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F2.3 · Compare growth patterns of two populations

Learn to compare growth patterns of two populations through clear examples and targeted practice.

Ontario Grade 12 Biology

Population Dynamics

Reading population change over time

In SBI3U ecology, you learned that a population is a group of individuals of the same species living in the same area. Population size is the number of individuals in that group. A growth pattern describes how population size changes over time. For example, two populations may both increase, but one may grow rapidly while the other levels off. Comparing their patterns means describing what they have in common and how they differ, using evidence such as counts collected at different times.

What you will learn

Describe a population growth pattern using population size and time.
Compare exponential and logistic growth patterns.
Use a data table to support a comparison between two populations.
Recognize that a simple growth model may not match every change in a real population.

From population counts to growth patterns

Imagine counting two populations at regular intervals. Population A rises from 20 individuals to 40, then 80. Population B rises from 20 to 35, then 45. Both populations increase, but their patterns are different. Population A increases by larger amounts over each interval. Population B continues to increase, but the increases become smaller.

To compare populations fairly, check that the counts use the same time intervals and a consistent method. A count of individuals is evidence about population size at a particular time. Several counts can show a pattern, but a small set of counts may not reveal what will happen later.

A growth rate describes how quickly population size changes over a stated interval. For a simple comparison, find the change in population size and divide by the time interval. The result is an average change per unit of time. This is useful when the intervals are equal, as in the examples below.

average change per time =

\frac{\text{later population size} - \text{earlier population size}}{\text{time interval}}

A population is a group of one species in one area.
A growth pattern is the change in population size over time.
State the time interval when comparing changes.

Two common patterns

An exponential growth pattern occurs when a population increases by a larger amount in each equal time interval. The increase can become rapid as the population becomes larger. A graph of population size against time has a curve that rises more steeply over time. This pattern can occur for a time when conditions allow continued increase, but it should not be assumed to continue indefinitely.

A logistic growth pattern begins with an increase, then the rate of increase slows and population size levels off. The level around which it remains is called the carrying capacity. Carrying capacity is the population size that the available conditions can support over time. It is a modelled level, not necessarily a fixed number in every situation.

The difference between these patterns is not simply that one population is larger. Compare the shape of the change: does the increase become faster, stay similar, or slow toward a level? A population can be smaller than another and still be increasing more quickly.

N_t = N_0(1+r)^t

Exponential growth: increases become larger over equal intervals.
Logistic growth: increases slow as population size approaches a carrying capacity.
Compare the pattern of change, not only the final population sizes.

Use evidence carefully

In the exponential model,

N_0

is the starting population size,

N_t

is the size after

t

time intervals, and

r

is the growth rate per interval written as a decimal. The expression is a simplified way to represent repeated proportional increase. It is not a claim that every real population follows this pattern.

For logistic growth, a useful course-level sketch is an S-shaped curve: slow increase at first, faster increase in the middle, then slower increase as the curve approaches a level. The carrying capacity helps describe that upper level. No exact prediction should be made from the sketch alone.

Population counts can vary because of the way they were collected and because conditions can change. A few observations may fit more than one pattern. Describe what the data show, identify the time period being compared, and avoid claiming that a short trend must continue.

logistic pattern: increase, then slow toward carrying capacity

Use counts and time intervals as evidence.
Models summarize patterns; they do not guarantee future population size.
A short data set may not show a clear long-term pattern.

A clear comparison

A strong comparison names both populations, describes the shared feature, and then explains the difference using counts or calculated changes. For instance, both populations may increase across the observations, while one has larger increases per interval. If one approaches a level and the other does not in the recorded period, say that this is what the observations show. Do not conclude that the second population will never level off.

Use a table to organize counts before interpreting them. If intervals match, compare the changes from one count to the next. Then describe whether those changes grow, shrink, or remain roughly similar. This links the numerical evidence to the growth pattern.

State a similarity and a difference.
Support the comparison with specific counts or changes.
Limit conclusions to the time span and evidence provided.

Patterns to look for in counts

Pattern	Change across equal intervals	What to say
Exponential	Increases become larger	Growth is accelerating in the observed period
Logistic	Increases slow toward a level	Growth is slowing near a possible carrying capacity
Not clear	Counts are too few or changes do not show a consistent trend	Describe the counts without assigning a firm pattern

Worked example

Compare increasing counts

Two illustrative populations are counted at the end of each year. Population A has counts 20, 40, and 80. Population B has counts 20, 35, and 45. Compare their changes over the two one-year intervals.

Find the interval changes
Subtract each earlier count from the next count. This shows how many individuals the recorded population size changed by in each year.
$\Delta N_A = 20, 40; \quad \Delta N_B = 15, 10$
Interpret the comparison
Both populations increase. Population A's increases become larger, while Population B's increases become smaller. The observations suggest an accelerating pattern for A and a slowing increase for B, but they do not establish a long-term pattern from only three counts.

Answer: Both populations increased. A increased by 20 and then 40 individuals; B increased by 15 and then 10. A's increases grew, while B's became smaller.

Check: The changes are calculated between adjacent counts, not by comparing only the first and last numbers.

Worked example

Compare average changes per year

An illustrative population rises from 48 individuals to 72 over 6 years. Another rises from 30 to 54 over the same period. Find and compare their average changes per year.

Calculate each change
For each population, subtract its starting size from its later size. Both populations increase by 24 individuals over the stated period.
$72-48=24; \quad 54-30=24$
Divide by the time
Each change is spread across 6 years. Their average changes per year are therefore equal. This comparison does not show whether their year-by-year patterns were identical, because only starting and ending counts are given. $\frac{24}{6}$ =4 individuals per year

Answer: Both populations have an average change of 4 individuals per year over the six years. The available counts do not show whether either population increased steadily or changed at a different rate within that period.

Check: Equal average changes over a period do not prove that the populations followed the same pattern at every point.

Worked example

Identify a pattern near a level

An illustrative population is counted at four equal time intervals: 10, 24, 34, and 38 individuals. Describe the pattern without claiming more than the data support.

Compare adjacent changes
Subtract each count from the next. The population increases each interval, but its increases become smaller.
$CAD 14, 10, 4$
Describe the evidence
The slowing increases are consistent with a logistic-like pattern over these observations. The counts suggest the population may be approaching a level, but four counts alone cannot establish its carrying capacity or show that it will stay near 38.

Answer: The population increases from 10 to 38 individuals, with smaller increases at each observation. This is consistent with growth slowing toward a level, but the evidence is not enough to determine a definite carrying capacity.

Check: A cautious description reports the observed slowing and treats the possible upper level as uncertain.

Common mistakes and how to avoid them

Calling a population exponential because its size increased.

Correction: Check whether the increases become larger across equal intervals. Increase alone is not enough to identify an exponential pattern.

Calling the largest observed count the carrying capacity.

Correction: A carrying capacity is the level a population approaches in a logistic model. A single high count does not establish that level.

Comparing populations only by their final sizes.

Correction: Compare their changes over matching time intervals as well as their sizes.

Predicting that a pattern will continue indefinitely.

Correction: Describe the observed time period. A model or short set of counts cannot guarantee future change.

Lesson summary

A growth pattern describes population size changing over time.
Exponential growth has larger increases across equal intervals; logistic growth slows toward a carrying capacity.
Use matched intervals and specific counts to compare populations.
Treat conclusions as limited by the evidence and the time period observed.

Check your understanding

Question 1

At equal intervals, Population X has counts 12, 25, and 50. Which description best fits the changes shown?

The population decreases at an accelerating rate.
The population increases, and its increases become larger.
The population levels off at 50.
The counts prove that its future growth will remain exponential.

Show answer and explanation

The population increases, and its increases become larger.

The changes are 13 and 25, so the population increases by a larger amount in the second interval. The observations do not prove what will happen in the future.

Question 2

A population has counts 40, 52, 60, and 64 at equal intervals. What is the strongest supported description?

It decreases toward carrying capacity.
It shows slowing increases, consistent with a logistic-like pattern in these observations.
It has a confirmed carrying capacity of 64.
It follows exponential growth because every count is larger.

Show answer and explanation

It shows slowing increases, consistent with a logistic-like pattern in these observations.

The increases are 12, 8, and 4. They become smaller, which is consistent with slowing growth. The counts do not confirm a particular carrying capacity.

Question 3

Two populations each increase by 18 individuals over 3 years. What can you conclude from those start and end counts?

They had the same size throughout all 3 years.
They had the same year-by-year growth pattern.
Their average change was 6 individuals per year over the period.
Both populations followed logistic growth.

Show answer and explanation

Their average change was 6 individuals per year over the period.

The average change is 18 divided by 3, or 6 individuals per year. Start and end counts alone do not establish the changes in each year or a particular growth pattern.

Key terms

Population: A group of individuals of the same species living in the same area.
Growth pattern: The way population size changes over time.
Growth rate: How quickly population size changes over a stated time interval.
Exponential growth: A pattern in which increases become larger across equal time intervals.
Logistic growth: A pattern in which growth slows as population size approaches a carrying capacity.
Carrying capacity: The population size that available conditions can support over time in a logistic model.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Biology (SBI4U), expectation F2.3. It is a study resource, not an official curriculum publication.

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