Non Random Mating to change Genetic Equilibrium through Inbreeding in small population

About Population Genetics

1. 1 WELCOME

2. Submitted to :- Dr. M.P.Patel Professor & H.O.D, Dept. of GPB SDAU, S.K. Nagar Submitted by :- Vaghela Gauravrajsinh K M.Sc. (Agri.) Reg.no:-04-AGRMA-01840-2018 SDAU, S.K. Nagar Non Random Mating to change Genetic Equilibrium through Inbreeding in small population

3. WHAT IS RANDOM MATING? Each male of a population has equal chance of mating with any female of population or vice-versa called as Random mating or Mendelian population or Panmixia or Panmictic population.

4. WHAT IS NON-RANDOM MATING? When the probability that two individuals in a population will mate is not the same for all possible pairs of individuals. OR In a population male does not mating with any female of population is called as non-random mating.

5. Types of Non-Random Mating Disassortative- Individuals only mate with others who are phenotypically different from themselves for selective traits (opposites ). Assortative- Individuals mate with others who are like themselves phenotypically for selected traits (similar ).

6. Assortative Mating There are only three possible mating patterns with respect to genotypes for traits controlled by two alleles (A and a). AA × AA Aa × Aa aa × aa

7. Net affect of Assortative Mating Progressive increase in the number of homozygous genotypes (AA & aa). Corresponding decrease in the number of heterozygous genotype (Aa). This trend will continue from generation to generation. POSITIVE ASSORTATIVE MATING Possible parent mating pattern Expected off spring genotypes AA Aa aa AA × AA 4 Aa × Aa 1 2 1 aa × aa 4 Total 5 (42%) 2 (17%) 5 (42%)

8. Disassortative Mating There are six possible mating patterns with respect to genotypes for traits controlled by two alleles (A and a). AA × Aa Aa × aa aa × AA AA × aa Aa × AA aa × Aa

9. Net affect of Disassortative Mating Progressive increase in the frequency of heterozygotes (Aa). Corresponding decrease in the number of homozygous genotypes (AA and aa). This trend will continue from generation to generation. It has the opposite effect as Assortative mating.

10. Net affect of Disassortative Mating NEGATIVE ASSORTATIVE MATING Possible parent mating pattern Expected off spring genotypes AA Aa aa AA × Aa 2 2 AA × aa 4 Aa × AA 2 2 Aa × aa 2 2 aa × AA 4 aa × Aa 2 2 Total 4 (17%) 16 (67%) 4 (17%)

11. WHAT IS GENETIC EQUILIBRIUM? 1 st reported by Yule (1902), Castle (1903) and Pearson (1904). W.E.Castle actually founder of genetic equilibrium principle. Genetic Equilibrium means no change in genetic structure of population (Gene & Genotype Frequency) from one generation to the next. The principle of genetic equilibrium in a large random mating population can be applied for any value of gene frequencies. Therefore, this law of genetic equilibrium under random mating is known as the Hardy-Weinberg law or Hardy-Weinberg principle.

12. INBREEDING Mating between two individuals related by descent ( i.e having a common ancestor) To study the Inbreeding , there are three types of population :- Idealized population Isolates Real population

13. TYPES OF POPULATION Idealized population :- In which all types of mating occur including self- fertilization. The average rate of change in heterozygosity can be illustrated very simply and clearly in an idealized population. Isolates :- Only the most distinct relatives may be mating with maximum avoidance of inbreeding. OR Continue mating of close relative breaks the entire population into lines of descents as Isolates or groups.

14. Real population :- In natural or Real population , the total no of individuals may be large but they all may not contribute to the genetic composition of the next generation because some of the them may not reach the sexual maturity, other may not be able to mate while other which mate may not leave offspring that survive to maturity in the next generation. Inbreeding changes genotype frequencies not allele frequencies.

15. Idealized Population RATE OF INBREEDING INCREMENT:- Consider that in an idealized population there are N individuals, each shedding equal number of gametes which unite at random. The male & female gametes produced by N individuals can be shown as under ; Individuals 1 2 3 N th Male gametes A 1 A 2 A 3 A 4 A 5 A 6 A 2N-1 A 2N Female gametes A 1 A 2 A 3 A 4 A 5 A 6 A 2N-1 A 2N CONT .

16. Any random pairs of opposite sex gametes will have (1/2N) chance for carrying identical genes. F 1 = 1/(2N) In second generation, identical homozygotes will be produced from inbreeding in the 1 st generation & from new replication of genes. Probability of random pairs to be identical:- 1/(2N) {newly replicated genes} Probability of remaining pairs(1-1/2N) to be identical:- (1-1/2N)F 1 {due to previous inbreeding} F 2 =1/2N + (1-1/2N)F 1 F t =1/2N + (1-1/2N)F t-1 =New Inbreeding + Old Inbreeding CONT.

17. Rate of inbreeding increment is 1/2N & symbolized by Δ F . F t = 1 + F t-1 - F t-1 2N 2N = F t-1 + 1 - 1 F t-1 2N 2N =F t-1 + 1 - F t-1 2N = F t-1 + 1 - H t-1 ={Old inbreeding + New 2N inbreeding( Δ F )} CONT.

18. F t = 1/2N + (1-1/2N)F t-1 = Δ F + (1- Δ F) F t-1 = Δ F + F t-1 – Δ F F t-1 = F t-1 + Δ F (1- F t-1 ) Thus, Δ F = F t -F t-1 1-F t-1 Therefore, the rate of inbreeding increment ( Δ F) each generation in an idealized population is:- Δ F = 1/2N = 1- F t-1 2N Δ F = 1 H t-1 2N

19. Isolates The continued mating of close relatives breaks the entire population into lines of descents called as Isolates or Group. The isolate size N = 2 k which is the number of mating individuals in a group or isolate. The N remain constant from generation to generation. The different isolates / groups are of different size , viz Selfed individual with N = 2 = 1. Full sibs with N = 2 1 = 2 Double first Cousin = 2 2 = 4 Quadruple second Cousin = 2 3 = 8 Octuple third Cousin = 2 4 = 16 Most distant Cousins have an isolate size of N = 2 k

20. For an example, in an isolate of size 4 (double first cousin mating's) it was observed that, H 1 = 1/2 H t-1 + 1/4 H t-2 + 1/8 H t-3 The expressions of change (decrease) in heterozygosity per generation under different systems of close inbreeding. In deriving these expressions it was obvious that coefficient of loss in H ( Δ H) was 2-K for distantly related cousin mating. This coefficient is 1/4 times the reciprocal of isolate size N. Therefore, 2+K = and hence,  

21. Δ H = - 2+K = - Since N= 2 k , the multiple of 2. The heterozygosity in t generation ; H t = H t-1 - 2+K H t- (2+k ) = H t-1 - H t-(2+k ) = H t-1 approximately. This indicates that H is decreasing at a rate of 1/4N per generation.  

22. Real Population Real population do not have self fertilization, have unequal number of breeding males and females, have varying number of breeding individuals in different generation, differential contribution of parents, overlapping generations, and minimum inbreeding. In natural or Real population, the total no of individuals may be large but they all may not contribute to the genetic composition of the next generation because some of the them may not reach the sexual maturity, other may not be able to mate while other which mate may not leave offspring that survive to maturity in the next generation.

23. In this male has lesser in number of contribution to equal to that of female which are more in number. So number of individuals affecting genetic constitution of next generation may be lesser than the real population. Effective population size was introduced by Wright (1931). In small population, there is increase in homozygosity (inbreeding effect) and a random drift in gene frequencies due to sampling variance.

24. The concept of effective population size can be made more clear by considering the different situations of real population that differ from ideal population. The different equations for different deviated situations will be derived situations will be derived to convert the actual number (N) to the effective number (N e ) so as the rate of inbreeding increment become equal in real and ideal populations. The is Δ F is related to population size in an ideal population as :- Δ F = 1/2 N The effective size is related is Δ F as N e = 1/2 Δ F. The rate of inbreeding ( Δ F) can be estimated after knowing the effective population size as :- Δ F =  

25. REFERENCES Text book of Population Genetics (Vol. I. Qualitative Inheritance) By S.S.Tomar. Genetics By B.D.Singh