Maths for Biology

Density =

Mass/volume

Allele frequency

no. of copies/total number

Allele frequence for diploid population

total alleles/2(no. of individuals)

Mean vs STD

mean describes centre, STD spread

Standard Error (SE)=

STD/SQR(n)

difference between STD and SE

STD = spread of observations, SE = precision of the mean

Magnification =

image size/actual size

r vs R²

r = direction + strength of linear correlation, R² explained variation of trend line

Percentage difference=

|A-B|/[(A+B)/2] x 100

Simpson’s reciprocal index

higher reciprocal index = greater biodiversity

Simpson’s Reciprocal index =

D=N(N-1) / ∑n(n-1), N= number of organisms, n = number of individuals in specific species

Lincoln index

Used to estimate population size with capture-mark-release-recapture

Lincoln index =

N=(n1 x n2)/m, n1=marked initially, n2 = caught in second sample, m = marked recapture

Assumptions of lincoln index

No immigration/emmigration

Marking does not affect organism

Marks remain visible.

Marked individuals mix back into the population.

Individuals have a reasonably equal chance of capture.

Chi squared

to compare observed frequencies with expected requencies

chi squared =

∑(Observed - expected)²/expected

Null hypothesis

observed differences are consistent with chance variation under the expected model

Degrees of freedom

number of categories - 1

Reject null hypothesis

chi squared greater that critical value, significant difference

Hardy Weinberg Equation

p² + 2pq + q² = 1

Hardy weinberg assumptions

no mutation, random mating, no new alleles, infinite population size, no nautral selection

Hardy weinberg equation meaning

if the real-world genetic data does not match result of equation, natural selection is occuring.