More complex models of selection Spatial variation Temporal variation Frequency-dependence

spatially heterogeneous selection patch typeA 1 A 1 A 1 A 2 A 2 A 2 i 1 + s 1 1 – s j 1 – s s introduce A 2 at low frequency initially, f(A 1 ) = 1 in 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 A 1 A 1 A 1 A 2 A 2 A 2 wet s dry 1-t 1 1

frequency-dependent selection frequency in array [input] rare common frequency eaten [output] random predation frequency-dependent predation fitness advantage when rare disadvantage when common

frequency-dependent selection A 1 A 1 A 1 A 2 A 2 A 2 geno. freq. p 2 2pq q 2 w ij 1-tp 2 1-2tpq1-tq 2 w ij 1-p 2 1-2pq1-q 2 w ij is a function of frequency: (1-t)(f ij ) = w ij lim w 22 1 andlim w 22 0 q 0 q 1

(1-t)(f ij ) = w ij frequency, f(A i A j ) relative fitness, 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 cichlid Peridossus microlepis (Hori 1993)

Lake Tanganyika 2 sites, 7 km apart follow 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) prey right-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, success by the two morphs of P. microlepis is either equal 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

dextral attacks sinistral attacks

frequency-dependent selection may be widespread self-incompatibility alleles in plants apostatic selection by predators mimicry complexes (negative f-d when the mimic is palatable; positive f-d when the mimic is 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