There are two types of sexual selection: Intrasexual and Intersexual.
Intrasexual[]
Intrasexual selection deals with members of the same sex in a given species. An example of this can be seen in elephant seals, polar bears, or any other animal that fights a same sex individual for mating, food, or territorial purposes. Any characteristic that can be used for defense when “sparing” with others of the same sex, as with polar bears, could be considered an intrasexual selected trait. Intrasexual selection is specifically used for competition (Freeman, 2007).
Intrasexual selection is many times simply referred to as competition; simply the competition between those of the same sex over access, or abilities for mating with the opposite sex. This is most commonly seen amongst males compared to females. Besides common examples of combat and physical competition between males there is another example that is not as common but has an interesting story in relation to fitness.
Infanticide
Infanticide has been seen among african lions, primates like chimpanzees and the Hanuman langur and a handful of others. It is considered rare because of the violence involved to follow through with infanticide. Infanticide is the killing of infants, usually by a perimeter or outside male who has come into a social group in hopes to take over (Freeman & Herron, 2007). This action does a couple important things.
First, it changes the dominant male. The social group structure that is commonly seen in conjunction with infanticide is one-male, multi-female groups, and occassionally multi-male, multi-female groups (Falk, 2000). An outside male, or solo male, who is usually just become sexually mature and is looking for a group of his own. Infanticide is one way he displays dominance and takes over the group. There is a second important things infanticide
accomplishes and this relates to fitness. The male kills all of the infants in an attempt to bring all the females back into estrus since they will cease nursing young. This allows the new male to mate with all of the females to increase his fitness, decrease the fitness of the previous male, and ensure his offspring have all the attention and resources (Arcadi & Wrangham, 1999).
Arcadi, A.C. & Wrangham, R.W. (1999). Infanticide in Chimpanzees: Review of Cases and a New Within-group Observation from the Kanyawara Study Group in Kibale National Park. Primates. 40 (2): 337-351.
Falk, D. (2000). Primate Diversity 1st Ed., pp 1-54; 172-339.
Freeman, S. & Herron, J. (2007). Evolutionary Analysis 4th Ed. Sexual Selection, pp 401-441.
Intersexual[]
Intersexual selection deals with members of the opposite sex within a given species. An example of this could be the bright colors of male birds. If one male had brighter colors, it would give him an advantage over other males of the same species for mating purposes. Color and size are two great examples of intersexual selection. Sometime females will choose their mates based on size and other times based on color. Intersexual selection is specifically used in mating selection (Moore, 1990).
References
Freeman, S. & Herron, J. (2007). Evolutionary Analysis 4th Ed. Sexual Selection, pp 401-441.
Moore, A.J. (1990). The evolution of sexual dimorphism by sexual selection: The separate effects of intrasexual selection and intersexual selection. Evolution 44(2): 315-331.