The members of natural populations often differ in size and relatedness to each other, which may affect the division of limited resources and have consequences on reproductive success and population dynamics. We modeled seasonal growth and dynamics in populations composed of different types of relatives (full-sibs, half-sibs and non-related individuals) under the continuum of competitive scenarios between complete symmetry and asymmetry. Growth was assumed logistic in proportion to individual biomass and the size-differences were weighted by the relatedness of individuals. The symmetric component of competition was experienced by all individuals in proportion to their biomass, whereas the asymmetric component was individual-specific, and influenced only by the individuals larger than the focal individual. Relatedness decreased and competitive asymmetry increased the variability of individual biomasses. Mortality of the smallest individuals and the size threshold of reproduction decreased population density. Population dynamics were stable when there was no size threshold for reproduction but the presence of the threshold led to cyclic dynamics under low competitive asymmetry. The effects of the threshold were greater among related than unrelated individuals. The results suggest that individual differences and the asymmetry of competition can greatly affect population dynamics. Full symmetry of competition may be evolutionarily unstable in populations of related individuals as it may increase the probability of extinction due to demographic stochasticity.