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We introduce two models of biological aggregation, based on randomly movingparticles with individual stochasticity depending on the perceived averagepopulation density in their neighbourhood. In the first-order model thelocation of each individual is subject to a density-dependent random walk,while in the second-order model the density-dependent random walk acts on thevelocity variable, together with a density-dependent damping term. The mainnovelty of our models is that we do not assume any explicit aggregative forceacting on the individuals; instead, aggregation is obtained exclusively byreducing the individual stochasticity in response to higher perceived density.We formally derive the corresponding mean-field limits, leading to nonlocaldegenerate diffusions. Then, we carry out the mathematical analysis of thefirst-order model, in particular, we prove the existence of weak solutions andshow that it allows for measure-valued steady states. We also perform linearstability analysis and identify conditions for pattern formation. Moreover, wediscuss the role of the nonlocality for well-posedness of the first-ordermodel. Finally, we present results of numerical simulations for both the first-and second-order model on the individual-based and continuum levels ofdescription.

Individual based and mean-field modelling of direct aggregation