The index of relatedness or the coefficient of relationship expresses the chance of a gene being shared between two individuals A and B. To calculate the relatedness find the common ancestor(s). Having located the common ancestor(s), count the generation distance between the common ancestor(s) and respectively A and B. Add up the generation distance of A and the generation distance of B to find the total generation distance of A and B.

r = a * (1/2)^g

where
r = relatedness
a = common ancestor(s)
g = generation distance

E.g.
First cousins have 2 common ancestors, thus a=2, with a generation distance of 2+2=4, thus g=4.
relatedness between first cousins = 2 * (1/2)^4 = 2 * (1/2 * 1/2 * 1/2 * 1/2) = 1/8

For relationships as distant as third cousin (2 * (1/2)^8=1/128) the relatedness is close to the baseline probability that a gene will be shared by any random individual taken from the population.

- Joe Chang, Professor of Statistics, Yale University (yale.edu)

Model Variables:

0. Initial Population: generated with size 1000
fertility, size, time,median age,sex ratio,males,females
2, 1000,10, 10.0, 99, 498, 502
fertility, size, time,median age,sex ratio,males,females
3, 1000, 10, 10.0, 94, 485, 515
1. life expectancy: 78
2. fertility: a) 2.0 and b) 3.0 / fertile female (maximum children per female)
3. fertility: if (sex == female AND fertility_minimum_age < age < fertility_maximum_age )
4. fertility_minimum_age = 25, fertility_maximum_age=30
5. begintime = 2009, endtime= begintime+n years (e.g. 250)

Fertility 2.0

Fertility 3.0

Running Larve 2 times, first time with birth rate = 2, second time with birth rate = 3.

Model Variables:
0. Initial Population: US census 2008 est./ 1000
1. life expectancy: 78 (US average 78.11)
2. birthrate: a) 2.0 and b) 3.0 / fertile female (maximum children per female)
3. fertility: if (sex == female AND fertility_minimum_age < age < fertility_maximum_age )
4. fertility_minimum_age = 25, fertility_maximum_age=30
5. begintime = 2009, endtime= begintime+n years (e.g. 250)

Thesis:
In the model's first test run, a few oddities in the behavior were shown. The most curious was the fact that the population died. This was not immediately worrisome, as there were a few build in factors leading to this behavior: 1. a large portion of the initial population has passed the fertility maximum age of the model, no longer being capable to reproduce by the model’s logic; 2. a significant portion of the initial population has passed the life expectancy age, at which the model kills a specimen; 3. the maximum number of children per female assuming a sex ratio of 100 would make it impossible for the population to grow.

Population Size


Comment: With a birth rate of 3 the population initially grows but reaches an Evolutionary Stable Strategy (ESS) after 75 years, while the population with a birth rate of 2 starts to die off after 30 years reaching close to extinction around 200 years.

Sex Ratio

Median Age


Comment: the peaks and lows in the Median Age are cause by the model’s logic, of forcing each woman at 25 years to give birth to 1 child each year for 3 years.

- Catalog of OMG Modelling and Metadata Specifications (omg.org)

Model Variables:
1. life expectancy: 78 (US average 78.11)
2. birthrate: 2.0 / fertile female (maximum children per female)
3. fertility: if (sex == female AND fertility_minimum_age < age < fertility_maximum_age )
4. fertility_minimum_age = 25, fertility_maximum_age=30
5. begintime = 2009, endtime= begintime+n years (e.g. 500)

Initial Population by Sex and Age

Size of Population over Time

Median Age of Population over Time

Sex Ratio of Population over Time

Larve is an application that simulates population reproduction and the evolution of inheritable characteristics under environmental conditions. Larve is an abbreviation that means Live Artificial Reproduction and Virtual Evolution.

The originating question or problem definition: how can non-reproductive homosexual behavior be persisted succesfully in a population where reproduction takes place via hetero-sexual fertilization, assuming there exist genes that inherit or influence homosexuality.

The thesis: homosexuality is genetically inherited in a population because it promotes certain homosexual/single sex bonds or single sex group cohesion (army, priesthood, sports, educational, professional, power groups, etc.) that are advantageous for the reproduction and prosperity of that population.

Concept of proof: Create a model or virtual simulation of a real population, allow the viariation of the genetic, behavioral and environmental values between competing populations, and measure the competetive advantage of different values over a certain period of time.

- Price equation and Evolutionary Stable Strategy ESS by George R. Price (wikipedia.com)