Common use of Materials and Methods Clause in Contracts

Materials and Methods. Description of Simulations. We used a lattice-based stochastic patch occu- pancy model (26) to simulate spatially explicit dynamics of large numbers of species with dissimilar ecological traits. The model assumes that different lattice cells may represent different habitat type, and that habitat type across the lattice may be spatially correlated (26). In the present simulations, we assumed a high degree of spatial correlation in habitat type (parameter ω = 2 in ref. 26). Interspecific interactions are not modeled, but each species has distinct ecological traits defined by five parameters: colonization rate (c), extinction rate (e), average dispersal distance (1/α), mean phenotype (φ), and niche width (γ). Colonization rate and extinction rate control the probability of a species populating an unoccupied lattice cell and the probability of extinction in an occupied cell in unit time, respectively. These probabilities are affected by the habitat type of the cell in relation to the mean pheno- type and niche width of the species (26). Cells with habitat type close to the species mean phenotype support populations best, whereas niche width controls the sensitivity of the species to habitat type. In the present simu- lations, a species typically reaches the stochastic stationary state from a few dozen to a few hundred time steps (26). We run the simulations for at least 500 steps to ensure that most species had reached the quasi-stationary state. Increasing the simulation time did not qualitatively alter the results, al- though it resulted in a few additional extinctions as expected due to sto- xxxxxxxxxx. Further details of the simulations are given in SI Text.