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mathematics

Sex ratio

Sex ratio is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Sex ratio rather than just read about it. In short: A sex ratio is the ratio of males to females in a population. As explained by Fisher's principle, for evolutionary reasons this is usually about equal in species which reproduce sexually.

Sex ratio — main illustration
Sex ratio — illustration

Key takeaways

  • Sex ratio belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Sex ratio to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Sex ratio from memory before moving on to harder problems.

Reference excerpt

A sex ratio is the ratio of males to females in a population. As explained by Fisher's principle, for evolutionary reasons this is usually about equal in species which reproduce sexually. However, many species deviate from an even sex ratio, either periodically or permanently. These include parthenogenetic and androgenetic species, cyclical parthenogens such as aphids, and some eusocial wasps, bees, ants, and termites.

Types In most species, the sex ratio varies according to the age profile of the population. It is generally divided into four subdivisions:

primary sex ratio — ratio at fertilization secondary sex ratio — ratio at birth tertiary sex ratio — ratio in sexually mature organisms The tertiary sex ratio is equivalent to the adult sex ratio (ASR), which is defined as the ratio of adult males to females in a population. The operational sex ratio (OSR) is the ratio of sexually active males to females in a population, and is therefore derived from a subset of the individuals included when calculating the ASR. Although conceptually distinct, researchers have sometimes equated the ASR with the OSR, particularly in experimental studies of animals where the difference between the two values may not always be readily apparent. quaternary sex ratio — ratio in post-reproductive organisms These definitions can be somewhat subjective since they lack clear boundaries.

Sex ratio theory Sex ratio theory is a field of academic study which seeks to understand the sex ratios observed in nature from an evolutionary perspective. It continues to be heavily influenced by the work of Eric Charnov. He defines five major questions, both for his book and the field in general (slightly abbreviated here):

For a dioecious species, what is the equilibrium sex ratio maintained by natural selection? For a sequential hermaphrodite, what is the equilibrium sex order and time of sex change? For a simultaneous hermaphrodite, what is the equilibrium allocation of resources to male versus female function in each breeding season? Under what conditions are the various states of hermaphroditism or dioecy evolutionarily stable? When is a mixture of sexual types stable? When does selection favour the ability of an individual to alter its allocation to male versus female function, in response to particular environmental or life history situations? Biological research mostly concerns itself with sex allocation rather than sex ratio, sex allocation denoting the allocation of energy to either sex. Common research themes are the effects of local mate and resource competition (often abbreviated LMC and LRC, respectively).

Fisher's principle

Fisher's principle (1930) explains why in most species, the sex ratio is approximately 1:1. His argument was summarised by W. D. Hamilton (1967) as follows, assuming that parents invest the same whether raising male or female offspring:

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. This means that the 1:1 ratio is the evolutionarily stable strategy. This ratio has been observed in many species, including the bee Macrotera portalis. A study performed by Danforth observed no significant difference in the number of males and females from the 1:1 sex ratio.

Human sex ratio

The human sex ratio is of particular interest to anthropologists and demographers. In human societies, sex ratios at birth may be considerably skewed by factors such as the age of mother at birth and by sex-selective abortion and infanticide. Some families also stop having children after they have both boys and girls. Exposure to pesticides and other environmental contaminants may be a significant contributing factor as well. As of 2024, the global sex ratio at birth is estimated at 105 boys to 100 girls. The sex ratio is reversed for people 65 and older, where there are 81 men for every 100 women. Across all ages, the global population is nearly balanced, with 101 males for every 100 females. A large 2025 epidemiological study of American nurses found the chances of a specific couple giving birth to a boy or girl are not always 50-50, and the overall pattern follows a beta-binomial distribution. The number of families with three or more children that have all boys or all girls is higher than would be expected by random chance. Families with three girls had a 58% chance of having a fourth, and families with three boys had a 61% chance of having a fourth. Women 29 or older at first birth had a 13% higher chance of having only boys or only girls. Some researchers questions why the same pattern was not seen in a study of the population of Sweden. Factors which may affect birth sex unconfirmed by large studies include vaginal pH, length of the follicular phase of the menstrual cycle, the menstrual cycle phase at conception, and genetic factors. Other unconfirmed correlations with inherited traits include attractiveness, wealth, aggression, and body size. A 2025 study of over 58,000 American women suggested a correlation with two single-nucleotide mutations in the mother — NSUN6 increasing the likelihood of only female children and TSHZ1 increasing the likelihood of only male children.

Examples in non-human species

… excerpt ends here. Continue reading the full article.

Illustrations

Sex ratio: Sex ratio at birth for human over time
Sex ratio at birth for human over time
Sex ratio: Sex ratio at five years old
Sex ratio at five years old
Sex ratio: Sex ratio at sixty years old
Sex ratio at sixty years old
Sex ratio: Map indicating the human sex ratio by country.[12]



.mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Countries with more males than females.
  Countries with the same number of males and females (accounting that the ratio has 3 significant figures, i.e., 1.00 males to 1.00 females).
  Countries with more females than males.
  No data
Map indicating the human sex ratio by country.[12] .mw-parser-output .legend{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .legend-color{display:inline-block;min-width:1.25em;height:1.25em;line-height:1.25;margin:1px 0;text-align:center;border:1px solid black;background-color:transparent;color:black}.mw-parser-output .legend-text{}  Countries with more males than females.   Countries with the same number of males and females (accounting that the ratio has 3 significant figures, i.e., 1.00 males to 1.00 females).   Countries with more females than males.   No data
Sex ratio: Adult female of the parasitoid wasp Sclerodermus. This genus is known for producing extremely female-biased sex ratios in communal broods, a pattern shaped by social dominance and infanticide.[37]
Adult female of the parasitoid wasp Sclerodermus. This genus is known for producing extremely female-biased sex ratios in communal broods, a pattern shaped by social dominance and infanticide.[37]

Worked examples

Example 1 — a first encounter with Sex ratio

Start with the simplest possible case. Write down what Sex ratio claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Sex ratio before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Sex ratio ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Sex ratio

In research
Sex ratio appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Sex ratio in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Sex ratio is common in secondary-school and first-year university syllabi. It links to neighbouring topics Biostatistics, Population, Selection, so understanding it makes those chapters shorter.
In everyday life
Look for Sex ratio outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Sex ratio in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Sex ratio means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Sex ratio out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Sex ratio in simple terms?

A sex ratio is the ratio of males to females in a population. As explained by Fisher's principle, for evolutionary reasons this is usually about equal in species which reproduce sexually.

Why does Sex ratio matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Sex ratio?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Sex ratio.

Tags

  • Biostatistics
  • Population
  • Selection
  • Sex ratio

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