Explain how mutualism, predation, and inter-specific competition are different from each other. How does each one affect the interacting populations of the two species?

Mutualism, predation, and inter-specific competition, are all categorized as inter-specific interactions between two species.  Each one of these include an interaction between two or more species in the same environment.  In each of these interactions, each species is either harmed or benefited by the type of interaction.

1. Mutualism is when two organisms work together in a way that is beneficial (or maybe even essential) for both parties.  An example of this is the relationship between bumblebees and flowers.  The bumblebee collects nectar, which is the essential source from which the bumblebee makes their food.  In the process of collecting nectar, the bee flies from flower to flower spreading pollen, helping the flowers in an area to pollinate, which is essential process for the reproduction of the flower.  This is an interaction between two species in which both species benefit.
2. Predation is the involvement of two organisms, when one species (the predator) kills and eats another species (the prey) that is subordinate on the food chain.  An example of this is a coyote, catching and feeding on a rabbit.  The coyote needs the nutrition of the rabbit, it is essential for survival.  If there were not predators such as coyotes to prey on rabbits, the rabbit population would expand to an unmanageable number.  The predator benefits from this interaction at the expense of the prey, who only receives harm, or in this case, death.
3. Inter-specific competition is when two different species compete for the same resource in a given ecosystem.  Predators, herbivores, and any type of plant encounter this issue.  An example is when the main diet of a hawk in a given ecosystem is a rabbit, but coyotes in that same ecosystem are supported by rabbits.  Both have a limited supply due to the pressure on the rabbit population caused by both species.  Neither species really benefits from this.