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Sex Ratio Equilibrium

If you download the NetLogo application, this model is included. You can also Try running it in NetLogo Web

WHAT IS IT?

This model investigates emergent patterns in a demographic property of a population: the adult sex ratio (ASR). ASR is defined as the ratio of males to females in the adult population. Most sexually reproducing organisms have an ASR of 1:1. Fisher (1930) explains a rationale for this phenomenon based on natural selection, irrespective of a particular mechanism of sex-determination, which is now known as Fisher’s principle (Hamilton, 1967).

This model is based on Fisher's assumptions of biparentism and Mendelian inheritance. It allows user to explore the emergence of the Fisherian Sex Ratio (1:1) across a wide range of initial sex-ratios and life-history traits.

HOW IT WORKS

This is a population dynamics model of sexually reproducing organisms. The demographic changes in the population as well as the adult sex ratio are plotted as the time progresses.

There are two types of individuals in the model: - Males (Indicated by green color) - Females (Indicated by blue color if not carrying a child and indicated by orange color if carrying a child)

At every time-step the individuals: - Age and check if dead – a random value of longevity is assigned at birth if an agent’s age is more than that value it dies - Move randomly - Search for an adult partner if male. This procedure involves mating, which is dependent on the assigned value of the mating chance. If agents mate, the female carries. (For simplicity, the mating chance in this model incorporates conception-chance as well.) - Reproduce if female

The genetic mechanism of influencing the proportion of male children in the litter is abstracted as a parameter, called MALE-CHILD-CHANCE. Each male and female carry a trait called MALE-CHILD-CHANCE. This determines the probability of a child being male. In this basic model, the sex of the child is equally influenced by the MALE-CHILD-CHANCE values of both the parents.

A child inherits this trait from its parents with a mutation. The inherited value for the trait is drawn from a random normal distribution with a mean equal to the average of MALE-CHILD-CHANCE of the parents.

HOW TO USE IT

Using the sliders, set your desired initial population and individual values (see the Sliders section below for more details). Click the SETUP button to setup the population. To run the model, click the GO button.

The plots and monitors allow users to observe population-level changes and see the emergence of the Fisherian sex-ratio equilibrium.

Sliders

INITIAL-POPULATION-SIZE: the initial number of individuals in the population INITIAL-ADULT-SEX-RATIO: the initial adult-sex-ratio (number of males/number individual * 100) in the population INITIAL-AVERAGE-MALE-CHILD-CHANCE: the initial average male-child-chance of all the individuals in the population MEAN-LONGEVITY: the average longevity (number of ‘ticks’ an individual lives) GESTATION-PERIOD: the number of 'ticks' a female is going to carry a child MAXIMUM-LITTER-SIZE: the maximum number of children a female would give birth to after she completes gestation MATING-CHANCE: the probability that a female mates with a male when a male finds a female partner

Plots

ADULT SEX RATIO: shows the percentage of male agents POPULATION AVERAGE MALE-CHILD-CHANCE: shows how the population's male-child-chance changes over time GENDER DISTRIBUTION: shows numbers of agents of both sexes MATING SUCCESS RATIO (MALE TO FEMALE): shows how the ratio of male mating success to female mating success changes over time

Monitors

ADULT SEX RATIO (ASR): the proportion of male agents, at the moment RUNNING MEAN OF ASR: the average of adult sex ratio in the past 1000 ticks RUNNING STD DEV OF ASR: standard deviation of adult sex ratio in the past 1000 ticks

THINGS TO NOTICE

When you run the model, notice how the number of males and females vary in the GENDER DISTRIBUTION plot. Also, notice that for a wide range of parameter values, if you run the simulation long enough (4000 to 5000 ticks), the ASR converges to 50% as seen in the ADULT-SEX-RATIO plot.

Notice that the average value of the trait male-child-chance across all agents in the AVERAGE MALE-CHILD-CHANCE plot also converges to 0.5 for a wide range of parameters.

Also notice that once the ASR reaches 50%, it is stable around the 50% point. The AVERAGE MALE-CHILD-CHANCE is also stable around the value of 0.5.

Vary the INITIAL-SEX-RATIO and INITIAL-AVERAGE-MALE-CHILD-CHANCE, which are the two variables that affect the sex ratio the most in this model. How do these variables relate to the mating success of each sex?

THINGS TO TRY

Try setting different values of INITIAL-ADULT-SEX-RATIO and INITIAL-AVERAGE-MALE-CHILD-CHANCE to see how that affects the emergence of the adult sex ratio equilibrium.

See if you can change the parameters and see if you can get to a different stable ASR.

EXTENDING THE MODEL

This model implements search-for-a-partner by a male. See if you can change it and make it a female action.

You can also add a variety of features related to evolutionary population genetics and sex ratio equilibrium studies, such as different mortality rates for males and females, sexual selection by females.

RELATED MODELS

• Red Queen
• Fish Tank Genetic Drift
• Plant Speciation

CREDITS AND REFERENCES

Fisher, R. A. (1930). The genetical theory of natural selection: a complete variorum edition. Oxford University Press.

Hamilton, W. D. (1967). Extraordinary sex ratios. Science, 156(3774), 477-488

HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

• Dabholkar, S., Lee, J.S. and Wilensky, U. (2020). NetLogo Sex Ratio Equilibrium model. http://ccl.northwestern.edu/netlogo/models/SexRatioEquilibrium. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

• Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

COPYRIGHT AND LICENSE

Copyright 2020 Uri Wilensky.

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

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