Is the rate of increase slowing as the population gets larger (or as density increases)? is this growth density independent or density dependent?

Growth is density dependent.

Explanation:

In population ecology, density-dependent processes occur when population growth rates are regulated by the density of a population. Usually, the denser a population is, the greater its mortality rate. Density-dependent regulation can be affected by factors that affect birth and death rates such as competition and predation. A dense population that is reduced in a density-independent manner by some environmental factor(s) will be able to recover differently than would a sparse population. For example, a population of deer affected by a harsh winter will recover faster if more deer are remaining to reproduce.

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