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How Landscape Heterogeneity Frames Optimal Diffusivity in Searching Processes 1 2 3 1 1,4 5,6 E. P. Raposo *, F. Bartumeus , M. G. E. da Luz , P. J. Ribeiro-Neto , T. A. Souza , G. M. Viswanathan ´ ´ ´ ´ 1 Laboratorio de Fısica Teorica e Computacional, Departamento de Fısica, Universidade Federal de Pernambuco, Recife, Brazil, 2 Centre d’Estudis Avanc¸ats de Blanes, ´ ´ CEAB-CSIC, Blanes, Spain, 3 Departamento de Fısica, Universidade Federal do Parana, Curitiba, Brazil, 4 Center for Polymer Studies and Department of Physics, Boston ´ ´ University, Boston, Massachusetts, United States of America, 5 Departamento de Fısica Teorica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, Brazil, ´ ´ 6 Instituto de Fısica, Universidade Federal de Alagoas, Maceio, Brazil Abstract Theoretical and empirical investigations of search strategies typically have failed to distinguish the distinct roles played by density versus patchiness of resources. It is well known that motility and diffusivity of organisms often increase in environments with low density of resources, but thus far there has been little progress in understanding the specific role of landscape heterogeneity and disorder on random, non-oriented motility. Here we address the general question of how the landscape hete