In panels (a–c) the receptor sensing matrix is based on Drosophila (Hallem and Carlson, 2006) and includes 24 receptors responding to 110 odorants. In panels (d–e), the total number of OSNs is fixed at 4000. In all panels, environmental odor statistics follow a random correlation matrix (see Appendix 4). Qualitative aspects are robust to variations in these choices (see Appendix 1). (a) Large OSN populations should have high receptor diversity (types represented by strips of different colors), and should use receptor types uniformly. (b) Small OSN populations should express fewer receptor types, and should use receptors non-uniformly. (c) New receptor types are expressed in a series of step transitions as the total number of neurons increases. Here, the odor environments and the receptor affinities are held fixed as the OSN population size is increased. (d) Correlation between the abundance of a given receptor type, , and the logarithm of its signal-to-noise ratio in olfactory scenes, , shown here as a function of the tuning of the receptors. For every position along the -axis, sensing matrices with a fixed receptor tuning width were generated from a random ensemble, where the tuning width indicates what fraction of all odorants elicit a strong response for the receptors (see Appendix 1). When each receptor responds strongly to only a small number of odorants, response variance is a good predictor of abundance, while this is no longer true for wide tuning. (e) Receptor abundances correlate well with the diagonal elements of the inverse overlap matrix normalized by the noise variances, , for all tuning widths. In panels (d–e), the red line is the mean obtained from 24 simulations, each performed using a different sensing matrix, and the light gray area shows the interval between the 20th and 80th percentiles of results. (f) Number of intact olfactory receptor (OR) genes found in different species of mammals as a function of the area of the olfactory epithelium normalized to account for allometric scaling of neuron density ((Herculano-Houzel et al., 2015); see main text). We use this as a proxy for the number of neurons in the olfactory epithelium. Dashed line is a least-squares fit. Number of intact OR genes from (Niimura et al., 2014), olfactory surface area data from (Moulton, 1967; Pihlström et al., 2005; Gross et al., 1982; Smith et al., 2014), and weight data from (Rousseeuw and Leroy, 1987; FCI, 2018; Gross et al., 1982; Smith et al., 2014).