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Many species of animals exhibit an intuitive sense of number, suggesting a fundamental neural mechanism for representing numerosity in a visual scene. Recent empirical studies demonstrate that early feedforward visual responses are sensitive to numerosity of a dot array but substantially less so to continuous dimensions orthogonal to numerosity, such as size and spacing of the dots. However, the mechanisms that extract numerosity are unknown. Here, we identified the core neurocomputational principles underlying these effects: (1) center-surround contrast filters; (2) at different spatial scales; with (3) divisive normalization across network units. In an untrained computational model, these principles eliminated sensitivity to size and spacing, making numerosity the main determinant of the neuronal response magnitude. Moreover, a model implementation of these principles explained both well-known and relatively novel illusions of numerosity perception across space and time. This supports the conclusion that the neural structures and feedforward processes that encode numerosity naturally produce visual illusions of numerosity. Taken together, these results identify a set of neurocomputational properties that gives rise to the ubiquity of the number sense in the animal kingdom. 

Dryland ecosystems are experiencing shifts in rainfall and plant community composition, which are expected to alter cycling and storage of soil carbon (C). Few experiments have been conducted to examine long‐term effects on (1) soil organic C (SOC) pools throughout the soil profile, and (2) soil inorganic C (SIC) pools as they relate to dynamic changes in C storage and climate change. We measured SOC and SIC from 0 to 1 m beneath plants and in adjacent interplant microsites following nearly 20 yr of experimental manipulations of plant community (native sagebrush steppe or monoculture of exotic crested wheatgrass) and the amount and timing of water availability (ambient, or doubling of annual rainfall in the dormant, DORM, or growing, GROW, season). Under sagebrush plants, GROW increased both SOC and SIC pools, resulting in total carbon (TC) pools 15% greater than plots receiving ambient precipitation, while DORM decreased SOC and SIC pools, decreasing TC pools 20% from ambient. Under crested wheatgrass plants, GROW increased SOC by 73% but decreased SIC by 11% relative to ambient, netting no change in TC pools, while DORM SIC pools were 5% greater than ambient, with no significant increase in either SOC or TC pools. GROW significantly increased TC pools for interplant microsites, regardless of vegetation treatment. At the community scale and summing C pools weighted by percent patch cover, patterns of TC pool were similar to plot measurements. Our findings suggest that sagebrush communities can become a net C source to the atmosphere with increases in dormant season rainfall rather than a C sink as previously predicted.We also provide evidence of SIC as an important and dynamic C sequestration mechanism in drylands. Consideration of vegetation type, all or most of the soil profile, and both organic and inorganic C pools are all important to accurately predict C sequestration with changing climate and disturbance in drylands.