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**Hardy-Weinberg Principle**

SBI3U

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Evolution Change of the gene pool of a population over time

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**Hardy –Weinberg Equilibrium**

In large populations where only random chance is at work, allele frequencies are expected to remain constant from generation to generation. Remaining constant = EQUILIBRIUM However, there are ‘disturbing factors’ that cause allele frequencies to change, which lead to evolutionary change

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‘Disturbing Factors’ To be in Hardy-Weinberg Equilibrium none of these disturbing factors can be present in the population Natural Selection- favours the passing on of some alleles over others Small Population Size- limited allele diversity Mutation- introduce new alleles to a population Immigration/ Emigration- introduce or remove alleles in a population Horizontal gene transfer- gaining of new alleles from a different species

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In Nature In reality, the conditions for Hardy- Weinberg equilibrium (no disturbing factors, therefore only random chance) are NEVER met There are ALWAYS disturbing factors HW can be approximated in the lab It has usefulness as a model for studying real populations

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**Equations A gene has two alleles, A and a**

p + q = 1 p2 + 2pq + q2 = 1 A gene has two alleles, A and a The frequency of allele A is represented by p The frequency of allele a is represented by q The frequency of genotype AA = p2 The frequency of genotype aa = q2 The frequency of genotype Aa = 2pq

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Example Assume a population in which 36% of the population are homozygous for a certain recessive allele, a. Assume the population is at equilibrium. Question 1: What is the frequency of the recessive allele, a, in this population? q2 = 0.36 q = 0.36 q = 0.60

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Example Assume a population in which 36% of the population are homozygous for a certain recessive allele, a. Assume the population is at equilibrium. Question 2: What is the frequency of the dominant allele, A, in this population? q = 0.60 p = 1 p = 0.40

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Example Assume a population in which 36% of the population are homozygous for a certain recessive allele, a. Assume the population is at equilibrium. Question 3: What percentage of the population are homozygous for the dominant allele, A? p = 0.40 p2 = p2 = 0.16 = 16 %

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Example Assume a population in which 36% of the population are homozygous for a certain recessive allele, a. Assume the population is at equilibrium. Question 4: What percentage of the population are heterozygous for this trait? 2pq = 2(0.40)(0.60) 2pq = 0.48 = 48 %

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Example Assume a population in which 36% of the population are homozygous for a certain recessive allele, a. Assume the population is at equilibrium. Question 5: Why do we have to start the problem with the percentage of the homozygous recessive in the population? It is not possible to tell the homozygous dominant (AA) from the heterozygous (Aa) by examining the phenotype.

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Troll Example Trolls are mythical creatures that live beneath flower gardens. Of the 100 trolls in a population, 91 have pink hair(T) and 9 have orange hair(t). Assuming genetic equilibrium: What are the gene frequencies of T and t? What are the genotypic frequencies?

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