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The distribution of the population kurtosis under different levels of sparsity, mutational kernels, and demographies. The sparsity is varied by changing the expected number of pairwise differences at sites affecting the trait. Normal and Laplace distributions of mutational effects are compared. A constant size population is compared to an exponential growth scenario with growth rate equal to the reciprocal of the final effective population size. Green triangles denote the mean kurtosis. The dashed red lines give the first order approximation to the expected kurtosis given in equation 26.