Question

Describe what happens to a population in an environment that reaches its carrying capacity.

Answer 1

pellet starts to happen. Sike. It starts to level off at the carrying capacity and more competition starts to occur because resources become scarce.

Answer 2

When a population reaches the carrying capacity of the environment, its habitat in particular, if you go along the Theory of Gradualism reinforced by Lamarck and Darwin then, it is certain that there is an intense struggle for survival and natural selection in full swing. Only better suited ones succeed, i.e. survive to pass their traits to their offspring. Thus within a few generations there considerable reduction in number of individuals and huge change in the allele frequency of the population, due to interaction between limited members of the population, and gradually speciation occurs; this provide the nature to rejuvenate its resources.
Since the gradualism is not much accepted these days, due to lack of continuous fossils records to support it, the Theory of Punctuated Equilibrium seems more efficient. Following theory, a new species break out after a long period of static and might replace its ancestors. A population to reach at a border of carrying capacity of the environment must be enjoying a long time of statics with less intra/inter specific competition and reproduce soundly. This really means the population have had a stable gene pool for a long period, thus following the concept of punctuated equilibrium a new species can be formed which finally results in the replacement of the ancestral population.
The other option can be the mass migration of larger portion of population or behavioral change in the population resulting to the decrease in the sexual interaction of the population, may be within small group, and finally leading to the repression and over expression of some vestigial or recessive character in the population finally leading to speciation.
Following any path it seems that speciation, i.e. formation of new species can be the only result and finally newly formed species, usually better equipped to survive the hostile environment towards the carrying capacity of their habitat replace the original population, and fill the different niches in there with a rapid evolution.
The most recent cases suggesting the theme of the questions can be found citing the latter days of Triassic era on earth with reptiles dominating the earth, comparing the analogies with the probabilities of the conditions and events then might be helpful.

Answer 3

mit above is talking more about evolution some of this comes into play in evolution but evolution takes a long time and is affected by more then a species carrying capacity. What causes a species (we while call this the predator) to reach its carrying capacity is an increase in its food source this causes the predator to reproduce more because of more food, as their population enlarges there are large numbers of the species eating their food source this causes the population of the food sources to drop which in turn causes the predators population to drop because of a lack of food.
Then beacuse the predators population has decreased the prey's population while increase which in turn while cause the predators populations to increase, this will continue to occur through the life of the species.
Sorry if anything above is unclear but it is hard to explain.