Carring capacity is the limit upto which the environment of the ecosystem can feed a species. When K is reached, the species stabalizes and nothing can increase in population at that time. So predicting K can be done via verhulst pearl equation.
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In advance of what? You can plot population trends and predict when the population will level out. If you are trying to introduce animals to a new area, you have to estimate based on the density of that animal in a similar habitat. Very tricky to define what is "similar".