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Musings on the genetics of small populations of killifish

 Start with an example of crossing two individuals, each of whom carry a lethal recessive version of one of two different genes, gene A and gene B.   A and B represent the good copies of the gene; a and b represent the bad copies of each gene.

Each individual requires at least one good copy of each gene to survive.   If he has one A and one a, he's fine.  If he has AA, he's fine.  If he has two aa, he's dead.  So having a A trumps, or is dominant to a, and a is recessive to A, and is recessive lethal because individuals having two a versions of the gene are dead.  And ditto for the B gene.

The parents being crossed are the first line of each table;


the possible combinations of genes that they can give to their offspring are shown on the edges;


the genotypes of the possible offspring are the shown in the colored squares:


There are duplications to represent the true frequency of each potential cross and offspring, to give a visual representation of the true frequencies of each possible combination.

 In this example, the yellow squares represent viable offspring

 the red squares represent non-viable offspring (they lack a good copy of A or of B).


In the F1 generation, all the offspring are viable


In the second generation, there are 16 possible matings--each of the F1 can mate with another individual of the same genotype, or each of the other three genotypes, four options for each of the four offspring, totalling 16 possible mating combinations.  I am including the duplicates possibilities to give a visual representation of the relative odds of each combination occuring.  In this example,  31 of 256 potential F2 offspring are not viable.

So if only 31 are not viable, that means 225 are viable, no problem, right?

But what you happened to pick these two F1--since they all look equally healthy--to produce the next generation?

Female AaBb
Male AaBb

Now your next generation looks like this:

AaBb x AaBb
Now 7/16--44%--of the offspring are not viable. 

But of course, I've stacked the deck in this example, right?  There's only a 1/16 chance you'll happen to pick that pair (or get only those two genotypes by chance).  15/16 of the time you'll get a higher proportion of viable offspring.  Heck, there's an equal (1/16) chance you'll pick AABB x AABB for the next generation, and if you did that, then you would have eliminated the bad a and b gene versions from your future stock completely with this one choice. 

Here's where it gets tricky, though:  it's very likely that that founders carry bad copies of more than two genes with somewhat deleterious effects on their offspring.  And  the more deleterious copies of genes in your original stock, the higher the proportion of the next generation that will end up with a two bad copies of at least one gene.  Here's an example of a cross between fish that each carry a bad version of three different genes:

Only 27/64 from this cross are viable, vs 9/16 in the previous example. 

And while I've again cherry picked to this example--picking the triple heterozygote parents for the sample F1 cross that yields the lowest proportion of viable offspring--the simple point that I'm trying to make is that, when your population is small, generation after generation, you have a high risk of losing the line through bad luck in the genetic lottery.  And the more bad alleles you start out with in the F0 founders, the worse the problem is.  Throw in some neglect here and there, unequal sex ratios, and no wonder it's hard to keep a line going--unless you have the luxury of keeping lots of fish every generation.

Even in a relatively small population in the wild, you're likely to have tens or hundreds of individuals contributing to the next generation, so the line continues.  And most deleterious mutations aren't 100% normal as heterozygotes and 100% lethal as homozygotes, so there is some viability difference for natural selection to act upon to gradually eliminate the deleterious versions from the gene pool.  

But in a tank, where predators are few and food is abundant, you don' have this degree of selection.  You can try to pick the healthiest looking fish, with the brightest colors and largest size as external indicators of robust genetics, but not all the deleterious genes have visible effects.  You're not likely to select as strictly as life in the wild will.  This lack of strict ongoing selection compounds the problem of a small gene pool, and increases the odds that, by chance, your stock may gradually end up with higher proportions of bad genes, and getting sicklier and sicklier, until it peters out.

I'd argue that the people who get 20 generations from a single founding pair probably got lucky, happening to end up with breeders in subsequent generations with a higher proportion of the best versions of their genes--maybe helped along by some good deliberate selections, and also were diligent in avoiding the neglect that leaves you with only one possible pair of breeders to restart the line.

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