Coefficient of Relationship

i.b.d.: identical by descent

Consider relatives A and B

What is the probability that for any gene the alleles are i.b.d.?

Probability # identical
$c_2$ both
$c_1$ one
$c_0$ neither

$c_2 + c_1 + c_0 = 1$

$a= 1 + \delta a + e$

From Haldan and Jayacar(1962) tables of r (coefficient of relationship) are presented.

f: coefficient of relationship or of inbreeding; the probability that if A has produced a gamete carrying a rare gene, the first tested gamete of B will carry the same gene.

$\phi$ is for sex linked genes in gametes

For diploid genotypes F and $\Phi$ are used

Relation Symbol Converse f F $\phi_{11}$ $\phi_{12}$ $\phi_{21}$ $\phi_{22}$ $\Phi$
Degree 1
Parent Child $\frac{1}{4}$ 0 0 $\frac{1}{2}$ $\frac{1}{2}$ $\frac{1}{4}$ 0
Degree 2
Mother’s Parent Daughter’s Child $\frac{1}{8}$ 0 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{8}$ 0
Father’s Parent Son’s Child $\frac{1}{8}$ 0 0 0 0 $\frac{1}{4}$ 0
Maternal half sib W S $\frac{1}{8}$ 0 $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{8}$ 0
Paternal half sib H S $\frac{1}{8}$ 0 0 0 0 $\frac{1}{4}$ 0
Full sib M S $\frac{1}{4}$ $\frac{1}{4}$ $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{4}$ $\frac{3}{8}$ $\frac{1}{2}$


White men can now tell black woman to stop having so many babies.



Wealthy widows, the Catholic church, and individualism.




Urban Tree Database


NY Census



“Demography is destiny” or “it’s all about reproduction”.

World’s most important graph according to Steve Sailer:


Sub Saharan Africa growth projected to double from 1.1 billion in 2013 to 2.4 billion in 2050 according to the Population Reference Bureau

It’s not just number of children per woman that is often referenced, but generation time, mortality, and even levels of altruism within a hosting population.

Let’s write a shiny app that will allow us to gain some insight by manipulating the relevant variables. The equations useful for estimates can be found in your population genetics textbook. I will use a simplified method of calculating population growth outlined by Wahl and DeHaan (2004). This simplified model will ignore complicating variables such as birth of males, gestation time and staggered births. Essentially I will be treating humans as dividing bacteria. Though a simplified model, you can still gain a sense of the synergism between generation time and fecundity.

In this model, the number of offspring N after some number of generations G given fecundtity (number of offspring per woman) F is:


I will fix the starting populations at 10 and perform calculations for 200 years, enough to get a feel for what our grandchildren might experience.

t <- seq(20, 200, by=20) ##t is in years

t (time in years) will serve as the abcissa of my plot.

The terminology I will use in the app is “Host” (suffix h; also called population 1, or p1) for the population accepting immigrants, and “Invaders” (suffix i; population 2 or p2) as the population of immigrants. To build your mental model, consider the host country something like America, and the immigrant source country some subsaharan country unconcerned with population growth and unaware of the concept of limited resources.

The growth equations:

x.h <- p1f^(t/p1g)
x.i <- p2f^(t/p2g)

p1f (fecundity) and p1g (generation time) hold input from the sliders. Consider the power t/p1g. If t is 20 years, and the input p1g is 20 years, 20/20 = 1 generation.

Next set up the plot. As it is difficult to get a sense of the magnitude of the differences generated with slider input, I want to calculate the difference in population size after 200 years and print that as annotation on the plot.

delta <- format(abs( x.h[10] - x.i[10] ), scientific=TRUE, digits=3)
ycoord <- 0.5*(max(x.h[10], x.i[10]))
ycoord2 <- 0.2*(max(x.h[10], x.i[10]))
xcoord <- 170
d <- data.frame(cbind(t, x.h, x.i))
ggplot(d, aes(t, x.h)) + geom_point( aes(size=3)) + labs(title="Fecundity X Generation Time") + geom_point(data=d, aes(t, x.i, col="red", size=3)) + annotate("text", x = xcoord, y = ycoord, label = paste("Difference after 200 years = ", delta, sep="")) + scale_y_log10() + theme(legend.position="none") + xlab("Years") + ylab("Population Size")

Consider a mixed population with equal numbers of Hosts and Invaders (10 each) after 200 years with equal fecundity (2) and a generation time of 20 years for the host, 15 years for the invaders. After 200 years the invaders outnumber hosts 10:1. It’s all downhill from there.

The app is hosted at

Code is available on github



Core features



…granted that the people involved in feature films are often super-talented and are often working at a very high level, I’d just rather not be around them, let alone be subjected to their hustle and overbearingness.
Paleo Retiree

One moves swiftly and imperceptibly from a world in which affirmative action can`t be ended because its beneficiaries are too weak to a world in which it can`t be ended because its beneficiaries are too strong. - Christopher Caldwell


Accelerated Aging of Spirits

10 year whiskey in weeks

One Man’s Quest to Make 20-Year-Old Rum in Just Six Days

This guy says he can make 20 year old rum in 6 days.

  • Oak catalyzed esterification
  • Fermentation distillation
  • Aldehydes phenols ethyl-butyrate esterification; ethyl octanoate; ethyl propanoate; isovaleraldehyde
  • Model 1 reactor
  • Break the wood polymers then force esterification
  • Terressentia
  • Terrepure;
  • Orville Tyler