Posted on 12/05/2005 3:00:51 PM PST by dawn53
They can't all be of breeding age, either. Some would be juveniles. Some would be aged. Males in such species typically fight each other for the right to breed, with the strongest animals passing along their genes. This means that a large number of males would not be able to breed even though they are sexualy mature.
In other words, I don't think the problem is intended to be taken as broadly as many on the thread are taking it. The idea is to solve the mathematical formula as posed in the question.
WHAT DIFFERENCE DOES IT MAKE WHERE YOU BUY UNDERWEAR?! UNDERWEAR IS UNDERWEAR!! IT'S UNDERWEAR WHEREEVER YOU BUY IT!! IN CINCINNATTI OR WHEREVER!!
Not in this problem. This problem implies massive dieoffs from such regularly occuring events as predation and/or disease. These other things aren't given to simplify the problem. What was given is the fact of stable population.
There's a predator-prey problem underlying this example. It shows swings about some average population number. The birthrate, populaiton average lifespan and the population average deathrate remains constant. At any particular time though, the deathrate can execede 1/avg lifespan by orders of magnitude.
The predator could even be the DNR and their licensed hunters. In that case, the negative swings are minimized.
I hate to say it but he may be right. We've been assuming that all the antelope born, lived; but if each one has 5 progeny in ten years and they all live, there's no way the population can stay at 24,000 antelope. So if a lot were killed to hold the population constant, their births add to the number of mutations even though they don't show up as a change in the population.
Thank God I'm a recognized numbers dolt; otherwise I'd be so embarrassed!
Depends on how many 5-12 y/os I package each year and their age distribution. Harvests vary from year to year. Averages are taken over a wide enough window to smooth out the bumps. Hard winters, drought, disease can also take a toll periodically. In general any particular ecosystem can only support some stable population. Dieoffs tend to be the rule that maintains it. The young and old are the most probable to die off. The average age is essentially constant.
Looking back at the original problem, I see the question is "how many mutations would enter the gene pool"; this makes the problem impossible to solve, since there's no way of knowing whether the large number of offspring killed are killed before or after reaching breeding age.
If ya see antelope wearing underwear, call the sheriff.
Time to beam up to the mother ship, guy.
I suggest that if you see antelope wearing underwear you call AA for it's time to join and quit drinking.
If a population has always contained 1,000 individuals and, over a thousand-year period there have been 500,000 births and 500,000 deaths, then (ignoring phasing effects) the average lifespan of the population will be two years. Even if 999 individuals live 1,000 years and the other 499,001 individuals live for 63 seconds each, the average lifespan would still be two years.
Likewise with lifetime birth rates. If there are 1,000 individuals and, over the course of a decade, one of them has 5,000 offspring and the others have zero, the average birth rate would be five per decade.
These averages are completely unaffected by distributions. It may well be that they do not represent typical members of the species, but numerically they are what they are.
Typically in a wild population death rate is a function of age. I can't post a plot, but consider death rate per age group vs. age. I'll use a step function for simplicity. The death rate for 0-2y/os is 0.4. The death rate for 18-20y/os is also 0.4. The death rate for 2 year periods in between is 0.025. The average lifespan is 10 years, but the death rate over those ten years is 0.5, the same as the birthrate in this thread.
In such situations as hard winters, drought, predators and hunting the death rate is also proportional to the number of animals present and the magnitude of the adverse situation. As the number of animals goes up, the death rate increases.
These complicaitons were simply left out of the problem. They are implied by the givens. There's no reason to claim contradiction.
Whatever.
5 per antelope or 5 per female antelope? What's the distribution of the sexes---that needs to be known and it is not 50-50 in the wild.
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