  In this paper, we consider the following single species model with nonlocal
dispersal strategy $$ d\mathcal {L} [\theta] (x,t) + \theta(x,t) [m(x)-
\theta(x,t)]=0 , $$ where $\mathcal {L}$ denotes the nonlocal diffusion
operator, and investigate how the dispersal rate of the species and the
distribution of resources affect the total population. First, we show that the
upper bound for the ratio between total population and total resource is
$C\sqrt{d}$. Moreover, examples are constructed to indicate that this upper
bound is optimal. Secondly, for a type of simplified nonlocal diffusion
operator, we prove that if $ \frac{\sup m}{\inf m}<\frac{\sqrt{5}+1}{2}$, the
total population as a function of dispersal rate $d$ admits exactly one local
maximum point in $\displaystyle (\inf m, \sup m)$. These results reveal
essential discrepancies between local and nonlocal dispersal strategies.
