a. What is the probability that the allele in that gamete is the one from the father of the individual making the gametes?
There is about a 50% probability that the allele is from the father.
b. What is the probability that the allele in that gamete is the one from the mother of the individual making the gametes?
There is about a 50% probability that the allele is from the mother.
a. In Figure 5, what is the frequency of Allele A1 in the population (i.e., what proportion of the alleles at Locus A are of the type A1)?
6 of the 10 alleles in the population are type A1.
b. In Figure 5, what is the frequency of Allele A2 in the population (i.e., what proportion of the alleles at Locus A are of the type A2)?
4 of the 10 alleles in the population are type A2.
Given that the population depicted in Figure 5 reproduces to make a generation of off spring and using the allele frequencies you calculated for that population:
a. What distribution can be used to calculate these probabilities?
A standard Hardy-Weinberg distribution is best to calculate probabilities in allele frequencies. The formula for the population in Figure 5 would be as follows: 1 = p^2 + 2pq + q^2, where p is the frequency of allele A1 and q is the frequency of allele A2.
b. What is the probability of an individual in the off spring generation being homozygous for A1?
There is a 36% chance of the offspring being homozygous for A1.
c. What is the probability of an individual in the off spring generation being homozygous for A2?
There is a 16% chance of the offspring being homozygous for A2.
d. What is the probability of an individual in the off spring generation being heterozygous?
There is a 48% chance of the offspring being heterozygous.
Given the population we used in the example above, answer the following:
a. What is the probability that Allele A1 eventually becomes fixed in the population?
There is a 60% chance that allele A1 becomes fixed in the population.
b. What is the probability that Allele A1 eventually disappears from the population?
There is a 40% chance that allele A1 disappears from the population.
c. What is the probability that Allele A2 eventually becomes fixed in the population?
There is a 40% chance that allele A2 becomes fixed in the population.
d. What is the probability that Allele A2 eventually disappears from the population?
There is an 60% chance that allele A2 disappears from the population.
a. Suppose that the data are bell shaped. How much data lies within two standard deviations of the mean? Explain your answer.
95% of the data should be within 2 standard deviations of the mean. A bell shape suggests normal distribution, which is structured in that format.
b. Suppose that the allele frequency p1 = 0.5 and the population size N = 25 (an accurate estimate of the population size of panthers in the early-mid-1990s). Now consider your percentage answer (from 5a above), y%. For that y% of cases, the allele frequency of p2 is in what range?
With an allele p1 frequency of 0.5, one standard deviation is +/- .07. So, the range of allele frequency is .36 to .64.
c. Repeat the calculation in 5b above for population sizes 33, 100, and 1000. What does an increased population size do to the range?
At a population of 33, the standard deviation of p2 is +/- .06. So, the range of allele frequency is .38 to .62. The standard deviation at population 100 drops to +/- .04, which makes the range between .42 to .58. Finally, with a standard deviation of +/- .01 at population 1000, the range is between .49 to .51.
d. In words, summarize how population size affects the probability distribution of the trait in the next generation.
As population increases, less frequent alleles decrease in frequency among the population. More frequent alleles come to dominate the population as more individuals in future generations come from parents with those alleles. Conversely, a smaller percentage of individuals come from parents with rare alleles, decreasing the prevalence in the population overall.
a. Calculate the average time, in generations, to fixation of an allele that starts at proportion 0.4 in populations of sizes 25, 33, 100, and 1000.
At population size 25, 76.6 generations are required to achieve allele fixation. At population size 33, 101.1 generations are required. At population size 100, 306.5 generations are required. Finally, a population size of 1000 reuires 3065 generations to achieve fixation.
b. Calculate the average time, in generations, to loss of an allele that starts at proportion 0.4 in populations of sizes 25, 33, 100, and 1000.
At population size 25, an allele will be lost after 61.1 generations. At population size 33, an allele will be lost in 80.6 generations. At population size 100, the allele will be lost in 244.3 generations. Finally, at population size 1000, the allele will be lost in 2443.4 generations.
c. Calculate the average time, in generations, to loss of an allele that starts at proportion 0.1 in populations of sizes 25, 33, 100, and 1000.
At population size 25, an allele will be lost after 25.6 generations. At population size 33, an allele will be lost in 33.8 generations. At population size 100, the allele will be lost in 102.3 generations. Finally, at population size 1000, the allele will be lost in 1023.4 generations.
Let’s calculate the effect of inbreeding on the expression of rare deleterious alleles.
a. Consider a rare deleterious recessive allele for a specific gene/locus. In this hypothetical population, the deleterious recessive allele exists at a proportion of 0.01. In an offspring with randomly chosen parents, what is the probability that the offspring will be homozygous for the deleterious recessive allele?
There is only a .01% chance of an affspring being homozygous for the deleterious allele.
b. Now let’s consider that the Florida panther population has 20,000 genes/loci (this is a reasonable estimate, and is about the number of genes that humans have). And let’s assume that for every gene/locus there is a deleterious recessive allele that exists at a proportion of 0.01 in the population. If all mating is random, in the average off spring, how many of its genes/loci are homozygous for deleterious recessive alleles?
About 2 genes/loci will be homozygous for the deleterious allele.
c. Now consider an offspring with full-sibling (brother and sister) parents. In this offspring, what is the probability that the offspring will be homozygous for the deleterious recessive allele? Note that full siblings share, on average, 50% of their genes. So, in order to calculate this, consider that one allele in an off spring is randomly inherited from the population. Then, given that the randomly inherited allele is the deleterious recessive allele, we can say that there is the normal chance of inheriting the deleterious recessive allele due to randomness, plus an increased chance that the other parent has the allele due to the fact that it is a full sibling of the other parent. This added increased chance must take into account that there is a 50% chance that the other parent has one copy of that allele due to relatedness, and the fact that that parent has two alleles, so there is a 50% chance they pass on that deleterious recessive allele if they have it.
There is a .25% chance that the offspring will be homozygous for the deleterious allele.
d. Now consider the same mating of full siblings with 20,000 genes/loci where each gene/locus has a deleterious recessive allele that exists at a proportion of 0.01 in the population. On average, how many of the offspring’s 20,000 genes/loci are homozygous for deleterious recessive alleles?
About 50 genes/loci would be homozygous for the deleterious allele.
e. Compare the results of 7b and 7d above and explain what this means about the effects of inbreeding.
These results show how inbreeding magnifies the chances of offspring inheriting deleterious alleles. Closer genetic relationships between mating individuals increases the number of genetic loci that would be homozygous deleterious.
Summarize the three major problems with population size.
A small population size increases the chance of homozygosity among offspring, which impacts the offspring’s health. A small population size reduces the likelihood of infrequent alleles to become fixated into the population. Finally, a small population size is highly vulnerable to extinction by chance events like weather or predation. If 10 females are killed by predators, it is much more impactful to a small population than to a larger population.
Summarize the observed trends in the traits in Table 1.
Table 1 shows that average heterozygosity decreases over the 25 year range. The proportion of cryptorchid males, however, increases significantly over the range. The proportion of individuals with atrial septal defects decreases initially, but then climbs back up marginally. This suggests that, despite the decreasing homozygosity, health issues associated with inbreeding continue to haunt the population.
It turns out that the Florida panther is closely related to a population of panthers (cougars) that still exist in Texas. In fact, the Florida population and the Texas population used to be part of one continuous population of panthers. So it is highly likely that they could and would interbreed. Based on the information available in the mid-1990s, some conservation biologists believed that the only way to save the population of Florida panthers would be to introduce several Texas cougars into Florida to revitalize the population of Florida panthers. Do you think this is a good idea? Also consider factors beyond probability that may influence society’s decision on this matter.
Introducing new individuals into the population would be beneficial to the Florida population. The individuals are close enough to breed, but genetically distinct enough to stem many of the health issues the Florida population experienced. Resistance to this decision likely came from safety concerns associated with introducing large predators into a human environment. However, proper respect for panther territories limits human interaction with the predators and help with safety concerns. Also, so long as the panthers do not associate people with food, they should avoid any human areas.
a. Summarize the change in the traits in Table 2 after the introduction of the Texas cougars.
Table 2 shows an interesting result of introducing the Texas females. Both health issues associated with inbreeding decrease significantly, an important step in improving species health overall. However, average homozygosity stays high within the population, even seeing marginal increase over the time range.
b. After seeing these data, do you think the introduction of the Texas cougars was a good idea?
Introduction of the Texas cougars was a good idea. Despite the persistent prevalence of homozygosity in the population, the manifestation of associated health issues significantly decreased. This is an important step to ensure the survival of each individual to sexual maturity, and therefore an important step to preserving the population.