explain what the theory of sexual selection is and give an example.
Sexual selection was first proposed by Charles Darwin in On the Origin of Species (1859) and developed in The Descent of Man, and Selection in Relation to Sex (1871) Darwin felt that natural selection alone was unable to account for certain types of non-survival adaptations. His work divided sexual selection into male–male competition and female choice. Ronald Fisher developed his ideas about sexual selection in his 1930 book The Genetical Theory of Natural Selection. The Fisherian runaway describes how sexual selection accelerates the preference for a specific ornament, causing the preferred trait and female taste for it to increase together. A positive feedback loop is created, producing extravagant physical structures in the non-limiting sex.

Reproductive success
The reproductive success of an organism is measured by the number of offspring left behind. Sexual preference creates a tendency towards assortative mating or homogamy. Bateman's principle states that the sex which invests the most in producing offspring becomes a limiting resource for which the other sex competes.

Honest signaling
Amotz Zahavi's work spurred a re-examination of the field and several new theories. In 1984, Hamilton and Marlene Zuk introduced the Bright Male hypothesis, suggesting that male elaborations might serve as a marker of health, by exaggerating the effects of disease and deficiency.

Male intrasexual competition
Male–male competition occurs when two males of the same species compete for the opportunity to mate with a female. Sexually dimorphic traits, size, sex ratio, and social situation may all play a role in the effects. Larger males tend to win male&###; male conflicts.

Multiple models 
More recently, the field has grown to include other areas of study, not all of which fit Darwin's definition of sexual selection. Elaborated characteristics that might seem costly, like the tail of the Montezuma swordfish, do not always have an energetics, performance, or even survival cost. This may be because compensatory traits have evolved in concert with sexually selected traits.

Toolkit of natural selection 
Sexual selection may explain how characteristics such as feathers had survival value at an early stage in their evolution. The earliest proto-birds such as Protarchaeopteryx had well-developed feathers but could not fly. The feathers may have served as insulation, helping females incubate their eggs. If proto-bird courtship combined displays of forelimb feathers with energetic jumps, the transition to flight could have been relatively smooth.

These are some examples of sexual selection

In mammals 
Darwin conjectured that heritable traits such as beards, hairlessness, and steatopygia in different human populations are results of sexual selection in humans. Humans are sexually dimorphic; females select males using factors including voice pitch, facial shape, muscularity, and height. Extreme sexual dimorphism is seen in mammals, with males as much as six times heavier than females.

In arthropods
Sexual selection occurs in a wide range of spider species before and after copulation. Post-copulatory sexual selection involves sperm competition and cryptic female choice. Sperm competition occurs when the sperm of more than one male competes to fertilize the egg of the female. Cryptic female choice involves expelling a male's sperm during or after copulation.

In amphibians and reptiles
Many amphibians have annual breeding seasons with the male–male competition. Males arrive at the water's edge first in large numbers, and produce a wide range of vocalizations to attract mates. Some species, like P. vibronic, are polyandrous, with one female mating with multiple males. Ritual combat between males for the females they want to mate with includes topping.

In birds
Birds have evolved a wide variety of mating behaviors and many types of sexual selection. These include intersexual selection (female choice) and intrasexual competition. Many species, notably the birds of paradise, are sexually dimorphic. Signals must be costly to ensure that only good-quality individuals can present these exaggerated sexual ornaments and behaviors.

In plants and fungi
Flowering plants have many secondary sexual characteristics subject to sexual selection. Fungi appear to make use of sexual selection, although they also often reproduce asexually. In the Basidiomycetes, the sex ratio is biased towards males, implying sexual selection there.
Does the degree of sexual dimorphism correlate to any other factors, such as environment, social behavior or development of offspring?