how does a population’s growth rate change as it goes through the phases of logistic growth?

June 28, 2026

A population’s growth rate in logistic growth starts slow, speeds up to a maximum in the middle, and then slows to zero as it reaches carrying capacity.

Big picture: the S‑shaped story

Logistic growth traces an S‑shaped (sigmoid) curve when you plot population size over time.

The key idea: resources are limited, so growth cannot stay explosive forever.

A classic way to describe it is with three phases:

Lag/early phase – growth rate low but increasing.
Middle/accelerating–then–decelerating phase – growth rate reaches a maximum at mid‑population.
Late phase – growth rate slows and eventually becomes zero at carrying capacity.

Phase 1: Early (lag) phase – slow but accelerating

At the start, the population is small and resources are plentiful.

Few individuals means few births per unit time, so total growth rate is low.

As individuals reproduce, each generation adds more breeders, so the growth rate increases over time (it’s speeding up).

On the graph: the curve is rising gently but getting steeper; the slope (growth rate) is small at first but increasing.

A simple mental picture: imagine a new colony of rabbits released in a big empty field; at first, even if each rabbit reproduces well, there just aren’t many rabbits yet, so population increases slowly.

Phase 2: Middle phase – maximum growth rate

In the mid‑section of logistic growth, the population is large enough that many individuals are reproducing, but resources are still reasonably abundant.

The growth rate increases up to a maximum as population size approaches about half the carrying capacity , N≈K/2N\approx K/2N≈K/2.

At N=K/2N=K/2N=K/2, the total growth rate of the population is highest : enough individuals to produce many offspring, but not yet so crowded that resources strongly limit survival or reproduction.

Right at this point, the curve has its inflection point : it switches from “speeding up” (accelerating) to “slowing down” (decelerating), but the slope itself is at its steepest.

After the inflection point, the population is still increasing in size , but the growth rate is now decreasing as crowding and competition intensify.

Phase 3: Late phase – slowing to zero at carrying capacity

As the population gets close to the environment’s carrying capacity KKK, resources (food, space, nesting sites, etc.) become limiting.

The growth rate continues to decline as crowding, competition, and mortality increase.

When N=KN=KN=K, growth rate is zero : births and deaths balance, so population size stops changing on average.

If the population exceeds carrying capacity N>KN>KN>K, the growth rate becomes negative , and the population tends to decrease back toward KKK.

On the graph, the curve flattens out and becomes almost horizontal as it nears KKK; the slope (growth rate) gets closer and closer to zero.

How the growth rate changes, step‑by‑step

Here’s a compact, phase‑by‑phase view of how a population’s growth rate changes through logistic growth:

[5][7] [7][5] [1][5] [5][1] [1] [7][1] [5][1] [7][5] [1][5] [5][1] [1] [1]

Phase / Population size	What happens to growth rate?	Why?
Very small population (early phase)	Growth rate is low but increasing over time.	Few individuals to reproduce, but each generation adds more breeders; resources are abundant.
Approaching half of carrying capacity ($$N < K/2$$)	Growth rate is higher and still increasing.	More individuals reproducing, while resources remain largely sufficient.
At about half of carrying capacity ($$N = K/2$$)	Maximum growth rate.	Optimal balance: many individuals and still plenty of resources; this is the inflection point of the S‑curve.
Between half and full carrying capacity ($$K/2 < N < K$$)	Growth rate is still positive, but decreasing.	Increasing crowding and competition reduce birth rates and/or increase death rates.
At carrying capacity ($$N = K$$)	Growth rate = 0 (no net change in population size).	Births balance deaths; resources just support the current population.
Above carrying capacity ($$N > K$$)	Growth rate is negative (population declines).	Resources are insufficient for everyone; mortality or emigration exceeds births.

Quick recap in plain words

At first: growth rate starts low but speeds up as the population builds momentum.
In the middle: growth rate reaches its highest value around half the carrying capacity , then begins to slow.

Near the end: growth rate keeps slowing and eventually drops to zero at carrying capacity; if the population overshoots, growth rate can become negative and the population shrinks.

In one sentence: in logistic growth, the growth rate accelerates at low density, peaks at about half the carrying capacity, and then decelerates to zero as the population reaches that limit.

TL;DR:
In logistic growth, a population’s growth rate increases from low to high during the early to mid phase, reaches a maximum around N=K/2N=K/2N=K/2, then steadily declines and becomes zero as the population reaches carrying capacity.

Information gathered from public forums or data available on the internet and portrayed here.