Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



A math problem
Posted:
Mar 15, 2013 1:07 AM


Let's imagine that we are the grand designers of life. Animal life as we know it consists of two sexes, male and female. This is, presumably, the most efficient way of mixing the chromosomes amongst different creatures, one male and one female, so that the offsping are immediately different from either of the parent, thus speeding the process of evolution.
While this may be the most efficient way to mix chromosomes, one might ask if it were the only way. What if instead of two sexes, one with two X chromosomes and the other with an X and a Y chromosome, we instead had various sexes due to a combination of chromosomes. The simplest situation to imagine would involve two chromosome pairs instead of one: for instance we could imagine that to be male would require one to not only have an X and a Y chomosome but also a W and a Z chromosome whereas females would have either two X choromosomes or two W chromosomes.
Well, did the math: the first generation would have males with the XYWZ chromosomes breeding with females with either XXWW, XXWZ or XYWW chromosomes. Alas if males breed with females with either Y or Z chromosomes then they can get offspring with two Y chromosomes or two Z chromosomes. These offspring would be either male (YYWZ or XYZZ) or female (YYWW or XXZZ).
It gets even more complicated when all the different types of males breed with all the different types of females. For example, the males with two Y chromosomes or two Z chromosomes breed with females at random then they have mostly males. Indeed, I calculate if there were an equal number of such males and a equal number of regular males as well as an equal number of females with either two Y chromosomes or two Z chromosomes and females with neither a Y chromosome or a Z chromosome then what you would get, all things otherwise being equal, is an equal number of males in females born as a result.
Basically then I just considered two generations and already there's an indication that there would eventually be an equal number of males and females. I'm wondering if this is inevitable. I mean, if you separate people into male in female based on their chromossome makeup are you eventually going to get a 50% male and 50% female population?
It isn't really a biology problem: it's a math problem and maybe it has already been effectively solved elsewhere.
Martin



