We used life-history theory to predict reaction norms for age and size at maturation. We assumed that fecundity increases with size and that juvenile mortality rates of offspring decrease as ages-at-maturity of parents increase, then calculated the reaction norm by varying growth rate and calculating an optimal age at maturity for each growth rate. The reaction norm for maturation should take one of at least four shapes that depend on specific relations between changes in growth rates and changes in adult mortality rates, juvenile mortality rates, or both. Most organisms should mature neither at a fixed size nor at a fixed age, but along an age-size trajectory. The model makes possible a clear distinction between the genetic and phenotypic components of variation. The evolved response to selection is reflected in the shape and position of the reaction norm. The phenotypic response of a single organism to rapid or slow growth is defined by the location of its maturation event as a point on the reaction norm. A quantitative test with data from 19 populations and species of fish showed that predictions were in good agreement with observations (r = 0.93, P < 0.0001). The predictions of the model also agreed qualitatively with observed phenotypic variation in age and size at maturity in humans, platyfish, fruit flies, and red deer. This preliminary success suggests that experiments designed to test the predictions directly will be worthwhile.

whose fates have been followed since 1971. Tissue sampling for DNA analyses started in 1988. Blood samples were taken from all captured sheep until 1993 and stored in preservative at 220 8C. Sampling resumed in 1997, when hair samples were taken from all captured sheep by plucking 50-100 hairs including roots from the back or flank. Hairs were kept either in paper envelopes or plastic bags containing about 5 g of silica at room temperature. From 1998 to 2002, a tissue sample from each captured sheep was taken from the ear with an 8-mm punch. Ear tissue was kept at 220 8C in a solution of 20% dimethylsulphoxide saturated with NaCl. We sampled 433 marked individuals over the course of the study.DNA was extracted from blood with a standard phenol-chloroform method, and from either 20-30 hairs including follicles or about 5 mg of ear tissue, using the QIAamp tissue extraction kit (Qiagen Inc., Mississauga, Ontario). Polymerase chain reaction amplification at 20 ungulate-derived microsatellite loci, 15 as described previously 5 plus MCM527, BM4025, MAF64, OarFCB193 and MAF92 (refs 25, 26), and fragment analysis were performed as described elsewhere 5 . After correction for multiple comparisons, we found no evidence for allelic or genotypic disequilibria at or among these 20 loci.Paternity of 241 individuals was assigned by using the likelihood-based approach described in CERVUS 27 at a confidence level of more than 95% with input parameters given in ref. 5. After paternity analysis, we used KINSHIP 28 to identify 31 clusters of 104 paternal half-sibs among the unassigned offspring. A paternal half-sibship consisted of all pairs of individuals of unassigned paternity that were identified in the KINSHIP analysis as having a likelihood ratio of the probability of a paternal half-sib relationship versus unrelated with an associated P , 0.05 (ref. 28). Members of reconstructed paternal halfsibships were assigned a common unknown paternal identity for the animal model analyses. Paternal identity links in the pedigree were therefore defined for 345 individuals. Animal model analysesBreeding values, genetic variance components and heritabilities were estimated by using a multiple trait restricted-estimate maximum-likelihood (REML) model implemented by the programs PEST 29 and VCE 30 . An animal model was fitted in which the phenotype of each animal was broken down into components of additive genetic value and other random and fixed effects: y ¼ Xb þ Za þ Pc þ e, where y was a vector of phenotypic values, b was a vector of fixed effects, a and c were vectors of additive genetic and permanent environmental, e was a vector of residual values, and X, Z and P were the corresponding design matrices relating records to the appropriate fixed or random effects 18 . Fixed effects included age (factor) and the average weight of yearling ewes in the year of measurement (covariate), which is a better index of resource availability than population size because it accounts for time-lagged effects 4 . The permanent environmental effect grou...

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Recent experiments on plant defenses against pathogens or herbivores have shown various patterns of the association between resistance, which reduces the probability of being infected or attacked, and tolerance, which reduces the loss of fitness caused by the infection or attack. Our study describes the simultaneous evolution of these two strategies of defense in a population of hosts submitted to a pathogen. We extended previous approaches by assuming that the two traits are independent (e.g., determined by two unlinked genes), by modeling different shapes of the costs of defenses, and by taking into account the demographic and epidemiological dynamics of the system. We provide novel predictions on the variability and the evolution of defenses. First, resistance and tolerance do not necessarily exclude each other; second, they should respond in different ways to changes in parameters that affect the epidemiology or the relative costs and benefits of defenses; and third, when comparing investments in defenses among different environments, the apparent associations among resistance, tolerance, and fecundity in the absence of parasites can lead to the false conclusion that only one defense trait is costly. The latter result emphasizes the problems of estimating trade-offs and costs among natural populations without knowledge of the underlying mechanisms.