The previous model is based on the premise that the foxes scavenge for food. The fox population was completely dependent on the number of dead rabbits, and in no way effected the live-rabbit population. However, this assumption is not accurate. Foxes are consummate hunters and prey as well as scavenge. The food available for the foxes depends on the number of rabbits killed and the number of rabbits that die of natural causes.

The number of rabbits alive at the end of a month is equal to the number of rabbits alive at the beginning of the month, plus the number of rabbits born, minus the number of rabbits that die of old age, minus the number of rabbits that starve, minus the number of rabbits killed.

Young rabbits are most at risk from predators. Predators kill 90% of all first year rabbits. Since the rabbits live for three years, that means that at least 1/3 of the rabbit population is killed every year - 1/36^th every month, in addition to the rabbits that die of old age.

The number of rabbits killed each month depends on the number of rabbits on the island. Fewer rabbits have more places to hide from the foxes. The larger the rabbit population density, the more likely a rabbit will be found and killed by a fox. Similarly, the number of rabbits killed depends on the number of foxes. The more foxes there are on the island, the greater then number of rabbits killed - the larger the fox population density, the more likely a rabbit will be killed.

 The number of rabbits killed depends on the rabbit density (the number of rabbits per unit area), p_r, and the fox density (the number of foxes per unit area), p_f:

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