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F3.3 · Explain changes in population size using limiting factors

Learn to explain changes in population size using limiting factors through clear examples and targeted practice.

Ontario Grade 12 Biology

Population Dynamics

Explaining why populations grow, shrink, or stay similar

A pond has a population of frogs. After a dry summer, fewer young frogs survive, and the population may become smaller. The change is not explained by counting frogs alone. We also need to consider the conditions affecting survival and reproduction. This lesson connects familiar ecology ideas to a simple way of explaining population change: identify the limiting factor, describe how it affects the population, and use evidence to support the explanation.

What you will learn

Explain what a population is and how its size can change.
Identify limiting factors and describe how they affect population size.
Distinguish density-dependent from density-independent factors.
Use evidence and a simple population-change model to explain a change in size.

1. SBI3U bridge: populations and changing numbers

A population is a group of individuals of the same species living in the same area at the same time. For example, all the frogs of one species in a pond may be treated as one population. Population size is the number of individuals in that population.

In ecology, organisms depend on their surroundings and on one another. Food, water, shelter, space, predators, and disease can affect whether individuals survive and reproduce. A factor that restricts population growth or causes a population to become smaller is called a limiting factor.

Population size can change when individuals are born, die, enter the area, or leave it. Births and immigration add individuals. Deaths and emigration remove individuals. Immigration means movement into the population’s area; emigration means movement out. These terms describe changes in location, not changes in species.

change in population size = (

\text{births}

\text{immigration}

) - (

\text{deaths}

\text{emigration}

)

A population is defined by species, area, and time.
A limiting factor affects population growth or survival.
Births and immigration add individuals; deaths and emigration remove them.

2. Limiting factors in a biological system

A biological system is a set of living things and the conditions around them that affect one another. In a pond, frogs depend on suitable food and habitat, while predators and disease can affect their survival. A change in one condition can affect several parts of the system.

Some limiting factors depend on population density. Density is the number of individuals in a given area. A density-dependent factor has a stronger effect as the population becomes more crowded. Competition is one example. If many animals use the same limited food supply, each may get less food. Disease can also spread more readily when individuals are in close contact. These factors can reduce survival or reproduction.

Other limiting factors can affect a population regardless of how crowded it is. A density-independent factor is one whose effect does not depend on population density. A severe storm, flood, or sudden cold period may harm individuals in a sparsely populated area as well as a crowded one. The size of the effect can vary, but it is not caused by crowding itself.

These categories describe how a factor acts, not whether it always changes a population in the same way. For instance, a storm might destroy shelter and increase deaths. In another place, it might have little effect. To explain a population change, connect the factor to a specific outcome such as fewer births, more deaths, or movement into or out of the area.

Density-dependent effects are linked to how crowded a population is.
Density-independent effects do not depend on population density.
State the pathway from factor to population change.

3. Connecting a factor to evidence and a model

A useful explanation follows a chain: identify the factor, describe what it changes for individuals, and state how that changes the population count. For example, limited food may reduce the number of young that survive. Fewer surviving young means fewer individuals are added to the population than there might have been without that limitation.

Evidence is information used to support an explanation. A count made at two times can show that population size changed. Notes about food availability, weather, or survival may help explain why. A count alone does not prove which factor caused the change. Other factors may have changed at the same time, and counting methods may miss individuals.

The population-change model is a bookkeeping tool. It helps organize additions and removals. It does not, by itself, identify the limiting factor or prove why births or deaths changed. A sound explanation uses the model together with relevant evidence and acknowledges what the evidence cannot establish.

N_{\text{later}} = N_{\text{earlier}} + B + I - D - E

Explain the link between a limiting factor and births, deaths, immigration, or emigration.
A change in counts is evidence of a change, but not automatic proof of its cause.
Use the model to organize population additions and removals.

4. Interpreting a population change carefully

The letter

N

represents population size. The letters

B

I

D

, and

E

represent births, immigration, deaths, and emigration during the time interval. The model says that later size equals earlier size plus additions minus removals.

When applying the model, define the area and time interval first. Include only individuals that belong to the population under that definition. Then identify which additions and removals are known. If a count is uncertain or a movement is not measured, say so rather than treating an estimate as an exact observation.

A limiting factor can help explain one or more terms in the model. For example, a shortage of food could be associated with more deaths or fewer births. The model records those changes; the biological explanation describes how the food shortage may have led to them. Avoid claiming more than the evidence supports.

Keep the same population boundary and time interval throughout a calculation.
Separate the numerical change from the proposed biological cause.
Use cautious language when observations do not establish a cause.

Two broad types of limiting factor

Type	How its effect is related to density	Example
Density-dependent	The effect is linked to how crowded the population is.	Competition for limited food or nesting space
Density-independent	The effect does not depend on population density.	A flood or severe storm

Worked example

Food shortage and fewer surviving young

A researcher counts 120 nesting birds at the start of a season. During the season, 28 young are added to the count, 6 birds immigrate, 19 birds die, and 3 emigrate. In the same period, food becomes scarce. Calculate the later population size and explain how food could be a limiting factor without claiming that the count proves it was the only cause.

Sort additions and removals
Young added and immigrants increase the count. Deaths and emigrants reduce it.
$B+I=28+6=34,\quad D+E=19+3=22$
Find the later count
The net change is 12 individuals, so add that change to the starting count.
$N_{\text{later}}=120+34-22=132$
Connect the factor cautiously
Scarce food could limit survival or reproduction. The count shows the population increased overall, but it does not show what the count would have been without the food shortage. Other factors could also have affected births, deaths, or movement.

Answer: The later population size is 132 birds. Food scarcity is a possible limiting factor because it could reduce survival or reproduction, but the counts alone do not establish that it caused a particular number of births or deaths.

Check: The net change is 34 additions minus 22 removals, or 12. Adding 12 to 120 gives 132.

Worked example

A density-dependent factor

A small mammal population rises from 75 to 91 individuals. Over the interval, 24 births and 5 immigrants are recorded, along with 10 deaths and 3 emigrants. The habitat has limited nesting space, and competition for nests is more common when many animals occupy the area. Explain whether nesting space is density-dependent and check the population count.

Calculate the expected count
Add births and immigration, then subtract deaths and emigration from the initial population.
$75+24+5-10-3=91$
Classify the limiting factor
Nesting space is density-dependent in this example because competition for nests becomes more common as more animals occupy the habitat. Competition may affect survival or reproduction. The population still grew overall during this interval.

Answer: The calculated later size is 91, matching the stated count. Limited nesting space is density-dependent here because its effect is linked to crowding. A limiting factor can restrict growth without making the total population shrink.

Check: Additions are 29 and removals are 13, so the net increase is 16. The initial 75 therefore becomes 91.

Worked example

A density-independent event

A population of 210 insects is counted before a major flood. After the flood, the count is 164. Assume no information is available about births or movement during the interval. Explain what can be concluded and what cannot be concluded.

Compare the counts
Subtract the later count from the earlier count to find the net decrease.
$210-164=46$
Relate the event to the change
A flood is generally treated as density-independent because its occurrence does not depend on how crowded the population is. The counts establish a decrease of 46 individuals. Without information about births, deaths, or movement, they do not show which population processes produced that net decrease or prove the flood was the sole cause.

Answer: The count decreased by 46. A flood can be a density-independent limiting factor, but the two counts alone do not establish the full cause of the decrease.

Check: The decrease is 46 because 210 minus 164 equals 46.

Common mistakes and how to avoid them

Assuming that every limiting factor makes a population shrink.

Correction: A factor may restrict how much a population grows while the population still increases overall.

Calling any factor that affects many individuals density-dependent.

Correction: Ask whether its effect is linked to crowding. A flood can affect many individuals without depending on population density.

Treating a change between two counts as proof of its cause.

Correction: The counts show what changed. Additional evidence is needed to support an explanation of why it changed.

Forgetting immigration or emigration when comparing population sizes.

Correction: Include movement across the defined population boundary as well as births and deaths.

Lesson summary

Population size is the number of individuals in a defined population.
Limiting factors affect population growth or survival.
Density-dependent factors are linked to crowding; density-independent factors are not.
Population change reflects births and immigration adding individuals, and deaths and emigration removing them.
Use evidence to connect a limiting factor to population change, while recognizing that counts alone may not prove a cause.

Check your understanding

Question 1

A population has 40 births, 8 immigrants, 21 deaths, and 5 emigrants. What is its net change?

An increase of 22
A decrease of 22
An increase of 74
A decrease of 34

Show answer and explanation

An increase of 22

Additions are 48 and removals are 26. The net change is an increase of 22.

Question 2

Which example is most clearly density-dependent?

A flood affects a population
Competition for limited food increases as a population becomes crowded
A cold period occurs regardless of population size
A storm damages habitat in a sparsely populated area

Show answer and explanation

Competition for limited food increases as a population becomes crowded

Competition for limited food can become stronger as more individuals share the same resource, linking its effect to density.

Question 3

A population is smaller after a dry period. Which conclusion is best supported by those two observations alone?

The dry period definitely caused every death.
The population decreased, but more evidence is needed to establish why.
The population must have emigrated.
The dry period is density-dependent.

Show answer and explanation

The population decreased, but more evidence is needed to establish why.

The counts establish a decrease. They do not, by themselves, identify its cause or show which population processes changed.

Key terms

Population: Individuals of the same species living in the same area at the same time.
Population size: The number of individuals in a population.
Limiting factor: A condition or interaction that restricts population growth or affects survival.
Density: The number of individuals in a given area.
Density-dependent factor: A factor whose effect is linked to how crowded a population is.
Density-independent factor: A factor whose effect does not depend on population density.
Immigration: Movement of individuals into a population’s area.
Emigration: Movement of individuals out of a population’s area.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 12 Biology (SBI4U), expectation F3.3. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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