Core Concept Biodiversity Collection Article Published: November 12, 2025

Using Math to Protect Fish in the Ocean

Abstract

Have you ever wondered how scientists count fish in the ocean? Fish are always moving, and the ocean is huge, so counting them is not easy! Scientists use stock assessments, a method that gathers clues such as how many fish are caught by fishing boats, how many are seen in surveys, and how fast fish grow. Using math and computer models, scientists predict how fish populations will change in the future. If too many fish are caught, there might not be enough left to reproduce, which is called overfishing. Stock assessments help managers decide how many fish can be safely caught. Scientists also protect special areas where fish lay eggs to help their numbers grow. By understanding stock assessments, we can help keep fish in the ocean for future generations. Thanks to ongoing work of scientists, we can enjoy fish today while making sure there are plenty left for tomorrow.

How Many Fish are Out There?

You are probably familiar with some fish species, and you might even have a favorite! Scientists estimate that at least 20,000 species of fish live in the ocean, but there may be twice as many. The total number of fish in the ocean is also still a mystery. There are billions or even trillions, but the exact number depends on the species, the region, and the time of year.

Counting fish is a job for science detectives! Unlike counting jellybeans in a jar, fish are constantly moving, and the ocean is vast. So how do scientists figure out how many fish live in the sea? They use computers, math, and stock assessment, which help estimate fish populations as accurately as possible. In stock assessments, scientists gather clues to determine how many fish are in the ocean (Figure 1). This information helps them figure out how many fish can be caught while ensuring there are still enough left for the future.

Illustration of a fishing boat above ocean water with fish representing stock levels from 2019 to 2025. Each year from 2019 to 2024 shows different fish numbers, with 2025 ending in a question mark. A world map with a location marker is in the top right.
  • Figure 1 - This graph shows how scientists estimate the number of fish in the ocean over time.
  • The number of fish in each column indicates the fish population size. Stock assessments help predict future trends and guide decisions on how much fishing is safe.

Why are Healthy Fish Stocks Important?

A fish stock is a group of fish of the same species that live in the same area and reproduce with one another. It is like an ocean neighborhood, but it can be huge! For example, all the Atlantic cod in the North Atlantic Ocean are considered one fish stock. Scientists study fish stocks to see if their populations are stable, growing, or shrinking over time.

Fish are key players in the ocean. They provide food for other animals and help keep marine life balanced. Humans also rely on fish as a food source and for jobs in fishing industries. However, if we take too many fish too quickly, stock populations can shrink, making it harder for them to recover. This is called overfishing. That is why scientists conduct stock assessments—to help manage fish populations sustainably and make sure there are enough fish for the future.

Why do Scientists Count Fish?

Fish are a renewable resource, meaning they can replenish their numbers if stocks are managed properly. But if overfishing happens, their populations can drop to dangerously low levels. Stock assessments help scientists estimate the size of fish populations and understand how they are affected by fishing and environmental changes like rising sea temperatures. These assessments predict what might happen in the future if fishing practices stay the same or change [1]. With this information, governments and fishery managers can set rules, like catch limits or temporary fishing bans, to protect fish populations while still allowing people to fish and enjoy seafood.

How do Scientists Count Fish?

Counting fish in the ocean is even harder than counting stars in the sky! Instead of counting each fish one by one, scientists collect clues and use math to estimate fish numbers. They gather data from three main sources: catch data, abundance data, and biology data.

Catch Data

Catch data comes from fishing boats. Scientists examine the fish that are brought back to shore, measuring how many were caught, how big they are, and what species they belong to. Fishers also record where and when they fished and what equipment they used. Sometimes, scientists ride along on fishing boats to collect data directly.

Abundance Data

Abundance data tells scientists whether there are a few or many fish in an area. Research ships survey fish populations using special nets, hydroacoustics (sound waves to detect fish underwater), and underwater robots with cameras. These tools help track how fish populations change over time [2].

Biology Data

Biology data helps scientists understand the life cycle of fish. They study fish ear bones to determine their age, just like counting rings on a tree. Scientists also measure how fast fish grow, how many eggs they lay, and how many young fish survive to adulthood [3]. By combining all this data, scientists can make the best decisions to protect fish populations.

How do Scientists Use Math in Stock Assessments?

Once all the data is collected, scientists use math to understand what it tells us. They create computer models that predict how fish populations will change in the future. These models take into account how fish grow, reproduce, and die, as well as how many are being caught (Figure 2). They work like a recipe, mixing data from catch, abundance, and biology to estimate how many fish are in the ocean. For example, one simple model might say:

Stock assessment infographic detailing sustainable fish catching: Step 1 shows collecting data on fish catch, abundance, and biology. Step 2 involves using mathematical models with collected data to predict future catches, with a virtual population example of fourteen thousand three hundred eighty-five fishes. Step 3 involves informing managers to apply management measures based on model results, emphasizing sustainable fish consumption.
  • Figure 2 - In step 1 of a stock assessment, scientists collect data on fish caught by commercial fishing boats, such as how many fish were caught and the length and width of each fish.
  • In step 2, they enter the data into computer models that can estimate fish populations (the dots represent model results) and figure out how many fish should be caught the next year. In step 3, scientists give decision makers advice based on the results of the model, to help set fishing rules and keep fish populations healthy.

New Population = Old Population + Growth – Fish Caught.

This helps scientists figure out how fish populations change over time. Scientists can then predict what will happen if fishing levels stay the same, increase, or decrease. This helps them make recommendations on how to keep fishing sustainable [4]. Did you know that scientists use similar methods to count other animals, like whales, birds, and even insects?

How do Stock Assessments Help Protect Fish?

Stock assessments help set fishing rules that balance the need for food with the need to protect fish populations. If a stock assessment shows that a fish population is shrinking, managers may lower catch limits to allow the fish stock to recover. If a population is healthy, more fishing may be allowed.

Some stock assessments reveal that certain areas called nurseries are especially important for fish reproduction. In these cases, managers may close the nursery areas to fishing, to allow young fish to grow. Stock assessments also help identify when fishing gear or methods need to change to reduce environmental harm. By counting fish and calculating how many can be safely caught, scientists help ensure that fishing remains sustainable for the future.

Why Does this Matter to You?

The ocean contains so many kids of fish—from tiny fish half an inch long to others over 50 feet long that weigh several tons. Some are popular for eating, while others are more important for the ocean than for our plates! But all of them play a key role in supporting ocean life and human communities. Ensuring we have the right number of fish at the right time is what scientists do—and now you know how they solve the mystery! Who said math is not cool?

Glossary

Stock Assessments: A scientific method that uses data and computer models to estimate the size and health of fish populations over time.

Fish Stock: A group of the same fish species living and reproducing in the same area.

Overfishing: Catching too many fish too quickly, making it hard for the population to recover.

Hydroacoustics: A way of using sound waves underwater to study fish and the sea. Scientists “listen” to echoes to find out where animals are and how many.

Computer Models: Digital tools that use math and data to imitate real-life processes, helping scientists test ideas, predict changes, and understand nature without always needing field experiments.

Sustainable: Using resources (like fish) in a way that they can keep growing or coming back, so we do not run out.

Nurseries: Special ocean areas where young fish grow safely before moving to adult habitats. Like underwater “kindergartens”, they provide food and shelter from predators.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

This publication is part of the FRESCO research project PID2022- 140290OB-I00 funded by MCIN/AEI/10.13039/501100011033/ and by “ERDF A way of making Europe”.

AI Tool Statement

The author(s) declare that Gen AI was used in the creation of this manuscript. Generative AI was used to correct English grammatical errors.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.


References

[1] Hilborn, R. and Walters, C. J. 1992. Quantitative Fisheries Stock Assessment: Choice, Dynamics and Uncertainty. New York, NY: Springer. doi: 10.1007/978-1-4615-3598-0

[2] Shuter, B. J., Milne, S. W., Hrenchuk, L. E., deKerckhove, D. T., and Rennie, M. D. 2023. Integrating hydroacoustic and telemetric surveys to estimate fish abundance: a new approach to an old problem. Can. J. Fish Aquat. Sci. 80:1562–78. doi: 10.1139/cjfas-2022-0183

[3] Campana, S. E. 2001. Accuracy, precision and quality control in age determination, including a review of the use and abuse of age validation methods. J. Fish. Biol. 59:197–242. doi: 10.1111/j.1095-8649.2001.tb00127.x

[4] Punt, A. E. and Donovan, G. P. 2007 Developing management procedures that are robust to uncertainty: lessons from the International Whaling Commission. ICES J. Mar. Sci. 64:603–12. doi: 10.1093/icesjms/fsm035