Although evolutionary transitions from sexual to asexual reproduction are frequent in eukaryotes, the genetic bases of these shifts remain largely elusive. Here, we used classic quantitative trait analysis, combined with genomic and transcriptomic information to dissect the genetic basis of asexual, parthenogenetic reproduction in the brown alga Ectocarpus. We found that parthenogenesis is controlled by the sex locus, together with two additional autosomal loci, highlighting the key role of the sex chromosome as a major regulator of asexual reproduction. We identify several negative effects of parthenogenesis on male fitness, and different fitness effects of parthenogenetic capacity depending on the life cycle generation. Although allele frequencies in natural populations are currently unknown, we discuss the possibility that parthenogenesis may be under both sex-specific selection and generation/ploidally-antagonistic selection, and/or that the action of fluctuating selection on this trait may contribute to the maintenance of polymorphisms in populations. Importantly, our data provide the first empirical illustration, to our knowledge, of a trade-off between the haploid and diploid stages of the life cycle, where distinct parthenogenesis alleles have opposing effects on sexual and asexual reproduction and may help maintain genetic variation. These types of fitness trade-offs have profound evolutionary implications in natural populations and may structure life history evolution in organisms with haploid-diploid life cycles.