On the Balance of Nature

Fattah Fathun Karim
15 min readAug 23, 2020


How many men are there to women?

Depends on who you ask.

If you ask hardline religious people like Dr. Zakir Naik, you will find the answer that females greatly outnumber males in nature everywhere, except for places where female infanticide is practiced like india, china etc. They outnumber males so greatly, that men has to practice polygamy, which is taking more wives for oneself, to ensure that the surplus women don’t become public properties. This is a very obnoxious thing to say, but as professor Zakir have put, this is the most sophisticated word he could say to explain the scenario. The overabundance of women in the wedding market, inevitably turns them into public properties or put in another way, a sexual object for the masses to enjoy.

But why am i quoting a preacher with regards to a scientific inquiry? Seems odd, and inappropriate. I know. I get your concerns. But the fact is that, such opinions are ingrained in the minds of millions of people, given the state of such preacher’s influences. Also it provides the lustful men a justification to take in more brides in terms of religion, since religion is deemed to be the highest moral authority by the most.

If you take a little time and bother yourself to check the statistics, you will see a completely different picture. The male to female population ratio is fairly balanced with approximately 1:1 ratio. Its not precisely balance, like exactly equal in number. But the ratio is fairly balanced with a rounded 1:1 ratio in terms of single digit. According to world bank’s report, the number of males in the world was reported to be 3.867 billions whereas the number of females in the world was reported to be 3.803 billions as of the year 2019. The global average of male to female thus tend to converge falling into a 50.416:49.584 ratio. Although the distribution is not the same in terms of age, country, race, ethnicity, subcultures, religion etc, but the tendency to reach towards an equilibrium state is quite evident, so evident that it starts to feel uncanny. It feels like some invisible hand is making sure the balance is kept intact.

But is there actually any need for a conscious control so that the sex ratio stays balanced among humans? Not just humans, but in most of the animal species similar characteristic is observed, that is, a balanced sex ratio. So what could be actually dictating the direction of this process?

Allow me to introduce you to our forever ignored friend in the nature department, Maths!!!!!

We’ve all heard about probability at some part of our life. Toss a coin, what do you get? You get either a head, or a tail, and what’s the probability of each of this options to occur? Its a 50–50 chance. a 50% probability for head, a 50% probability for tail. the formula went like this,

Now, lets start tossing coins. For this i will take the help of the following website, and their interactive coin toss simulation service.

In my first toss, i got a tail. The service lets you see list of cumulative results, ratios which would soon come to our use.

1st test toss

We got a tail, making the ratio of tail to head 100:1

Let’s start to increase our toss count. let’s make it 4.

2nd test toss. total 4 toss

the ratio dropped to 75:25 for tail to head.

Lets increase more.

3rd test, 10 tosses in total

the ratio came to 70:30. both sides seemingly are trying to come forth each other.

Now, for 100 toss.

4th test. 100 toss

check how both of the numbers are slowly moving towards each other with the increasing number of tosses.

Now for a 1000 toss,

5th test, 1000 toss.

For 10000 toss,

6th test, 10000 toss

For 1001000 test, (pardon the extra 1000, the application doesn’t allow erasure of accidental tosses ).

7th test, 1001000 toss

We can notice a trend from these tests, that the results start to converge with the increasing count of tests. This is what happens when large number of samples or iterations are incorporated in an event having totally random results. This is a popular phenomena in probabilistic theory, known as LLN or Laws of Large Numbers.According to the law, the average result of a large number of trials should come close to the expected value, and come even closer as the trials are increased. Expected value here intuitively signifies the generalization of weighted average, or the arithmetic mean of the large dataset.

LLN visualization

Now considering two biological sexes, that is two possible outcome of childbirth, male and female. We can bring the coin toss analogy to the nature department. Notice how just one-tenth of a million dataset took us towards the expected value in the coin toss tests. Although practically speaking it doesn’t even need that much. in 1000 coin toss we in fact started to reach converging point. Looking at the LLN graph, it shows less than 100 can even yield results close to expected value. If that is the case, imagine how the results would behave for 7.674 billions of data, which is the global population count as of 2019. It will undoubtedly come to converge.

Therefore, even in other species, apart from homo sapiens, we see similar LLN trends. And see a balance in their numbers. Therefore it really doesn’t require an overseer to steer things into balance, but just simple unconscious mathematics.

Apart from mathematics, there are some biological drives towards equilibrium as well. Evolutionary stable strategy being one of them. This strategy is basically an appropriation of Nash equilibrium from Game Theory, which states that in a non-cooperative game individual players always adopt the strategies which works the best in response to their opponents moves (assuming each player are aware of their opponent’s strategies), and changing strategies until their opponent changes theirs won’t aid them in increasing their own payoffs. In nature, once a trait is adopted by a certain population, it would remain the same since against natural selection it fared the best so far for the population’s existence. Natural selection would eliminate all mutative strategies thereby, keeping an equilibrium state for the whole population. The balanced sex ratio is the evolutionary stable strategy as well for most of the animal species. To understand why so, we got to understand Fisher’s principle. In his 1930’s book “The Genetical Theory of Natural Selection”, Ronald Fisher argues that an approximate sex ratio of 1:1 is the evolutionary stable strategy for most animals. W.D Hamilton who outlines the process in a more concise manner,

Suppose male births are less common than female.

A newborn male then has better mating prospects than a newborn female, and therefore can expect to have more offspring.

Therefore parents genetically disposed to produce males tend to have more than average numbers of grandchildren born to them.

Therefore the genes for male-producing tendencies spread, and male births become more common.

As the 1:1 sex ratio is approached, the advantage associated with producing males dies away.

The same reasoning holds if females are substituted for males throughout. Therefore 1:1 is the equilibrium ratio.

Following Fisher’s theories, came MacArthur who proposed to look into this issue from the perspective of Game Theory. W.D Hamilton picked it up from there and termed the equilibrium point as “unbeatable strategy”. From then on John Smith and George Price coined ESS, or Evolutionary Stable Strategy which lays out the point that, for a given population, invading mutations don’t sustain against natural selection, unless they had some greater advantage to offer. Fisher was aware of one fact that male births tended to be higher. He reasoned it like this — Higher frequency of males die at infancy or before reaching the ability to mate or procreate, which eventually cancels out the surplus male births and reducing the passing of the genes favoring male births.

But wait, weren’t our births random coin toss occurrence, where the results (head or tail) are completely independent from each other?

This is true only if the other factors aren’t in play. If there are other factors in play, then there would be extra parameters in the equation, the calculations would not be totally independent, as what LLN requires. For LLN theory to work, it requires complete independence. But sadly, sex ratio is not a completely random occurrence, or in other words, it isn’t actually totally independent. We already saw how fisher’s theory, and ESS influences sex selection in childbirth. in coin toss there are no such ESS factors which influence head or tail occurrences. There are a good bunch of other factors which influence the sex ratio as a whole. In case childbirth, the ratio is more inclined more to males offsprings than females. Not a single column in the wiki entry shows a ratio below 1 for childbirth cases. Through the link below you can navigate to the whole stat as presented in wikipedia.

The reasons for this may vary. Climate for example is one of those reasons. A study carried out by catalano, bruckner and smith found out that ambient temperature plays some role in determining sex selection. Their team found out that a degree rise in temperature causes 1 extra male birth per 1000. Other researches, for example, a study conducted by Helle, Samuli and others found that warm periods and excessive stressful periods like in world war situations, male births peaked compared to female births. Although unclear, gestational environments are also reported to have influences on sex selection of the child. Like gestational stress, or maternal malnutrition might be a cause to increased death of male fetuses which lower down the sex ratio eventually. Chemicals like dioxins are reported to have influenced increased female proportions, along with other chemicals like PCB and DDT, which are well known endocrine disruptors, causing abnormally low sex ratio in some villages of greenland and canada. Although environmental factors are highly debated in academia and also vaguely understood but nonetheless, some aberrations in the sex ratio is quite apparent from places to places.

Researches looked into age factors as well. A research by Bernstein et. al concludes that the higher birth ratio might be a result of males procreating at a younger age. The studies didn’t find any correlation between females who conceive early and sex ratio, but they concluded that the father’s might play a certain role in sex selection of the baby. Statistically older fathers tend to breed females more than their younger counterparts. Another interesting biological fact is the order of the offsprings. In a study published in 1962, Renkonen, Raimo and Mäkelä found out that the order of the offspring’s sex tends to favour one sex over the other.

influence of childbirth order on sex selection- Renkoren, Raimo

Other than natural causes, there are man made social factors too. For example, sex selective abortions and infanticide. Such practices eventually increase male proportion in the ratio. For example in china and india where male births are more preferred than female births. In china the one child policy only exacerbated the scenario. More sex selective abortions started to surface for couples to get their desired male offspring. In china the ratio went as high as 1.181 as per 2011 survey, which is pretty abnormal ratio and traces its roots at sex selective abortions. In india female fetus abortions have been a long occurring problem too, although things are improving through constant awareness and govt. initiatives. In countries where the general people prefer male births more like Georgia, Armenia, Azerbaijan the ratio eventually ends up favouring men as well, which is quite evident given their abnormally high sex ratio (between 1.11 and 1.2).

Economic factors also weirdly play a role here. In a study on east germany’s and west germany’s population who have identical genetic footprint, Catalan et al. found out that the economy of those regions had a significant role to play in the existing sex ratio of that region. According to gestational stress as we saw before, the sex ratio should decline. In 1991 when East germany’s economy collapsed, and the sex ratio dropped compared to it’s previous years. Whereas, the sex ratio at west germany remained the same, which didnt face such gigantic economic collapse like the east. This observation only corroborated the population stressor theory, concluding the fact that economical conditions play a significant role in sex ratio of a given population.

Now, recall that i used approximately 1:1 sex ratio for most of the animals, not all. Animals who abide by the Fisher’s law are called Fisherian animals and animals who defy the law are called non fisher animals. Reptiles are a good example for this. Usually birds and mammals have balanced fisherian sex ratio. But for reptiles whose sex selection is temperature dependent, like that of turtles, alligators, lizards etc. the scenario is different. There are two category of sex determination in offsprings. One is GSD which is Genetic Sex Determination (based on chromosomal inheritance) and the other is ESD, or Environmental Sex Determination (Based on environmental conditions). ESD is also known as TSD, or Temperature Based Sex Determination. Alligator females are hatched if the eggs are incubated between 27.7 to 30 degree celsius and males are hatched if the temperature is kept 32.2 to 33.8 degree celsius. For turtles, the case is different. Turtles hatch female hatchlings at higher temperatures and male hatchlings at lower temperatures. Below 27.7 degrees celsius, males are hatched and above 30 degrees celsius females are hatched. Based on this difference TSD are categorized into two patterns, Pattern I and Pattern II. Pattern I is divided into two categories, Pattern IA and Pattern IB. Most turtles are of Pattern IA type, who produce females at higher temp. range and male at lower. The remaining turtles are Pattern II type along with crocodiles, lizards etc, who produce females at extreme highs or extreme lows, and produce males in between. Tautara reptiles are of category IB type who produce males at higher temperature and females at lowers, just the opposite of turtles.

So, we can see that there is no random occurrence in sex selection for these particular species. The environment gets to decide what to come out of the brood. Hence, the Laws of Large Number doesn’t fit here, like it does in higher level species, for example, mammals, birds etc. The reason for this is fitness adaptation. With the variance of climate and temperature in the atmosphere, one particular sex would get to have advantage over the other in terms of survival. Hence before hatching, the sex determination inside the shell happens in such a way that the fittest sex is hatched out, in order to cope up with the existing environment outside the shell. Thus they achieve an optimum evolutionary strategy, which makes sure that their species don’t go extinct in any given environmental condition. In fact sometimes this poses a problem. For example, in turtle species, climate change have driven them to produce 99% female offsprings in the span of twenty years. Whereas it used to be 1:6 sex ratio, now it rose up to 1:116 sex ratio. This rose concerns among researchers that if the turtles might go extinct at some point, due to overabundance of female turtles and negligible males.

What can be said for sea turtles can be said for other TSD species as well. Would rising global warming threat their existence and vanish them out of the wild?

At this point, it might feel great to know that we don’t have to worry since we are higher level GSD species following Fisher’s principles and maintain LLN balance to the full. But as we pointed out earlier, we aren’t actually completely immunized from this thing. Superstitious stereotypes, fundamentalist ideas and cultures and medieval perspect on gender roles tend to do a disservice towards female birth. Also wars and violence claim a lot of male lives. Thus regional aberrations occur, which breeds conflicts. Gender imbalance can generate serious troubles. It can cause the excess males at the lower status level to congregate and get violent. A scarcity of female partners may drive a large portion of the population go crazy, eventually creating huge social unrest. Also an excess of such young, agitated angry males may ease the way for terrorist organization to recruit more people in their team. They also might get absorbed into militaristic political factions as disposable foot soldiers. There are ample evidences that where a group of single, agitated, hyperactive young males congregate, violence and organized aggression becomes more apparent. Hudson et Al. even went further to consider such particular problem as a potential regional threat. In india and china many homicidal cases and violence against women could be largely attributed to their rising anomalous sex ratio. Kidnapping and trafficking also increases as a result, since the shortage of women expands the sex industry. In fact, in the Middle East , where sex ratio is pretty high up ( Qatar 2.84, UAE 2.73 ), many girls from asian countries are illegally trafficked for sexual slavery. Its not just the sex ratio behind this, but polygamy is another contributing factor behind this, which only worsens the crisis. But middle easterners being the richie rich of the region can afford buying women from poorer nations to stave off their crisis, unlike south sudanese where polygamy eventually breeds civil war.

The south sudanese exhibit the exact findings of Hudson et Al. If you want a more rigorous look into the findings of the correlation between sex ratio and violence especially in the context of china and india, you can refer to this paper from NCBI for further queries.

Therefore, in conclusion it is always wise to resort to expert opinions from relevant fields to understand the overall nuances of a particular matter. When some know it all preacher enters the stage and sells you the lucrative justifications for polygamy to uphold his belief systems in high regards, take his words with a grain of salt. Just keep in mind that his job is to sell an ideological system to you, not exactly hard sciences. Hence he has to act like a jack of all to entice you, has to manipulate, fabricate or distort scientific truth so that you are not left dissatisfied with his version of truth. Scientific nuances won’t come to his assistance so he has to cover them up, cover the parts that conflicts his interests. Although i am pretty sure Dr. Zakir never went through one single study regarding this field. And of course, why would he, it won’t help his preaching business at all. He has to brand unmarried women as “public property” and condemn them to justify his polygamous worldview. But if he had to undergo the scientific nuances, if anyone really had to be branded “public property”, it would have to be men, the sex that is inherent to his identity. And as we all patriarchal torchbearers know well enough, its the women who are our property, not vice versa, right?

Okay since we are at the end of our article, let me confuse you a little more. Is a coin toss actually a completely random occurrence? Or is there some kind of extremely intricate mathematics behind this, which dictates which side is to fall? As my respected teacher Professor Hashem used to once say, “There is nothing random in Computer Science, everything follows rules.” I would like to extend that from computer science to the whole universe.

I would say that the whole universe is just a manifestation of mathematics. Its just a bunch of mathematical processes getting intertwined with each other, directing the dynamics and the course of the universe. Nothing is random. It just looks random to us since we are either too lazy or unable to calculate the faintest mathematical relations and prefer to look on generalized, bigger, comprehensible mathematical relations instead, counting the rest as just stochastic and random phenomena.

We be livin’ inside a mathematical simulation for real!

Quick Mafs!



Fattah Fathun Karim

Love to explore and learn interesting things. This blog is a way to organize my thoughts on certain topics and communicate them with my friends and peers.