A species response to environmental change is one of today’s most challenging issues for life scientists; it contributes to determine the extent to which human-induced environmental perturbations will affect human society. While theory is expected to play a key role in the understanding this complex and topical issue, current investigations are typically limited to the study of evolution of a single trait. This sharply contrasts with our usual understanding that a species response to environmental change is likely to involve many traits, where many genes pleiotropically affect several characters. Interestingly, the only brief attempt to investigate the effect of pleiotropy has demonstrated that adaptation of a single trait to a gradual environmental change can be substantially impeded by selection on a second pleiotropic trait. However, Waxman and Peck have shown that in a static environment, a qualitatively new phenomenon occurs when mutations pleiotropically affect not two, but three or more traits in an effectively infinite asexual population. When this holds, the genotypic distribution has a different equilibrium form to usual (where all genetic sequences are rare): a single optimal genetic sequence become predominant. Since the genotypic distribution is a key factor to adaptation, such a qualitative change will have significant impacts on the response of a population to a changing environment. In this proposal, we plan to theoretically investigate evolutionary adaptation to environmental change when the number of pleiotropic traits is larger than two. This first implies the need to generalize the theory of Waxman and Peck, in a static environment, by extending the analysis to: (i) finite populations, (ii) haploid sexual populations and (iii) diploid sexual populations. We will then be able to introduce environmental changes into this theory, in order to investigate how pleiotropy and drift combine to affect the adaptive response of a population to such changes.