “sneakers” do not defend a territory, but steal copulations. The orange throats cannot defend all their females. However, a population of yellow-striped males can be invaded by blue-throated males, which maintain territories large enough to hold one female, which they can defend against sneakers. Once sneakers become rare, it pays to defend a large territory with several females. Orange males invade, and we are back where we started. In the field, the frequencies of the three colour morphs cycled with a period of about 6 years.”

Synopsis of the behaviours seen among male morphs
The following descriptions are taken from Barry Sinervo’s website. If you go to this website you can see video clips of the behaviours of different male types on encountering each other.
http://bio.research.ucsc.edu/~barrylab/classes/animal_behavior/video_only.html

Yellow-Throated Sneaker Male Behaviour
Yellow males are "sneakers" in that they mimic the throat colour of receptive females, and yellows also mimic female behaviour. When a yellow male meets a dominant male, he pretends he is a female -- a female that is not interested in the act. The head bobs ("vibrations") involved in actual female rejection behaviours are of very high frequency compared to the low frequency aggressive challenge displays shown by aggressive males. In many cases, females will nip at the male and drive him off. By co-opting the female rejection display, yellow males use a dishonest signal to fool some territory holding males. The ruse of yellows works only on orange-throated males.

Blue-Throated Male Behaviour
Blue males are not fooled by yellows. Blue males root out yellow males that enter the territory of the blue male. Blue males are a little more circumspect when they engage another blue male during territory contests. Blue males spend a lot of time challenging and displaying, presumably allowing males to assess one another. Attack may or may not follow as blue males very often back down against other blue males. Indeed, neighbouring males use a series of bobs to communicate their identity, and the neighbours usually part without battle.

Orange-Throated Male Behaviour
Orange males are ultra-dominant and very aggressive owing to high levels of testosterone, and attack intruding blue males that typically have more modest levels of testosterone. Attacks by orange males on blue males do not involve the ritualized head bobs that are seen when blue males engage blue males, orange males just attack with little advanced warning. When an orange male encounters a more equally matched orange male, they are both a little more circumspect, and they will not necessarily attack one another (as is seen when blue meets blue).

Summary

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.

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