The human sex ratio from conception to birth.

We describe the trajectory of the human sex ratio from conception to birth by analyzing data from (i) 3- to 6-d-old embryos, (ii) induced abortions, (iii) chorionic villus sampling, (iv) amniocentesis, and (v) fetal deaths and live births. Our dataset is the most comprehensive and largest ever assembled to estimate the sex ratio at conception and the sex ratio trajectory and is the first, to our knowledge, to include all of these types of data. Our estimate of the sex ratio at conception is 0.5 (proportion male), which contradicts the common claim that the sex ratio at conception is male-biased. The sex ratio among abnormal embryos is male-biased, and the sex ratio among normal embryos is female-biased. These biases are associated with the abnormal/normal state of the sex chromosomes and of chromosomes 15 and 17. The sex ratio may decrease in the first week or so after conception (due to excess male mortality); it then increases for at least 10-15 wk (due to excess female mortality), levels off after ∼20 wk, and declines slowly from 28 to 35 wk (due to excess male mortality). Total female mortality during pregnancy exceeds total male mortality. The unbiased sex ratio at conception, the increase in the sex ratio during the first trimester, and total mortality during pregnancy being greater for females are fundamental insights into early human development.

The influence of demographic stochasticity on evolutionary dynamics and stability.

We derive the frequency-dependent selection coefficient caused by "demographic" stochasticity resulting from the random sampling of opponents an individual faces during behavioral "contests" with other individuals. The mean, variance, and higher moments of fitness all influence the direction and strength of selection. A frequency-dependent trait can be stable when an individual's fitness depends upon an infinite number of contests with other individuals and unstable when it depends upon a finite number of contests. Conversely, unstable equilibria for an infinite number of contests can be stable when there is a finite number of contests. At stable equilibria for a finite number of contests, higher moments of fitness can outweigh the joint influence of the first two moments so that natural selection favors "within-generation" or developmental-trait variation (also known as phenotypic plasticity) contrary to the claim that natural selection always acts against such variation. We use second-moment estimates of the fitness functions in a diffusion approximation to compute fixation probabilities of competing strategies. These estimates are shown to be qualitatively consistent with those derived from simulations when population sizes are sufficiently large to ignore the contribution of higher-moment terms. We also show that explicit solutions to the diffusion approximation only exist for pair-wise interactions that lead to positive frequency-dependent selection.

Resource transfers and evolution: helpful offspring and sex allocation.

In some vertebrates, offspring help their parents produce additional offspring. Often individuals of one sex are more likely to become "helpers at the nest". We analyze how such sex-biased offspring helping can influence sex-ratio evolution. It is essential to account for age-structure because the sex ratios of early broods influence how much help is available for later broods; previous authors have not correctly accounted for this fact. When each female produces the same sex ratio in all broods (as assumed in all previous analyses of sex-biased helping), the optimal investment strategy is biased towards the more-helpful sex. When a female has facultative control over the sex ratio in each brood and each helper of a given sex increases the resource available for offspring production by a fixed amount, the optimal strategy is to produce only the more-helpful sex in early broods and only the less-helpful sex in later broods. When there are nonlinear returns from helping, i.e., each helper increases the amount of resource available for reproduction by an amount dependent upon the number of helpers, the optimal strategy is to maximize resource accrual from helping in early broods (which may involve the production of both sexes) and then switch to the exclusive production of the less-helpful sex in later broods. The population sex ratio is biased towards the more-helpful sex regardless of whether the sex ratio is fixed or age-dependent. When fitness returns from helping exhibit environmental patchiness, females are selected to produce only males on some patches and only females on others, and the population sex ratio may be biased in either direction. We discuss our results in light of empirical information on offspring helping, and we show via meta-analysis that there is no support for the claim of Griffin et al. [Griffin, A.S., Sheldon, B.C., West, S.A., 2005. Cooperative breeders adjust offspring sex ratios to produce helpful helpers. Amer. Nat. 166, 628-632] that parents produce more of the helpful sex when that sex is rare or absent.

The philosophy of modelling or does the philosophy of biology have any use?

Biologists in search of answers to real-world issues such as the ecological consequences of global warming, the design of species' conservation plans, understanding landscape dynamics and understanding gene expression make decisions constantly that are based on a 'philosophical' stance as to how to create and test explanations of an observed phenomenon. For better or for worse, some kind of philosophy is an integral part of the doing of biology. Given this, it is more important than ever to undertake a practical assessment of what philosophy does mean and should mean to biologists. Here, I address three questions: should biologists pay any attention to 'philosophy'; should biologists pay any attention to 'philosophy of biology'; and should biologists pay any attention to the philosophy of biology literature on modelling? I describe why the last question is easily answered affirmatively, with the proviso that the practical benefits to be gained by biologists from this literature will be directly proportional to the extent to which biologists understand 'philosophy' to be a part of biology, not apart from biology.

Static and dynamic expression of life history traits in the Northern Fulmar (Fulmarus glacialis).

Understanding the static and dynamic expression of life history traits is a prerequisite for the development of a causal theory of the evolution of aging and of life histories. We analyzed the statics and dynamics of reproduction and survival in a wild population of the Northern Fulmar, Fulmarus glacialis (Procellaridae). Survival rate is most influenced by year as compared to age and cohort. When temporal variation is ignored, survival rate increases slowly with age and then declines more rapidly at late ages. Survival rate contingent upon reproductive "stratum" (producing an egg, hatching an egg, fledging a hatchling) also exhibits this pattern. Survival and reproduction have a positive static association in that survival rate increases as the apparent energy allocated to reproduction increases (as indexed by stratum). There is a broad distribution of realized lifetime reproductive success, which could be due to "fixed" heterogeneity, with some individuals always having low survival and reproduction and others always having high survival and reproduction, or be due to "dynamic" heterogeneity, with all individuals having the same expected reproductive and survival rates. Analysis of stochastic stratum dynamics indicates that individuals do not remain long in any given stratum and suggest that the variation among individuals with respect to lifetime reproductive success is due to dynamic heterogeneity. The probability of producing an egg increases with age for both sexes, whereas the probability of producing a fledgling initially declines with age and then increases. These results underscore the necessity of understanding the static and dynamic expression of demographic traits when making a causal claim about their evolution.

Dynamic heterogeneity and life history variability in the kittiwake.

1. Understanding the evolution of life histories requires an assessment of the process that generates variation in life histories. Within-population heterogeneity of life histories can be dynamically generated by stochastic variation of reproduction and survival or be generated by individual differences that are fixed at birth. 2. We show for the kittiwake that dynamic heterogeneity is a sufficient explanation of observed variation of life histories. 3. The total heterogeneity in life histories has a small contribution from reproductive stage dynamics and a large contribution from survival differences. We quantify the diversity in life histories by metrics computed from the generating stochastic process. 4. We show how dynamic heterogeneity can be used as a null model and also how it can lead to positive associations between reproduction and survival across the life span. 5. We believe our approach to identifying the nature of among-individual heterogeneity yields important insights into the forces that generate within-population variation of life-history traits. It provides an alternative to claims that fixed individual differences are a major determinant of heterogeneity in life histories.

Dynamic heterogeneity in life histories.

Longitudinal data on natural populations have been analysed using multistage models in which survival depends on reproductive stage, and individuals change stages according to a Markov chain. These models are special cases of stage-structured population models. We show that stage-structured models generate dynamic heterogeneity: life-history differences produced by stochastic stratum dynamics. We characterize dynamic heterogeneity in a range of species across taxa by properties of the Markov chain: the entropy, which describes the extent of heterogeneity, and the subdominant eigenvalue, which describes the persistence of reproductive success during the life of an individual. Trajectories of reproductive stage determine survivorship, and we analyse the variance in lifespan within and between trajectories of reproductive stage. We show how stage-structured models can be used to predict realized distributions of lifetime reproductive success. Dynamic heterogeneity contrasts with fixed heterogeneity: unobserved differences that generate variation between life histories. We show by an example that observed distributions of lifetime reproductive success are often consistent with the claim that little or no fixed heterogeneity influences this trait. We propose that dynamic heterogeneity provides a 'neutral' model for assessing the possible role of unobserved 'quality' differences between individuals. We discuss fitness for dynamic life histories, and the implications of dynamic heterogeneity for the evolution of life histories and senescence.

A comparative method for studying adaptation to a randomly evolving environment.

Most phylogenetic comparative methods used for testing adaptive hypotheses make evolutionary assumptions that are not compatible with evolution toward an optimal state. As a consequence they do not correct for maladaptation. The "evolutionary regression" that is returned is more shallow than the optimal relationship between the trait and environment. We show how both evolutionary and optimal regressions, as well as phylogenetic inertia, can be estimated jointly by a comparative method built around an Ornstein-Uhlenbeck model of adaptive evolution. The method considers a single trait adapting to an optimum that is influenced by one or more continuous, randomly changing predictor variables.

The evolution of strategy variation: will an ESS evolve?

Evolutionarily stable strategy (ESS) models are widely viewed as predicting the strategy of an individual that when monomorphic or nearly so prevents a mutant with any other strategy from entering the population. In fact, the prediction of some of these models is ambiguous when the predicted strategy is "mixed", as in the case of a sex ratio, which may be regarded as a mixture of the subtraits "produce a daughter" and "produce a son." Some models predict only that such a mixture be manifested by the population as a whole, that is, as an "evolutionarily stable state"; consequently, strategy monomorphism or polymorphism is consistent with the prediction. The hawk-dove game and the sex-ratio game in a panmictic population are models that make such a "degenerate" prediction. We show here that the incorporation of population finiteness into degenerate models has effects for and against the evolution of a monomorphism (an ESS) that are of equal order in the population size, so that no one effect can be said to predominate. Therefore, we used Monte Carlo simulations to determine the probability that a finite population evolves to an ESS as opposed to a polymorphism. We show that the probability that an ESS will evolve is generally much less than has been reported and that this probability depends on the population size, the type of competition among individuals, and the number of and distribution of strategies in the initial population. We also demonstrate how the strength of natural selection on strategies can increase as population size decreases. This inverse dependency underscores the incorrectness of Fisher's and Wright's assumption that there is just one qualitative relationship between population size and the intensity of natural selection.

Assessing current adaptation and phylogenetic inertia as explanations of trait evolution: the need for controlled comparisons.

The determination of whether the pattern of trait evolution observed in a comparative analysis of species data is due to adaptation to current environments, to phylogenetic inertia, or to both of these forces requires that one control for the effects of either force when making an assessment of the evolutionary role of the other. Orzack and Sober (2001) developed the method of controlled comparisons to make such assessments; their implementation of the method focussed on a discretely varying trait. Here, we show that the method of controlled comparisons can be viewed as a meta-method, which can be implemented in many ways. We discuss which recent methods for the comparative analysis of continuously distributed traits can generate controlled comparisons and can thereby be used to properly assess whether current adaptation and/or phylogenetic inertia have influenced a trait's evolution. The implementation of controlled comparisons is illustrated by an analysis of sex-ratio data for fig wasps. This analysis suggests that current adaptation and phylogenetic inertia influence this trait.

Analysis and exploration of the use of rule-based algorithms and consensus methods for the inferral of haplotypes.

The difficulty of experimental determination of haplotypes from phase-unknown genotypes has stimulated the development of nonexperimental inferral methods. One well-known approach for a group of unrelated individuals involves using the trivially deducible haplotypes (those found in individuals with zero or one heterozygous sites) and a set of rules to infer the haplotypes underlying ambiguous genotypes (those with two or more heterozygous sites). Neither the manner in which this "rule-based" approach should be implemented nor the accuracy of this approach has been adequately assessed. We implemented eight variations of this approach that differed in how a reference list of haplotypes was derived and in the rules for the analysis of ambiguous genotypes. We assessed the accuracy of these variations by comparing predicted and experimentally determined haplotypes involving nine polymorphic sites in the human apolipoprotein E (APOE) locus. The eight variations resulted in substantial differences in the average number of correctly inferred haplotype pairs. More than one set of inferred haplotype pairs was found for each of the variations we analyzed, implying that the rule-based approach is not sufficient by itself for haplotype inferral, despite its appealing simplicity. Accordingly, we explored consensus methods in which multiple inferrals for a given ambiguous genotype are combined to generate a single inferral; we show that the set of these "consensus" inferrals for all ambiguous genotypes is more accurate than the typical single set of inferrals chosen at random. We also use a consensus prediction to divide ambiguous genotypes into those whose algorithmic inferral is certain or almost certain and those whose less certain inferral makes molecular inferral preferable.

SEX-RATIO CONTROL IN A PARASITIC WASP, NASONIA VITRIPENNIS. II. EXPERIMENTAL ANALYSIS OF AN OPTIMAL SEX-RATIO MODEL.

An optimal theory of facultative sex-ratio adjustment (Werren, 1980) was tested using the data from a series of sequential oviposition experiments (Orzack and Parker, 1986). Sex ratios produced by several genotypes in previously parasitized hosts differ significantly from the theoretical prediction. In addition, there is more variance of these "second" sex ratios than would be generated purely by sampling. I outline an alternative model of sex-ratio determination, based upon an imperfect ability of second females to detect previous parasitization, which accounts for the trends observed in the data. These results imply that selection on second sex ratios is weak or that females cannot control sex ratios finely enough to manifest the proper response. This analysis along with other results (Orzack and Parker, 1986; Parker and Orzack, 1985; Grant et al., 1974; Werren et al., 1981; Skinner, 1982) suggests that we need a more comprehensive theory of sex-ratio evolution, one which accounts for the diversity of first and second sex ratio phenotypes in this species.

SEX-RATIO CONTROL IN A PARASITIC WASP, NASONIA VITRIPENNIS. I. GENETIC VARIATION IN FACULTATIVE SEX-RATIO ADJUSTMENT.

The precision of sex-ratio control in a parasitic wasp, Nasonia vitripennis (Pteromalidae) was investigated using a series of "sequential oviposition" experiments in which a female oviposits on hosts previously visited by another female. There are clear genotypic differences in the averages of these "second" sex ratios. Indeed, one genotype does not alter sex ratio detectably. Two genotypes with identical average sex ratios on previously unparasitized hosts have distinct second sex ratios. Artificial selection on one strain to produce less female-biased "first" sex ratios in previously unparasitized hosts has not affected the ability of that strain to adjust sex ratio, suggesting that the proximal mechanisms controlling first and second sex ratios can change independently. Adjustment of sex ratios is accomplished by the production of fewer females and more males. Sex ratios produced in control hosts indicate that sex ratios are adjusted in hosts independently of one another. Second sex-ratio response also appears to be independent of host clumping. These results represent both a challenge to our present understanding of sex-ratio evolution (see Orzack, 1986) and a foundation for experimental description of this important adaptation.