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according to the theory of evolution, what happens to the appearance of beneficial traits in a species over time?

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3 Answers

Cecil,
 
In a genetically diverse population, a beneficial trait will increase in frequency. 6% of traits linked to a beneficial trait also evolve and increase in frequency by the virtue of their linkage to a beneficial trait. This continues until there is a change in population size due  climate or man-made conditions such as industrialization. Spontaneous mutation my alter a beneficial trait or the trait may stop to offer the advantage due to environmental modulation. It is a topic of much discussion and research. I am also including a link of scientific paper for you to look at and do additional literature search  in relevant journals
 
Christopher J.R. Illingworth,
Leopold Parts,
Stephan Schiffels,
Gianni Liti,
and Ville Mustonen
Quantifying Selection Acting on a Complex Trait Using Allele Frequency Time Series Data Mol Biol Evol (2012) 29 (4): 1187-1197
 
Hope this helps.
If a trait is somehow beneficial to a species, it increases the survival of that species in some manner. Since that gives individuals with that trait an advantage to those without it, that means the trait is more likely to be passed to descendents and increase among the total population (albeit, possibly as a recessive trait) over time.