Fitness improving innovations occur in populations of organisms as genetic changes (mutations) that allow better fit with the environmental niche of the organisms. Similarly, fitness improving innovations may occur in the context of human communities as well in terms of socio-economic innovations (e.g. new ways of organizing the military, new products or services) that lead to more efficient use of available resources. Here we explore the link between such innovations and the harshness of the environment, where the populations live. Environmental harshness characterizes the availability of population growth supporting resources in the environment. Our analysis shows that if the harshness of the environment varies smoothly with the distance, the expected extent of fitness improving innovations and of the resource utilization efficiency of populations depends in a combined linear and harmonic manner on the harshness of the environment at the location of origin of the populations. We explore the implications of this result for particular cases of both biological and social environments (e.g. gene drives, business innovation).

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