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.KEY WORDS: Adaptation, maladaptation, optimality, Ornstein-Uhlenbeck process, phylogenetic comparative method, phylogenetic effect, phylogenetic inertia.Optimality models and other adaptive hypotheses are often tested by comparing their predictions to the trait values of species in different environments (e.g., Ridley 1983;Harvey and Pagel 1991). Most comparative methods are, however, based on models that are inconsistent with evolution toward an optimum. For example, the method of independent contrasts makes the assumption that traits evolve according to a Brownian-motion process (Felsenstein 1985), but if evolution is governed by this process, the expected trait value of a descendant species must equal the trait value of its ancestor, and there can be no systematic evolution toward an optimal state. If the ancestral species' trait value does not match the optimum, then the trait value of the descendant species is not expected to match it any better. Hansen and Orzack (2005) 4 Current address: Department of Zoology, University of Hawaii at Manoa, Honolulu, Hawaii 96822 called this the problem of inherited maladaptation. A multivariate Brownian-motion process can be used to represent correlated evolutionary changes in two or more traits, but correlated evolution is not equivalent to adaptive evolution. For example, suppose we predict that the optimal relation between two traits, x and y, is y = x. This simple prediction is incompatible with evolution as a Brownian-motion process. Even if there is a positive correlation between changes in y and x, any deviation from the 1:1 line will be inherited by the descendant species and there will be no systematic tendency to evolve toward the predicted relationship.This lack of attention to the fundamental nature of adaptive evolution has influenced the application of phylogenetic comparative methods. Such methods are often used erroneously to "correct" for phylogeny when they should only correct for the residual effects of phylogeny that remain after adaptation has been accounted for. A phylogenetic signal in the data can arise both from the influence of ancestral character states due to a lag or inertia in adaptation to the current niche, and from the effects of adaptation to niche variables that are themselves phylogenetically structured. One should correct only for the former. Correcti...

Longitudinal data on natural populations have been analyzed using multi-stage 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 analyze 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 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.

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We model density-independent growth of an age-(or stage-) structured population, assuming that mortality and reproductive rates fluctuate as stationary time series. Analytical formulas are derived for the distribution of time to extinction and the cumulative probability of extinction before a certain time, which are determined by the initial age distribution, and by the infinitesimal mean and variance, # and a2, of a diffusion approximation for the logarithm of total population size. These parameters can be estimated from the average life history and the pattern of environmental fluctuations in the vital rates. We also show that the distribution of time to extinction (conditional on the event) depends on the magnitude but not the sign of t. When the environmental fluctuations in vital rates are small or moderate, the diffusion approximation gives accurate estimates of cumulative extinction probabilities obtained from computer simulations.The theory of extinction times for single populations has applications in diverse fields, including paleontology, island biogeography, community ecology, and conservation biology. Various analytical models have been constructed to estimate extinction times, probabilities of extinction, or both for a population subject to stochastic variation in demographic parameters (e.g., refs. 1-7). Two sources of random variation in population growth can be distinguished: first, demographic stochasticity caused by finite population size, in which each individual independently experiences age-specific probabilities of survival and reproduction; and second, environmental stochasticity, which affects the vital rates of all individuals similarly. Demographic stochasticity is important only in small populations, since chance variation in vital rates among individuals tends to average out in large populations (greater than about 100 individuals), whereas environmental factors can produce substantial fluctuations in demographic parameters in populations of any size. In natural populations subject to substantial abiotic and biotic perturbations, environmental stochasticity is usually far more important than demographic stochasticity in causing extinction (6, 7). Previous analytical models of stochastic population growth and extinction either lacked age structure or dealt only with demographic stochasticity (1-7).Here we analyze the extinction dynamics of a population subject to environmental fluctuations in age-specific birth and death rates. The theory of population growth developed by Cohen (8,9) and Tuljapurkar and Orzack (10, 11) is used to derive a diffusion approximation for the logarithm of total population size in a population subject to density-independent fluctuations in vital rates. THE MODELAssumptions. A standard model of density-independent growth in an age-(or stage-) structured population specifies a recursion formula for the numbers of individuals in each age class or developmental stage at time t + 1 in terms of those at the previous time t, n(t + 1) = A(t)n(t), [1] where n...

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 malebiased. 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.he sex ratio at conception in humans is unknown, despite hundreds of years of speculation and research. Investigations of the sex ratio date back at least as far as Graunt (1) who described a net excess of male births (2). By the late 1800s, it was clear that more males than females die during later pregnancy (3). Beyond these facts, the demographic and genetic dynamics of the sex ratio from conception to birth are poorly resolved.The claim that the conception or primary sex ratio (PSR) is more male-biased than the birth sex ratio appears often in textbooks (4, 5) and in the scientific literature (e.g., refs. 6-11), usually with little or no description of evidence. Estimates of the PSR in these studies are typically 0.56 (proportion males) or greater. Many fewer researchers have claimed that the PSR is unbiased or slightly male-biased (12-16). A handful of researchers has claimed or implied that the PSR is female-biased (17-19) or claimed that the PSR cannot be estimated due to lack of appropriate data and/or methodological problems (20)(21)(22).Previous estimates of the PSR have no meaningful basis in data from the time of conception (or within at least a month of it). At best, the PSR has been estimated via backward extrapolation from data on induced or spontaneous abortions, fetal deaths, or live births; most of the non-live-birth data stems from the second or third trimester of pregnancy. In addition, even if one ignores the fallibility of extrapolation, biased estimates of the PSR based on spontaneous abortions and fetal deaths have usually been regarded as arising from unbiased samples of a population of embryos or fetuses having a biased PSR. The alternativ...