11. A new allele arises in a single individual in a population of 50 diploid ind

Question

11. A new allele arises in a single individual in a population of 50 diploid individuals.
Assuming this new allele has no affect on survival or fecundity, what is the probability
that this allele becomes fixed in the population?

12. Populations of sand lizards (Uma notata) live
in large, isolated sand dunes in the southwestern United States. Herpetologists studying
these lizards in Imperial County, California found that the frequency of the Fringe-toed
allele was 0.88 in an eastern dune population and only 0.12 in a western dune
population. Suppose that a brutal windstorm comes along and blows enough sand
around to create a corridor in which some of these lizards can boldly migrate from the
eastern dune to the western dune. After the storm is over, 279 individuals are collected
from the western dune, 37 of which are from the eastern dune in the last generation.
(a) Calculate the migration rate into the western dune.
(b) What would the frequency of the Fringe-toed allele be in the western sand dune after
one generation of migration?
(c) Use this example to explain why a population experiencing migration is NOT in
Hardy-Weinberg equilibrium.

Explanation / Answer

11. As given in the question the new allele has no effect on survival or fecundity. Hence, its a neutral allele. The probability of allele being fixed in the population is equal to its frequency. Since, the allele is new and has arisen in a diploid population, this frequency is 1/2N.

Here, N=Population Size

In this case N= 50

Frequency of allele= 1/2*50

=1/100

Probability of allele to be fixed in population= .01

12. a) Migration rate is calculated as the difference of immigrants and emigrants in an area divided by 1000 inhabitants. In this case immigrants are the lizards of eastern dune and no emigrants have been given. So the migration rate can be calculated as:

37-0/1000= .037

So, the migration rate in the western dune is .037

b) The frequency of the Fringe-toed allele be in the western sand dune after one generation of migration can be calculated by equation:

q1=mqm+(1-m) q0

Here,

q1= is the frequency of fringe-toed allele after migration

m= proportion of immigrants from eastern dune

1-m= proportion of native lizards

qm= allele frequency of immigrants

q0= allele frequency of natives

substituting values in equation 1

q1= 37/279* .88+(1-37/279)* .12

On solving we get,

.265*.76+.12

=.32

So the frequency of Fringe-toed allele in the western dune after one generation of migration will be .32.

c) One of the major assumption necessary for Hardy-Weinberg equilibrium to hold is that no migration takes place. Due to migration allelic frequencies may change which nullifies the Hardy-Weinberg principle of equilibrium. In the above example we can see that migration has occured and the allelic frequency changed from .12 to .32. Hence, due to this reason the population experiencing migration is NOT in Hardy-Weinberg equilibrium.

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