Maths for A Level Biology - updated edition

In summary so far: total population = A number in ϐirst sample = a  } Proportion of population caught = a A number in second sample = B number marked in second sample = b  } Proportion of second sample marked = b B a A = b B ∴ A = a × B b i.e. total population = number in ϐirst sample × number in second sample number marked in second sample 2.4.2 Simpson’s index Simpson’s index , D , is a measure of the biodiversity of a community, such as the invertebrates in a stream. Its measurement takes into account: ▪ The species richness, i.e. the number of different species. ▪ The species evenness, sometimes called the ‘relative abundance’. If there is a similar number of organisms in each of the species present, the community has a high species evenness. But if one species is dominant, like in an oak wood, then there is a low species evenness. There are different ways of calculating Simpson’s index and your examination board may require you to use a particular formula. You are not expected to remember the formula but you are expected to be able to substitute into it, derive an answer and explain what the answer means. Imagine a stream with four invertebrate species. The table shows the total number of organisms ( N ), the number in each species ( n ). Calculated from this are ( n N ) 2 , used in the first formula and, in the second, third and fourth formulae, ( n − 1) and n ( n − 1). ∑ n ( n − 1) shows all the values of n ( n − 1) added together. Species Number ( n ) n N ( n N ) 2 N − 1 n ( n − 1) Mayϐly nymph 12 0.31 0.10 11 132 Water shrimp 13 0.33 0.11 12 156 Stoneϐly nymph 11 0.29 0.08 10 110 Bloodworm 3 0.08 0.01 2 6 Total N  = 39 Σ ( n N ) 2 = 0.30 (2 dp) ∑ n ( n − 1) = 404 2 Processed numbers 45