Sex

(the ratio of males to females)

Ratio

ChromosomesIn humans and most other mammals, sex is determined by the X and Y chromosomes.

Females have two X chromosomes, and males have one X and one Y chromosome.

When offspring are produced, there is a 50/50 chance that the male will contribute the Y chromosome and produce a male offspring, as opposed to contributing the X chromosome and producing a female offspring.

But this is too simple.

Half the offspring will be male, and half will be female.

In some reptiles, sex determination is temperature dependent: the temperature of the eggs during incubation determines the sex.

For example, American alligators incubated at 27.7° – 30°C will be female, while those incubated at 32.2° – 33.8°C will be male.

In the wild, American alligators have an overall sex ratio of five females to one male.

The Cleaner Wrasse is a tiny fish that cleans parasites off larger fish.

They are born with only one male in a group of 6 – 8 females. If the male dies, the largest female turns into a male.

The largest in the group turns into a female, and the second largest develops reproductive ability as a male.

Clownfish are all born as nonreproductive males.

They live in a group inhabiting a sea anemone.

In mammals, females have some “control” over which sperm succeed in fertilizing eggs. This may occur through subtle chemical changes which favour one kind of sperm.

As a result, the 50:50 sex ratio determined by the X and Y chromosomes is not what actually happens.

In humans, more males are born than females in most cultures.

But more males get themselves killed before they mature.

Females live longer, on the average, so among seniors, there are more females than males.

Presumably, the proportions are equal at some intermediate age.

Under 15 years old

Red – more malesBlue – more females

Total Population

Red – more malesBlue – more females

Over 65 Years Old

Red – more malesBlue – more females

Fisher’s LawThe simple version of Fisher’s Law is that we should after all expect a 50/50 sex ratio.

Consider a population with more females than males.

On the average, each male passes on more copies of his genes than does each female: twice as many in this example.

If a parent can control the sex of her offspring, she would do better to produce males. More of her genes will be passed on to her grandchildren if she does so.

The genes to produce a higher proportion of males will be favoured, and gradually the population will start producing more males.

But this effect will diminish and cease as the population approaches a 50/50 sex ratio.

Exactly the same argument applies in reverse if there are more males than females.

Any genes which lead to the production of a higher proportion of females will be favoured, and gradually the population will start producing more females.

Again the effect will diminish and cease as the population approaches a 50/50 sex ratio.

However, while they do not agree on the details, the experts do accept that in humans, more males are born than females. A commonly cited figure is that the excess of males is 7% or 8%, i.e., that 107 — 108 males are born for every 100 females.

Why?

A simple answer appears to be that males have higher mortality; this too is generally accepted.

So perhaps the excess at birth is exactly what is needed to offset the juvenile mortality, so that by the time they are ready to breed, the numbers are equal.

Ronald Fisher proposed a slightly more subtle argument.

Parents “invest” in their young, especially through the resources they commit to caregiving.

Consider the moment at which all parental care ceases.

Evolution will favour genes that make the optimal use of the resources that parents invest in offspring. It will cause the population to evolve towards a situation in which the value of each parent’s investment is optimal.

At that moment, the total “value” of all the male offspring must equal the total “value” of all the female offspring, because each group will go on to contribute exactly half of the genes passed on to future generations.

So the numbers of males and females at that moment should be equal.

Otherwise, by the kind of argument outlined above, there would be an advantage to producing more of whichever sex was in the minority.

This combined with higher juvenile mortality for males explains why more males should be born than females.

Evolution will cause the population to evolve towards a situation in which the numbers of males and females are equal at the end of the period of parental care.

Ronald Fisher’s work on this and related questions became the beginnings of the subject now known as population genetics.

However, Fisher also held some views that by today’s standards are rather suspect.

In addition to rejecting claims about health risks from tobacco, he was a staunch supporter of eugenics.

He also expressed views about racial differences that were controversial in his day and would be almost totally unacceptable today.

The above discussion presents evolution in terms of “optimizing” the behaviour of individuals.

Selection will favour genes that behave in an optimal way, so the population is expected to move towards such behaviour.

If we want to understand what happens, we can try to solve the optimization problem ourselves, and figure out what the optimal behaviour is. Then we can test our results against experiment and observation.

This general idea is the beginning of the mathematical study of evolution, and in particular of the use of “game theory” as applied to evolution.