# Biomathematics: An Introduction by David Machin (auth.)

By David Machin (auth.)

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**Extra resources for Biomathematics: An Introduction**

**Example text**

N i=l I where ai = i and hence ai+l i+l. 4 may be written i=n sn z: i=l b. l. where b i -- i 2 and hence b i+l = (i + 1) 2 . Now in some situations it is possible to evaluate the sum of a series for general n. 2 l. 6) n(n + 1)(2n + 1) 6 are the sums of these series for non-negative integers. These you should check for the particular value, n = 5, that we discussed earlier. If we consider the data of Qroblem 9, chapter 1, then we could number the whales 1, 2, ••• , 7. Let xi denote the total length o f the 1..

This cross is represented in the table below, the main body of which gives the genotypes of the offspring. AA If among the male gametes in a population the proportion of allele 'a is P and of allele A is Q, where P + Q = 1, and the same is true for the females, then assuming random mating and similar viabilities, the proportions of the offspring types are given by the above ~able with aa replaced by P x P = P2 , aA by 2 PQ, Aa by QP, and AA by Q • If we pool the heterozygotes - that is we do not distinguish between a A and Aa offspring - then the genotype proportions in the population are Offspring genotype Offspring proportion Aa 2PQ 44 These proportions are just the terms in the product (P + Q) x (P + Q), since p2 + 2PQ + Q2 = (P + Q)2 We call P 2 (3.

Use this expression to determine the distance between the points (1, 2) and (-2, -2). 39 10. Narise (1965) has described a series of competition experiments between two species of Drosophilie in which two-dayold virgin female and male flies of Drosophila melanogaster and of D. simulans were mixed together and maintained in 284 ml bottles for 5 days to allow mating and laying of eggs; at the end of this time they were discarded. The sex ratio in both species was 1:1. Ten pairs of flies were introduced into each bottle but with the species in differing relative proportions.