Populations and Carrying Capacity

Every winter, crews from Virginia and Maryland drag metal dredges along the bottom of the Chesapeake Bay at about 1,500 sites, sampling blue crabs buried in the mud. From one winter to the next, the estimated number of crabs in the Bay can change by more than 100 million. The Bay is the same size every year. So why does the number of crabs it holds rise and fall so much? And is there a largest number of crabs it could ever support?

Explore: grow a population, then add limits

The simulation lets you grow a model population. You set the starting number, the growth rate and the carrying capacity, all in made-up units. You can switch between unlimited growth and limited growth, and you can add a disturbance, such as a cold winter or more predators, and watch what happens next.

• your population
• carrying capacity

Growth type Unlimited growth Limited growth

Starting population 10 relative units Growth rate (r) 0.30 new individuals per individual, each step Carrying capacity 500 relative units

Run 20 steps Add 1 step Reset

Add a disturbance Cold winter More predators

In this sketch, more predators lower the carrying capacity, so they work only with limited growth. Each disturbance adds one step, and three disturbances is the maximum.

Time step

0

Population (relative units)

10

Added in the last step

none yet

Carrying capacity now

500

Assumptions in this sketch: all numbers are relative units, not counts of any real animal. Each step adds the growth rate times the population. With limited growth, that gain shrinks to zero as the population reaches the carrying capacity. In this sketch a cold winter is a one-time loss: it removes 40% of the individuals present, before that step’s growth, and leaves the carrying capacity as set. The lesson says a hard freeze can also lower carrying capacity. More predators lower the carrying capacity by 25%. The 40% and 25% are invented sizes, in relative units. There is no chance in this sketch, so expected and observed are the same.

With plenty of resources a population grows in a J shape; as limits set in, the curve bends into an S shape that levels off near the carrying capacity, and that level can move when conditions change.

Try this.

1. Choose unlimited growth. Predict the shape of the graph after 20 time steps, then run it.
2. Switch to limited growth with the same starting number and birth rate. Predict where the line will end up, then test it.
3. Raise the birth rate. Predict whether the population will end up higher or only get there sooner.
4. Once the line is level, add a cold winter. Predict what happens right after the disturbance and later on, then watch.

Explain: who lives together and what holds them back

Think about one creek that flows into the Bay. It holds blue crabs, fish, clams, marsh grass and microbes, along with mud, water and sunlight.

A population is all the members of one species that live in the same area at the same time and can breed with each other. The blue crabs in the Bay this winter are a population. Its members compete for food, water, shelter and mates.

A community is all the populations of different species that live in an area and interact. The crabs, fish, clams and marsh grass of the creek form a community.

An ecosystem is a community together with its nonliving surroundings, such as water, mud, air and sunlight.

Two kinds of factors shape a population:

• A biotic factor is a living part of the environment, such as predators, food, competitors and disease.
• An abiotic factor is a nonliving part of the environment, such as temperature, moisture, air, salinity (salt level) and pH.

Living things in a community interact in many ways, such as predation (one eats another). Two important ones are these. Competition happens when individuals need the same limited resource, such as food or a hiding place. Cooperation happens when individuals work together and both gain, as when wolves hunt in a pack.

A limiting factor is anything that keeps a population from growing larger. Here are examples for the blue crab.

Factor	Kind	How it can limit blue crabs
Larger crabs	Biotic: predators	Adult blue crabs eat young crabs, so fewer young survive.
Clams and fish	Biotic: food	Less food can mean less energy for making eggs.
Other crabs	Biotic: competitors	In a crowd, more crabs need the same food and shelter.
Disease	Biotic	Sickness can spread faster through a crowded group.
Cold water	Abiotic: temperature	Very cold winters can kill crabs.
Fresh water	Abiotic: salinity	Low salt in cold water lowered crab survival in lab tests.

Other species meet other limits. Land plants and animals depend on moisture, land animals take oxygen from the air, and the pH of soil helps decide which plants grow where.

Explain: J-shaped and S-shaped growth

Suppose 10 bacteria land in a dish of fresh food, and each one splits in two every 30 minutes. After one step there are 20, then 40, 80, 160 and 320. The number added gets bigger every step. This is exponential growth, growth in which a population increases by the same fraction in each time period. On a graph it makes a J shape.

Exponential growth happens when a population is small and resources are plentiful. No real population can keep it up for long. Food runs short, waste builds up, and crowding makes competition, predation and disease worse.

When limits set in, the curve bends into an S shape. Scientists describe the parts of that curve like this:

1. Initial growth. A small population grows slowly at first, because there are few individuals to have young.
2. Exponential growth. Numbers rise faster and faster while resources last.
3. Steady state. Growth slows and the line levels off near the carrying capacity.
4. Decline. If conditions get worse, deaths outnumber births and the population shrinks.
5. Extinction. If the decline continues, the population falls to zero.

Carrying capacity is the largest population that an environment can support over time, with its resources and its challenges. At the steady state, births and deaths are about equal, if few individuals move in or out. The numbers still go up and down a little around that level. This balance, kept by constant change, is called dynamic equilibrium.

These five parts are a model, and real populations do not have to pass through all of them in order. Many populations stay near a steady state for a long time. Also, extinction of a population in one place is different from extinction of a whole species. Blue crabs could vanish from one creek and still live in the rest of the Bay.

Explain: carrying capacity moves

Carrying capacity is not one number stamped on a species. It changes when the environment changes. A mild winter, more food or more hiding places can raise it. A hard freeze or the loss of marsh grass can lower it.

Hiding places matter for young crabs. In a 2023 tank study, young blue crabs survived better when the tank held more stems of a model marsh grass, with adult crabs present as predators. The authors said the result still needs testing in real marshes.

Some limits get stronger as a population gets more crowded. These are called density-dependent factors, such as competition, disease and predators. Other limits hit a population whatever its size, such as a storm or a hard freeze. These are density-independent factors.

People change carrying capacity and population size too. Crabbing removes crabs from the Bay each year, and building on shorelines can remove marsh. You will look at these pressures in The Chesapeake Under Pressure.

The tension in every population is the same. Living things can produce more young than their environment can support, and the environment’s limits push back.

Elaborate: read the crab survey

Survey winter	Total crabs (millions)	Adult females (millions)	Juveniles (millions)
2018–2019	594	191	324
2019–2020	405	141	185
2020–2021	282	158	86
2021–2022	227	97	101
2022–2023	323	152	116
2023–2024	317	133	138
2024–2025	238	108	103
2025–2026	349	81	228

These are Bay-wide estimates from the Winter Dredge Survey, run each winter by the Maryland Department of Natural Resources and the Virginia Institute of Marine Science, as published by Maryland DNR (series opened October 2026; the 2026 values also appear in the VIMS release of May 2026). They come from about 1,500 sites, not one station. Each is an estimate, corrected for crabs the dredge missed. The total also includes adult males, which are not shown, so it is larger than the other two columns added together.

1. In which winter was the total lowest? In which was it highest?
2. From 2024–2025 to 2025–2026, did the total and the adult females change in the same direction? By how much did each change?
3. Find the mean total for the eight winters. Could that mean be the Bay’s carrying capacity? Explain why or why not.

Design problem

You want to test whether salt in the water is a limiting factor for duckweed, a tiny floating plant that multiplies by budding. Plan a fair test that shows how salt affects the population’s growth and the level it reaches.

One way to do it

• Question: How does the amount of salt in the water affect the growth of a duckweed population?
• Independent variable: salt added to each cup, for example 0, 1, 2 and 4 grams per liter.
• Dependent variable: the number of duckweed leaves, counted every two days for three weeks.
• Control: cups with no added salt.
• Constants: the same pond water and plant food, cup size, water volume, light, temperature and starting number of leaves (for example 10).
• Repeated trials: at least four cups for each salt level, placed in a random order under the lights.
• What results would mean: if the no-salt cups level off at the highest count and saltier cups grow more slowly, salt slows growth in these cups. If the saltier cups also level off lower, salt lowers the carrying capacity.
• Safety and ethics: wash your hands after handling pond water, and do not release the plants into a stream or pond afterwards.

Evaluate: check your thinking

The Bay does not hold the same number of crabs every year, probably because its carrying capacity and its limiting factors keep changing. Cold, salinity, predators, food, hiding places and crabbing all change how many crabs are born and survive. The survey shows that much of the year-to-year change comes from how many young crabs there are.

Science practices you used: asking a question about a real pattern, using a model and naming its limits, reading a data table and finding a mean, planning a fair test with a control and repeated trials, and making a claim backed by evidence and reasoning.