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Estimates of Population Parameters


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1. Population size

Capture–recapture (for small population sizes)N = s / p where p = r / swhere

s is the sample size captured and marked, and the sample size of the second capture;

r is the number of marked individuals in the second capture;

N is the population size

2. Measures of diversity

(a) Species diversity:

(i) Simpson's indexD = 1 ∑ i = 1 S P i 2where

Pi is the proportion of individuals/biomass to the total sample of the ith species;

s is the total number of species

(ii) Shannon–Wiener indexH = − ∑ i = 1 s P i l n P i

(b) Population diversity:

(i) Nucleotide diversity (π)π = Π / LwhereΠ = 1 [ n (n - 1) / 2 ] Σ Π i jand E (Π) = θ θ = 4 Ne uwhere

L is the length of DNA sequence;

n is the number of sequences examined;

Πij is the number of nucleotide differences between the ith and jth sequences;

Ne is the effective population size;

u is the mutation rate

(ii) Allele frequency data

Homozygosity of population j (Hj)Hj = ∑ i = 1 L p i j 2heterozygosity (allele diversity) of population j (hj)h j = 1 - H javerage heterozygosity of s populations (hs)h s = ∑ j = 1 s h j / sgene frequency variations between populations (FST)F ST = (h - h s) / h where h = 1 - ∑ ι = 1 L (p ¯ ι) 2where

L is the number of alleles examined of a given locus;

pij is the gene frequency of allele i in population j;

i is the average gene frequency of allele i in s populations

(c) Genetic distance:

(i) Genetic distance between two DNA sequences (K) using the Kimura 2 parameter modelK = 1 / 2 ln a + 1 / 4 ln bwhere a = 1 1 - 2 P - Qand b = 1 1 - 2 Qwhere

P is the proportion of transitions;

Q is the proportion of transversions;

K is the number of substitutions per base site

(ii) Estimate of genetic distance based on allele frequencies (D)b = 2 ∑ j = 1 s n j h j s (2 n ? - 1) a + b = ∑ j = 1 s n j ∑ i = 1 L (p i j - p ? i) 2 n (s - 1) + (2 n - 1) b 2 n where n ¯ = ∑ j = 1 s n j / sand n = n ¯ s s - 1 - ∑ ϕ = 1 s n ϕ 2 n ¯ s (s - 1) Θ = a / (a + b) D = - ln (1 - Θ)where

nj is the sample size of population j

From A Dictionary of Ecology in Oxford Reference.

Subjects: Ecology and Conservation.



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