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Biology question
- Thread starter Pete Harcoff
- Start date
lucaspa
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Yes. It's in Mayr's What Evolution Is and can also be calculated by the delta p formula I posted in another thread. As population size increases, it takes longer for a given trait to become "fixed".
Also, a large population indicates adaptation to the environment. At that point directional selection tends to convert to stabilizing selection and the rate of change slows as the population gets to the adaptive peak.
Remember, selection comes in three flavors: directional, stabilizing, and disruptive.
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That's what I thought. Let me follow up with another question:
How much is the rate of change affected by population size? Is it linear? Exponential? Etc...
How much is the rate of change affected by population size? Is it linear? Exponential? Etc...
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DNAunion: In addition to what others have stated...
Small population size can lead to genetic drift, during which alleles - whether deleterious, neutral, or beneficial - can be lost from the population. That can result in rapid changes in allelic frequencies in the population (i.e., evolution).
Also, a particular beneficial mutation is less likely to arise in a small population than in a large one.
Small population size can lead to genetic drift, during which alleles - whether deleterious, neutral, or beneficial - can be lost from the population. That can result in rapid changes in allelic frequencies in the population (i.e., evolution).
Also, a particular beneficial mutation is less likely to arise in a small population than in a large one.
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lucaspa
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Pete, I have to backtrack on this one. Looking thru Futuyma, the rate of evolutionary change is not related to population size. The equations are about the proportion of individuals with a particular allele, which applies to any population size. The rate of change of p is proportional to the coefficient of selection.
Mayr's graph portrays chage in a species over time, and the rate does become asymptotic. Mayr denies that this is due to stabilizing selection, saying stabilizing selection is always present, but then doesn't offer an alternative explanation. It looks to me that earlier in the lineage directional selection is stronger than stabilizing, but later, as the population reaches its fitness peak, then stabilizing takes over. But I need to do some more research on this.
Population size becomes important when comparing the importance of selection to genetic drift. From Futuyma, pg 392: "the effective size Ne of a population and the strength of selection (s) both affect changes in allele frequency. The effect of genetic drift is negligible if selection on a locus is strong relative to the population size -- if s is much greater than 1/(4Ne). Conversely if s is much less than 1/(4Ne), selection is so weak that the allele frequencies change mostly by genetic drift: the alleles are nearly neutral. For instance, ifthe genotypes AA, AA', and A'A' have fitnesses of 1.0, 0.995, and 0.990(where 0.990 = 1-s, so s = 0.01), selection is overwhelmingly important if the effective population size is greater than about 250; but if it less than about 10, genetic drift is more important."
Mayr's graph portrays chage in a species over time, and the rate does become asymptotic. Mayr denies that this is due to stabilizing selection, saying stabilizing selection is always present, but then doesn't offer an alternative explanation. It looks to me that earlier in the lineage directional selection is stronger than stabilizing, but later, as the population reaches its fitness peak, then stabilizing takes over. But I need to do some more research on this.
Population size becomes important when comparing the importance of selection to genetic drift. From Futuyma, pg 392: "the effective size Ne of a population and the strength of selection (s) both affect changes in allele frequency. The effect of genetic drift is negligible if selection on a locus is strong relative to the population size -- if s is much greater than 1/(4Ne). Conversely if s is much less than 1/(4Ne), selection is so weak that the allele frequencies change mostly by genetic drift: the alleles are nearly neutral. For instance, ifthe genotypes AA, AA', and A'A' have fitnesses of 1.0, 0.995, and 0.990(where 0.990 = 1-s, so s = 0.01), selection is overwhelmingly important if the effective population size is greater than about 250; but if it less than about 10, genetic drift is more important."
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lucaspa
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While genetic drift can remove alleles, it can also fix alleles. The probability of fixation of an allele A where q = the initial frequency of A in the population becomes:
P (probability) =(1-e^2Nsq)/(1 - e^-4Nq)
If s = 0, this reduces to P = 1(2N). If s>0
P=(1- e^-2s)/(1- e^4Ns) which becomes P = 2s/(1 - e^-4Ns) if s is small and P = 2s if N is large.
Examples:
N = 1,000 individuals and s = 0.01, the probability of eventual fixation is 0.02. If A has a selective advantage of s = 0.01 and an initial frequency q = 0.01, then P = 0.04. If A is deleterious and and s = -0.001, then P = 0.00004. This will increase if N is very small.
So, both advantageous and slightly deleterious mutations can become fixed by genetic drift, although the odds are very small for the deleterious mutations.
However, Pete, this may be where our intuitive feeling that small populations evolve more rapidly. The probability of fixation of a new mutation is going to increase with small N but respecttable s.
P (probability) =(1-e^2Nsq)/(1 - e^-4Nq)
If s = 0, this reduces to P = 1(2N). If s>0
P=(1- e^-2s)/(1- e^4Ns) which becomes P = 2s/(1 - e^-4Ns) if s is small and P = 2s if N is large.
Examples:
N = 1,000 individuals and s = 0.01, the probability of eventual fixation is 0.02. If A has a selective advantage of s = 0.01 and an initial frequency q = 0.01, then P = 0.04. If A is deleterious and and s = -0.001, then P = 0.00004. This will increase if N is very small.
So, both advantageous and slightly deleterious mutations can become fixed by genetic drift, although the odds are very small for the deleterious mutations.
However, Pete, this may be where our intuitive feeling that small populations evolve more rapidly. The probability of fixation of a new mutation is going to increase with small N but respecttable s.
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