This paper is concerned with the spreading speed of a food-limited population model with delay. First, the existence of the solution of Cauchy problem is proved. Then, the spreading speed of solutions with compactly supported initial data is investigated by using the general Harnack inequality. Finally, we present some numerical simulations and investigate the dynamical behavior of the solution.

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<p style='text-indent:20px;'>This paper is concerned with the traveling wave fronts for a lattice dynamical system with global interaction, which arises in a single species in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction by delay. We prove that all non-critical traveling wave fronts are globally exponentially stable in time, and the critical traveling wave fronts are globally algebraically stable by the weighted energy method combined with the comparison principle and the discrete Fourier transform.</p>