The queens of eusocial ants, bees, and wasps only mate during a very brief period early in life to acquire and store a lifetime supply of sperm. As sperm cannot be replenished, queens have to be highly economic when using stored sperm to fertilize eggs, especially in species with large and long‐lived colonies. However, queen fertility has not been studied in detail, so that we have little understanding of how economic sperm use is in different species, and whether queens are able to influence their sperm use. This is surprising given that sperm use is a key factor of eusocial life, as it determines the fecundity and longevity of queens and therefore colony fitness. We quantified the number of sperm that honeybee (Apis mellifera) queens use to fertilize eggs. We examined sperm use in naturally mated queens of different ages and in queens artificially inseminated with different volumes of semen. We found that queens are remarkably efficient and only use a median of 2 sperm per egg fertilization, with decreasing sperm use in older queens. The number of sperm in storage was always a significant predictor for the number of sperm used per fertilization, indicating that queens use a constant ratio of spermathecal fluid relative to total spermathecal volume of 2.364 × 10−6 to fertilize eggs. This allowed us to calculate a lifetime fecundity for honeybee queens of around 1,500,000 fertilized eggs. Our data provide the first empirical evidence that honeybee queens do not manipulate sperm use, and fertilization failures in worker‐destined eggs are therefore honest signals that workers can use to time queen replacement, which is crucial for colony performance and fitness.

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This paper presents a quantitative analysis of the model developed by Galor and Moav [Galor, Oded and Omer Moav (2002) Natural selection and the origin of economic growth.Quarterly Journal of Economics117(4), 1133–1191] in which agents vary genetically in their preference for quality and quantity of children. The simulation produces a pattern of income and population growth that resembles the period of Malthusian stagnation before the Industrial Revolution and the take-off into a modern growth era. We also investigate the stability of the modern growth era as an absorbing state of the model under the introduction of a strongly quantity-preferring genotype. We show that, given the absence of a scale effect of population in the model, the economy can regress to a Malthusian state under this change in the initial distribution of genotypes.

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We present an evolutionary theory of long-term economic growth in which technological progress and population growth are driven by the population size and the innovative potential of the people in the population. We expand on current theory proposing that population growth is proportional to population size due to greater production of ideas, and submit that technological progress and population growth are also driven by the accelerating evolution of people with a higher innovative potential.As a larger population implies a larger number of mutations, population growth will increase the rate at which innovation-enhancing traits may emerge. Heritable traits that increase idea development or productivity increase the fitness of the bearer, increase in frequency in the population and drive technological progress. This dual-driver model of economic growth has a sharper acceleration in population growth and greater robustness to technological shocks than a model without human evolution. We also show that as the population size increases, increases in population size become a relatively more important driver of the acceleration of technological progress than further increases in innovative potential.