The adult sex ratio (ASR) is a key parameter of the demography of human and other animal populations, yet the causes of variation in ASR, how individuals respond to this variation, and how their response feeds back into population dynamics remain poorly understood. A prevalent hypothesis is that ASR is regulated by intrasexual competition, which would cause more mortality or emigration in the sex of increasing frequency. Our experimental manipulation of populations of the common lizard (Lacerta vivipara) shows the opposite effect. Male mortality and emigration are not higher under male-biased ASR. Rather, an excess of adult males begets aggression toward adult females, whose survival and fecundity drop, along with their emigration rate. The ensuing prediction that adult male skew should be amplified and total population size should decline is supported by long-term data. Numerical projections show that this amplifying effect causes a major risk of population extinction. In general, such an ''evolutionary trap'' toward extinction threatens populations in which there is a substantial mating cost for females, and environmental changes or management practices skew the ASR toward males.adult sex ratio ͉ Lacerta vivipara ͉ male behavior ͉ population extinction ͉ sexual coercion

A distinctive signature of living systems is Darwinian evolution, that is, a propensity to generate as well as self-select individual diversity. To capture this essential feature of life while describing the dynamics of populations, mathematical models must be rooted in the microscopic, stochastic description of discrete individuals characterized by one or several adaptive traits and interacting with each other. The simplest models assume asexual reproduction and haploid genetics: an offspring usually inherits the trait values of her progenitor, except when a mutation causes the offspring to take a mutation step to new trait values; selection follows from ecological interactions among individuals. Here we present a rigorous construction of the microscopic population process that captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by the trait values of each individual, and interactions between individuals. A by-product of this formal construction is a general algorithm for efficient numerical simulation of the individual-level model. Once the microscopic process is in place, we derive different macroscopic models of adaptive evolution. These models differ in the renormalization they assume, i.e. in the limits taken, in specific orders, on population size, mutation rate, mutation step, while rescaling time accordingly. The macroscopic models also differ in their mathematical nature: deterministic, in the form of ordinary, integro-, or partial differential equations, or probabilistic, like stochastic partial differential equations or superprocesses. These models include extensions of Kimura's equation (and of its approximation for small mutation effects) to frequency- and density-dependent selection. A novel class of macroscopic models obtains when assuming that individual birth and death occur on a short timescale compared with the timescale of typical population growth. On a timescale of very rare mutations, we establish rigorously the models of "trait substitution sequences" and their approximation known as the "canonical equation of adaptive dynamics". We extend these models to account for mutation bias and random drift between multiple evolutionary attractors. The renormalization approach used in this study also opens promising avenues to study and predict patterns of life-history allometries, thereby bridging individual physiology, genetic variation, and ecological interactions in a common evolutionary framework.

There is concern that the rate of environmental change is now exceeding the capacity of many populations to adapt. Mitigation of biodiversity loss requires science that integrates both ecological and evolutionary responses of populations and communities to rapid environmental change, and can identify the conditions that allow the recovery of declining populations. This special issue focuses on evolutionary rescue (ER), the idea that evolution might occur sufficiently fast to arrest population decline and allow population recovery before extinction ensues. ER emphasizes a shift to a perspective on evolutionary dynamics that focuses on short time-scales, genetic variants of large effects and absolute rather than relative fitness. The contributions in this issue reflect the state of field; the articles address the latest conceptual developments, and report novel theoretical and experimental results. The examples in this issue demonstrate that this burgeoning area of research can inform problems of direct practical concern, such as the conservation of biodiversity, adaptation to climate change and the emergence of infectious disease. The continued development of research on ER will be necessary if we are to understand the extent to which anthropogenic global change will reduce the Earth's biodiversity.