Sex ratio and sex allocation These are two major contributions of evolutionary biology that provide deep insight into frequency dependent selection, individual selection, and group selection. We will use sex ratio theory to illustrate an evolutionarily stable strategy. We will then use sex allocation theory to illustrate some fundamental adaptations of individuals to get their genes into future generations. Shaw-Mohler equation for sex ratio Consider a population of N reproductive females that each produce C eggs, with proportion r of them being sons Proportion Sm and Sf of sons and daughters survive to breed. Introduce into population a mutant female who alters the sex ratio of her offspring to ȓ. Will this female contribute more or fewer genes to the next generation, compared to the typical female in the population? Now suppose that the current population of reproductive adults, the offspring of the N + 1 females, themselves produce a total of K offspring (grandchildren of the original females plus mutant female). Half of the genes in the grandchildren came via males and half came via females. Call mutant female “mom” Mom will contribute genes to the following number of grandchildren through her sons and daughters ½ * (number of grandchildren) * (proportion of reproductive males who are mom’s sons) SmCȓ = ½ (K) [ --------------------- ] (SmCȓ + N SmCr) expression for sons ½ * (number of grandchildren) * (proportion of reproductive females who are mom’s daughters SfC(1-ȓ) = ½ (K) [ ------------------------- ] SfC(1-ȓ) + N Sf(1-r) expresssion for daughters Now, we add these, call it Wt for total fitness. If N is large, then can eliminate first term in denominator. Result is: SmCȓ Wt = ½ (K) [ Let: ṁ = surviving sons from mom m = surviving sons from each additional female + + SfC(1-ȓ) -------NSmCr ------- ] NSfC(1-r) Refer to as equation 1 ḟ = surviving daughters from mom f = surviving daughters from each additional female ṁ ḟ ṁ ḟ Then Wt = (1/2) (K/N) [ ------ + ----m f ] , proportional to [ ------ + ----- ] m f Wt ṁ ḟ [ ------ + ----- ] m f ȣ is the general form of the Shaw-Mohler equation for sex ratio In words, it says that total fitness of mom is the sum of that of her surviving sons and daughters relative to that of surviving sons and daughters of other females in the population. Selection favors a mutant gene which alters various life history parameters if the percent gain in fitness through one sex function exceeds the percent loss through the other sex function. If ṁ = m and ḟ = f, then Wt = 2. The mutant is selected for if Wt > 2, and is selected against if Wt < 2. Let us consider the Shaw-Mohler equation graphically SmCȓ Wt = ½ (K) [ -------NSmCr + + SfC(1-ȓ) --------- ] NSfC(1-r) equation 1 ½ K/N is a proportionality factor and the Sf and Sm and C cancel out ȓ 1-ȓ -- + -----r 1-r Wt If r = 0.25, then Wt = ȓ/0.25 + (1 - ȓ)/(1 – 0.25) = 4/3 + 8/3 (ȓ) If r = 0.75, then Wt = ȓ/0.75 + (1 - ȓ)/(1 – 0.75) = 4 – 8/3 (ȓ) If r = 0.5, then Wt = ȓ/0.5 + (1 - ȓ)/(1 – 0.5) = 2 ȣ This is a linear equation in ȓ Sex ratio of 0.5 is an evolutionarily stable strategy Now, imagine r = 0.49 or r = 0.51. The lines will become flatter and approach the line Wt = 2 when r = 0.50. QED Experimental Modification of Sex Ratio Biases in Sex Ratio from 0.5 Local Mate Competition Mating may not occur randomly among members of a large population In many species of parasitoid wasps, progeny of one or a few females emerge from a single host and almost immediately mate with each other. The daughters then disperse in search of new hosts. Within each host (group), the sex ratio favored by individual selection is 0.5. However, groups founded by female-biased genotypes contribute more individuals and genes to the population as a whole than groups founded by unbiased genotypes. This can result in female-biased sex ratios. The greater the number of founders of a group, the more nearly even the optimal sex ratio should be. In the hymenoptera, haploid males have all genes identical by descent from their diploid mother. Therefore, as inbreeding increases, mothers will transmit more genes to subsequent generations through their daughters. Female biased sex ratios in fig wasps Predicted by local mate competition theory Observed in three species of fig wasps Sex Allocation The allocation of reproductive effort to male versus female function in hermaphrodites (individuals with both sexes) and to male versus female offspring in species with separate sexes. Sex ratio is a characteristic of the population. Circumstances might differ among individuals that may favor production of one sex over the other, IF they can achieve more fitness from that sex. Trivers-Willard Hypothesis Trivers-Willard hypothesis and Red Deer Experimental modification of female condition Lesser black-backed gull Normally lay 3 eggs in clutch Forced protracted egg-laying by removing 1 egg/day beginning on day 2. Provided food supplements to some birds. Males larger than females and suffered disproportionately during experiment Offspring sex ratio became more female-biased in female gulls without food supplementation Sex ratio differences between first and second broods in house wrens Sex bias in Seychelles Warbler Daughters stay to help, males disperse, but too many helpers compete for food. Biased sex allocation has been identified with the following: 1. Seasonal variation in food availability – females produce larger sex when food is more abundant. Ex. Females in birds of prey and males in songbirds. 2. Attractive secondary sexual characters or parental quality – produce more sons when mated with males of exceptional quality Ex. Blue tits that mate with males with large ultraviolet patch In some polygynous systems, primary females produce more sons while secondary females produce more daughters. Male Female Male flowers can be larger than female flowers Perianth consists of the petals and sepals together. Comparative study showing more male investment in animal-pollinated flowers * * * Sex allocation in relation to sex change The size advantage hypothesis Sex allocation will change from male-function to female-function, or vice-versa, when fitness increases differentially as a function of size. Flowering plants, shrimp, and fishes are the main organisms in which sex change has been documented. Switch from male to female in plants Sex change in fishes represents change in sex allocation carp silverside sea bream wrasse Sex allocation in the Hawaii akepa Bird has clutch size of 2 eggs. Any bias means entire clutch is one sex. The bird breeds during a seasonal decline in food There is more food for nests in March and April than during May and June Male fledglings (solid dots) captured in June are larger than female fledglings (open dots). Sexual dimorphism of bill length is greater in June fledglings than in adults 13 67 8 77 12 9 10 Bill length (mm) 11 8 10 9 8 Male Female 7 6 June fledglings July fledglings Adults Delayed Plumage Maturation in Male Hawaii Akepa Hatch year Second year Third year Fourth year and older Female Akepa also can become more colorful with age * * Dull females are 0.39 of females, but all 6 TY males were paired with these P = 0.004 * More colorful females (*) survive better, have higher nesting success, and avoid third year males Stabilizing selection on bill length in akepa, surviving males had longer bills than non-surviving males 13 A 18 23 3 Male 13 B Female 46 12 9 9 12 2 14 3 36 16 Bill length (mm) 11 11 11 10 10 survive non-survive 9 SY TY ATY 9 SY TY AHY Age Male akepa must survive to their fourth year in order to mate with females that are the fittest. To do so, they need adequately long bills. That is the adaptation of seasonal variation in sex allocation.