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\frac{dA_i}{dt} = A_i ( K_a - A_i - \epsilon A_{i+1} - \epsilon A_{i-1} + \frac{\alpha^{AP}}{\lambda_i^q} \sum_{j<=i} P_j ) \nonumber   \end{equation}  At $\epsilon = 0 $ (i.e no competition between different pollunator species), the equilibrium populations satisfy:  \begin{equation}  A_i^* +\frac{\alpha^{PA} \alpha_{AP}}{\lambda_i^q} \sum_{j} A_j* - i K_p \frac{\alpha^{PA}}{\lambda_i^q}  = 0 K_a  \label{denklem6}  \end{equation}     
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