along with other invasive species introduced by Westerners
I just want to state for the record that I have never been within 1000 nautical miles of New Zealand. Don't blame this on me too. I have enough White Guilt baggage to contend with as it is.
On a more serious note, it seems that this plan does not take into consideration the most basic principle of natural selection: survival of the fittest (or in other words, the genes of those that are able to produce the most offspring will start to dominate in a population). This plan on the other hand wants to introduce just a small number of individuals in the population in the hopes that their genes will spread to the whole population, while at the same time the very same genes are responsible for the carriers eventually having less offspring than non-carriers (even if it is not in the first generation). Well, I assume they know more about biology than I do...
Yeah, but evolutions doesn't "know" about later generational effects - it only works on the basis of the following generation - to first approximation. Yes, having helpful grandparents might increase your breeding effectiveness by a few percentage over your neighbours, but there is a HUGE advantage to having all of your kids being able to mate with the scare resource of the available females compared to having only half of your children being able to mate with the scare resource of available females. The fraction of modified mice in each generation should increase by quite a bit.
If the odds of finding a mate and having kids is the same for modified (MM) and unmodified (UM) male mice, and they are competing for the same number of unmodified (UF) female mice, for a stable population, the chances of breeding have to be about equal to the inverse of the average number of males in the average litter (AL), so that (for the unmodified case) the population each generation is about the same. Some mice get eaten or stepped on before having kids.
In the first generation (UM)1 = (UF)1 and (MM)1 is however many are introduced, and the total (TM) male mice population would be (TM)1 = (MM)1+(UM)1. The fraction of modified mice is (FMM)1= (MM)1 / (TM)1, the fraction of unmodified males is (FUM)1 = (UM)1 / (TM)1.
Since the odds of living until having kids and the average litter size cancel each other out, in the second generation the number of unmodified females would be found by multiplying the number of females by the fraction of unmodified males in the previous geneation: (UF)2 = (UF)1 x (FUM)1, similarly the number of unmodified males would be found by multiplying the number of unmodifed males by the fraction of unmodified males in the previous geneation: (UM)2 = (UF)1 x (FUM)1. The number of modified males would be found by multiplying the number of females by the fraction of modified males in the previous geneation and then multiplying that by two since all of their kids are male compared to half of the kids of unmodified males being boys: (MM)2 = 2(UF)1 x (FMM)1
In the second generation the number of unmodified males and unmodified females is equal, and less then it was in the previous generation by a factor of (FMM)1. Since for the modified males, all of their kids are males they get he fraction of modified males in the second generation is
(FMM)2 = (MM)2 / (TM)2
= (MM)2 / [(MM)2 + (UM)2]
= [2(UF)1 x (FMM)1] / [2(UF)1 x (FMM)1 + (UF)1 x (FUM)1]
= 2(FMM)1 / 2(FMM)1 + (FUM)1]
This happens each genration, the fraction of modifed males increase each breeding cycle. For generation n we have
(FMM)(n+1) = 2(FMM)n / 2(FMM)n + (FUM)n]
In any generation, if the number of modified males is only a small fraction of the total, their fraction of the total grows by a factor of almost two each generation (when FMM FUM). If FMM is about the same size as FUM (the modified males make up about half of all males) then the next generation would be about 2/3 modified males. If FMM is ten times as big as FUM (thus FMM = 10/11 = 0.909090... and FUM = 1/11 - 0.101010...), then the next generation would be 20/21 modified males (= 0.95238...).
Even with a small number of introduced, their fraction of the total would soon grow to being a maority due to the factor of two.
Of course this assumes that there is good mixing of the population each generation, with more realistic spread of mice, the pockets of modified mice would tend to spread out as they looked for females to mate with, since where the modified mice are dominant there are few females. Regions with a majority of unmodified mice would quickly change to majority modified.