Profitability of prey determines the response of population abundances to enrichment.

Theoretical and empirical evidence in a one-predator two-prey system consistently indicates a regular trend that the less profitable (therefore, less vulnerable) prey increases in abundance with enrichment. The response in the abundance of the more profitable (more vulnerable) prey to enrichment has, however, remained unclear. Previous theoretical models have assumed the less profitable prey as inedible, though its actual profitability is unknown. Here, relaxing this assumption, we show that the response of the more profitable prey abundance to enrichment depends critically on the profitability of the less profitable prey. Specifically, the more profitable prey increases in abundance with enrichment if the profitability of the less profitable prey is lower than a critical value so that it cannot support the predator population by itself even at high densities (in this case, the prey is referred to as 'unpalatable') and decreases otherwise. This establishes a more general rule which unifies the previous works and resolves the indeterminacy on the response of the more profitable prey.