More complex models of selectionMore complex models of selection

Spatial variation

Temporal variation

Frequency-dependence

spatially heterogeneous selection

patch type A1A1 A1A2 A2A2

i 1 + s 1 1 – s j 1 – s 1 1 + s

introduce A2

at low frequency

initially, f(A1) = 1in all patches

pr(polymorphism)-- relative frequency of patch types-- strength and symmetry of selection-- initial allele frequencies (some models)-- dispersal capabilities of the organism

temporal heterogeneity in selection

-- random fluctuations-- long-term change-- regular oscillations

A1A1 A1A2 A2A2

wet 1 1 1-sdry 1-t 1 1

frequency-dependent selection

frequency in array [input]

rare common

frequ

ency

eate

n [

outp

ut] random

predation

frequency-dependent predation

fitness advantage when rare

disadvantage when common

frequency-dependent selection

A1A1 A1A2 A2A2

geno. freq. p2 2pq q2

wij 1-tp2 1-2tpq 1-tq2

wij 1-p2 1-2pq 1-q2

wij is a function of frequency: (1-t)(fij) = wij

lim w22 1 and lim w22 0 q 0 q 1

(1-t)(fij) = wij

frequency, f(AiAj)

rela

tive fi

tness

, w

ij

at equilibrium allele frequencies, all genotypes can have the same fitness

w is not necessarily maximized at equilibrium

frequency dependent selection in the cichlidPeridossus microlepis

(Hori 1993)

Lake Tanganyika

2 sites, 7 km apartfollow populations for 11 years, sampling at

1-2 year intervals

P. microlepis eats scales from living fish

mouth is asymmetrical: left- or right- mouthed ‘mouthedness’ determined by a single locus with 2 alleles –

dextral (DD, Dd) is dominant to sinistral (dd)

preyright-mouthed (dextral)

left-mouthed (sinistral)

fluctuations in the frequency of left-mouthed fish

explanation: prey fish learn which side to protect, depending on which morph of P. microlepis is common

null hypothesis: no learning response by prey, successby the two morphs of P. microlepis is eitherequal or proportional to their frequency

alternate hypothesis: the common morph will have lower success than the rare morph

test by measuring success rates at times when each morph is common

dextr

al att

ack

s

sinistral attacks

frequency-dependent selection may be widespread

self-incompatibility alleles in plants

apostatic selection by predators

mimicry complexes (negative f-d when the mimicis palatable; positive f-d when the mimicis distasteful

sexual reproduction and parasites

sexual selection

sex determination in haplodiploids

spatial heterogeneity can maintain a genetic polymorphism- relative frequency of patch types- relative strength of selection within patch types- dispersal capabilities of the organism

temporal heterogeneity will maintain genetic variation under certain conditions

- random fluctuations or (slow) long-term change in selection pressures promote genetic polymorphisms

- regular oscillations (i.e., seasonality) in selection tend to eliminate all but one allele from the population

frequency-dependent selection- negative frequency-dependent selection will maintain a polymorphism with dynamic (vs. stable) allele frequencies- frequency-dependent selection may be widespread in nature