F. Population Dynamics · Population DynamicsManaging Populations: Indigenous Knowledge, Sustainable Harvests and Careers
F1.2 F1.1 F3.3 F2.2 A2.1 A2.2About 75 minutes
Learning goals- I can use the logistic model to explain maximum sustainable yield and why harvesting at that level is risky.
- I can explain the collapse of the northern cod fishery using population dynamics.
- I can describe how First Nations, Métis and Inuit knowledge and co-management contribute to sustaining populations, with specific examples.
- I can describe careers related to population dynamics and the education they require, and identify Canadian contributors to the field.
Words to know
sustainable yield
A harvest that can be taken year after year without reducing the population, because it is no larger than the population's growth.
maximum sustainable yield (MSY)
The largest harvest that can in theory be taken indefinitely; in the logistic model it is rK/4, taken when the population is kept at K/2.
precautionary approach
Managing cautiously when information is uncertain: harvesting less than the estimated maximum and acting before a population falls to critical levels.
co-management
Shared decision-making about land, water or wildlife between governments and Indigenous nations or communities.
Two-Eyed Seeing (Etuaptmumk)
A guiding principle introduced by Mi'kmaw Elders Albert and Murdena Marshall: learning to see with the strengths of Indigenous knowledge in one eye and Western science in the other, and using both together.
Inuit Qaujimajatuqangit (IQ)
Inuit traditional knowledge, values and ways of doing, used in governance and wildlife management in Nunavut.
stock assessment
The scientific estimation of a fish population's size, age structure and growth, used to set catch limits.
From models to decisions
Every hunting season, fishing quota and conservation plan in Canada is a population-dynamics decision. In this final lesson you will apply the logistic model to harvesting, learn from one of Canada's hardest lessons (the collapse of the northern cod), see how Indigenous knowledge and co-management help sustain populations, and explore careers that use everything in this unit.
Maximum sustainable yield
If a harvest equals the population's growth, the population stays the same: ΔN = growth − harvest = 0. From Logistic Growth and Carrying Capacity, growth is fastest at N = K/2, where dN/dt = rK/4. So in theory, the maximum sustainable yield (MSY) is rK/4, taken from a population kept at K/2.
But look at the graph below. For any harvest smaller than MSY, there are two population sizes where growth equals harvest:
- The upper one is stable: if N rises a little, growth falls below the harvest and N comes back down; if N falls a little, growth rises above the harvest and N recovers.
- The lower one is unstable: if N falls below it, growth is less than the harvest, so the population keeps shrinking, faster and faster, toward collapse, unless harvesting is reduced.
At MSY itself, the two points merge, so any small overestimate of the stock or bad year can tip the population into decline. That is why modern fisheries management uses a precautionary approach: harvest less than the estimated MSY and cut catches early when a stock declines. Fisheries and Oceans Canada classifies stocks into healthy, cautious and critical zones and is supposed to reduce fishing as a stock moves toward the critical zone.
Logistic growth for a fish stock with r = 0.4 and K = 50 000. A constant harvest of 3200 fish per year matches growth at two stock sizes; only the upper one (40 000) is stable. MSY is 5000 per year at 25 000 fish.Worked exampleLet's test a harvest plan
A fish stock has r = 0.4 per year and K = 50 000. (a) Find the MSY. (b) Managers set a quota of 5000 per year, but the stock has actually been overestimated: it is really 20 000 fish. What happens? (c) What quota would be sustainable at 20 000 fish?
- (a) MSY = rK/4 = 0.4 × 50 000 ÷ 4 = 5000 fish/year, at N = K/2 = 25 000.
- (b) Growth at 20 000: dN/dt = 0.4 × 20 000 × (1 − 20 000/50 000) = 8000 × 0.6 = 4800/year. The harvest (5000) exceeds growth by 200, so the stock falls.
- As N falls further, growth falls too (for example at 15 000, growth = 0.4 × 15 000 × 0.7 = 4200), so the gap widens: a spiral toward collapse.
- (c) A quota at or below 4800/year would hold the stock at 20 000; to let it rebuild toward 25 000 or higher, the quota should be well below that (precautionary approach).
(a) MSY = 5000/year. (b) At 20 000 fish, growth is only 4800, so a 5000 quota drives the stock down, faster and faster. (c) At most 4800/year, and less if the goal is recovery.
The collapse of the northern cod
For centuries, Atlantic cod off Newfoundland and Labrador supported fishing communities. Beginning in the 1950s and 1960s, large foreign and domestic factory trawlers using new technology (sonar, powerful engines and huge nets) took enormous catches, and catches crashed in the 1970s. Canada extended its fishing zone to 200 nautical miles in 1977, and Canadian fleets expanded. Through the 1980s, stock assessments overestimated the population, partly because catches per trawler stayed high even as the stock shrank (fish gathered in dense schools that modern gear could still find), and inshore fishers' warnings that fish were getting scarcer and smaller were not given enough weight.
On 2 July 1992, the federal government declared a moratorium on the northern cod fishery. It was one of the largest layoffs in Canadian history: tens of thousands of people lost work. Recovery has been very slow. Cod mature at several years old, the fishing had removed many of the largest, most fecund females, and the ecosystem had changed.
Population dynamics explains much of this: harvests above sustainable growth, uncertainty in N, a lowered effective K from ecosystem change, and the slow recovery of a later-maturing species. The I = P × A × T idea applies too: technology (T) multiplied fishing power far faster than scientists could measure the stock. Researchers such as Ransom Myers of Dalhousie University went on to show that many of the world's large predatory fish populations had declined sharply under industrial fishing.
Indigenous knowledge and resource management
First Nations, Métis and Inuit peoples have managed relationships with the animals, plants and waters of their territories for thousands of years, and continue to do so today. Their knowledge systems are diverse; each nation has its own knowledge, laws and practices. Many share principles that match what you have learned in this unit: take only what is needed, share, watch the land over long periods, and think about future generations. A few examples:
- Two-Eyed Seeing (Etuaptmumk). Mi'kmaw Elders Albert and Murdena Marshall of Unama'ki (Cape Breton) introduced this principle: learning to see from one eye with the strengths of Indigenous knowledge and from the other with the strengths of Western science, and using both eyes together. It now guides many Canadian research and management projects. The Mi'kmaw concept of netukulimk describes using what the land provides for the community's well-being without harming the integrity, diversity or productivity of the environment.
- Inuit Qaujimajatuqangit. In Nunavut, wildlife decisions are made through co-management under the Nunavut Agreement (1993). The Nunavut Wildlife Management Board includes Inuit and government appointees, and Inuit hunters' long-term observations of caribou, polar bears and other species are used alongside scientific surveys in setting harvest levels.
- Haida Gwaii. Gwaii Haanas National Park Reserve, National Marine Conservation Area Reserve and Haida Heritage Site is managed jointly by the Haida Nation and the Government of Canada through a board with equal representation.
- Clam gardens. On the Pacific coast, Coast Salish, Kwakwaka'wakw and other peoples built rock walls at the low-tide line, creating terraces of sand and gravel. Studies have found that these clam gardens can produce more clams than unmodified beaches, a form of raising carrying capacity that has been sustained for generations.
- Manoomin (wild rice). Anishinaabe communities in northwestern Ontario harvest wild rice by canoe, gently knocking ripe grain into the boat so that much of it falls back into the water to reseed, and they speak up to protect rice waters from damage such as changing water levels.
- Indigenous Guardians. In many First Nations, Métis and Inuit communities across Canada, Guardians monitor wildlife, water quality and land use in their territories, combining traditional knowledge with tools such as GPS and water testing.
In the northern cod story, inshore fishers' local knowledge was underused; in co-management, long-term knowledge holders have a formal role in decisions. This is one reason co-management is increasingly seen as both more just and more effective.
Two-Eyed Seeing, as described by Mi'kmaw Elder Albert Marshall: Indigenous knowledge and Western science each bring strengths, and decisions draw on both.Careers in population dynamics (A2.1)
- Wildlife biologist / ecologist: surveys populations (mark-recapture, aerial surveys, camera traps), models growth and recommends harvest limits. Usually a B.Sc. in biology or ecology; many positions need an M.Sc.
- Fisheries scientist (stock assessment): estimates fish populations and sets catch advice, for example at Fisheries and Oceans Canada. B.Sc. plus graduate study in fisheries science or quantitative ecology; strong math and statistics.
- Fish and wildlife technician: fieldwork, trapping and tagging, data collection. Ontario colleges offer two- and three-year fish and wildlife technician programs.
- Conservation officer: enforces hunting and fishing laws and educates the public; college or university training in natural resources plus law enforcement training.
- Indigenous Guardian: monitors and protects lands and waters for First Nations, Métis and Inuit communities; training often combines community knowledge with certificates in field skills.
- Demographer: studies human populations (births, deaths, migration) for Statistics Canada, governments and companies; degrees in statistics, sociology, economics or geography.
- Epidemiologist: studies how diseases spread through populations (Public Health Ontario, the Public Health Agency of Canada); usually a master's in public health or epidemiology.
- Agronomist / plant breeder: develops crop varieties and practices to feed growing populations; B.Sc. in agriculture or plant science, often graduate study.
- Environmental consultant or planner: assesses development projects' effects on populations and ecological footprints.
Canadian contributors you met in this unit (A2.2): Charles Krebs (snowshoe hare research in the Yukon), David Schindler (Experimental Lakes Area), William Rees and Mathis Wackernagel (ecological footprint), Robert MacArthur (born in Toronto; r- and K-selection, resource partitioning), Charles Saunders (Marquis wheat), Baldur Stefansson and Keith Downey (canola), Stanley Zlotkin (Sprinkles), Ransom Myers (fisheries decline), and Albert and Murdena Marshall (Two-Eyed Seeing).
Just for funWhy did the fisheries biologist bring a calculator to the dock? Because rK/4 is a lot easier to work out before the boat leaves than after the fish are gone.
Hands-on activityHarvest game: tragedy or co-management?
You need: 60 dried beans (the "fish"), a bowl (the lake), 3 to 4 players (family members), paper and a pencil.
Rules: the lake starts with 40 fish. Its carrying capacity is 60. Each round is a year.
- Game 1, everyone for themselves: each player secretly decides how many fish to take (0 to 10). Reveal at once and remove them. Each player needs at least 2 fish per year to "feed their family".
- Reproduction: the fish left in the lake grow. Use a simple logistic rule: add round(0.5 × N × (1 − N/60)) beans (for example, 20 fish left → add round(0.5 × 20 × 0.667) = 7). Never exceed 60.
- Play 8 years or until the lake is empty. Record N each year.
- Game 2, co-management: start again with 40. Before each year, players talk, agree on a total catch, and may use "local knowledge" (one player, the Elder or knowledge keeper, can see the true count and advise). Play 8 years.
- Compare the graphs and the total catch over 8 years. Calculate what catch would be sustainable at N = 30 (= K/2): 0.5 × 30 × 0.5 = 7.5, about 7 fish per year in total.
What to look for: in Game 1, players often take too many, so N falls below K/2, growth shrinks and the lake can collapse within a few years. In Game 2, groups that keep the total catch around 6 or 7 per year and keep N near 30 or higher can fish every year, and the total catch over 8 years is usually larger. Connect this to the northern cod and to co-management. Keep beans away from small children.
Your turn
1Using the logistic model, at what population size is a sustainable harvest largest, and what is that harvest?
At N = K/2; the MSY is rK/4.
2A deer herd has r = 0.3 per year and K = 2000. Find the MSY.
MSY = 0.3 × 2000 ÷ 4 = 150 deer/year (at N = 1000).
3Why is the lower of the two harvest-equals-growth points unstable?
Below it, growth is less than the harvest, so N falls; as N falls, growth falls further, so the population keeps declining unless harvest is cut.
4Give three reasons the northern cod collapsed.
Any three: harvests exceeded growth; stock overestimated in assessments; powerful fishing technology; removal of large, fecund females; inshore fishers' warnings underused; ecosystem changes lowering K and slowing recovery.
5What is Two-Eyed Seeing, and who introduced it?
A principle of using the strengths of Indigenous knowledge and Western science together, introduced by Mi'kmaw Elders Albert and Murdena Marshall.
6How do clam gardens relate to the idea of carrying capacity?
By building rock walls that create more suitable habitat (flatter terraces of sand and gravel), clam gardens can raise the carrying capacity for clams, so more can be harvested sustainably.
7Name two careers that use population dynamics and the education each typically needs.
Sample: fisheries scientist (B.Sc. plus graduate study with statistics); wildlife technician (college diploma). Others: demographer, epidemiologist, conservation officer, Indigenous Guardian, wildlife biologist, plant breeder.
More practice: warm-up
1Write the formula for MSY in the logistic model.
2When was the northern cod moratorium declared?
3What does co-management mean?
Shared decision-making about land, water or wildlife between governments and Indigenous nations or communities.
4In which territory is Inuit Qaujimajatuqangit used in wildlife co-management?
5Which Canadian scientist led the Lake 226 whole-lake experiment at the Experimental Lakes Area?
More practice: on your own
1A lake trout stock has r = 0.2 and K = 10 000. Managers set a quota of 400 per year. Find the two stock sizes where growth equals the quota.
Solve 0.2N(1 − N/10 000) = 400: 0.2N − 0.00002N² = 400, so N² − 10 000N + 20 000 000 = 0. N = [10 000 ± √(100 000 000 − 80 000 000)] ÷ 2 = [10 000 ± 4472] ÷ 2. So N ≈ 2764 (unstable) and N ≈ 7236 (stable).
2Why is the precautionary approach especially important for late-maturing species such as cod or lake trout?
Late-maturing species have low r and recover slowly, and their stock estimates are uncertain. A mistake that drives them below the unstable point may take decades to reverse, so harvesting well below MSY and cutting catches early reduces risk.
3Explain how Inuit hunters' long-term observations can improve a caribou population estimate based on one aerial survey.
One survey gives a snapshot with sampling error and may miss animals that have moved. Hunters observe over many years and seasons: changes in body condition, calf numbers, migration routes and range use. Combining these gives a more complete picture of trends and causes, and can flag problems early.
4A student says, "Indigenous knowledge is just stories, so it can't help with real management." Respond using evidence from this lesson.
The claim is wrong. Indigenous knowledge is based on careful, long-term observation and tested practice. Examples: clam gardens that measurably increase clam productivity; Inuit observations used with surveys in Nunavut co-management; inshore fishers' warnings about cod decline that proved correct. Under Two-Eyed Seeing, both knowledge systems are valued for their strengths, and decisions are better when both are included.
5Explain, using I = P × A × T, why technology contributed to the cod collapse.
T (impact per unit of fishing effort) rose sharply with sonar, larger trawlers and bigger nets, so the same number of boats could catch far more fish. Catches stayed high even as the stock shrank, hiding the decline until it was too late.
Challenge
1For the logistic stock with r = 0.4 and K = 50 000, compare two management rules for a stock at 40 000: (a) a constant quota of 4800 per year; (b) a constant harvest rate of 10% of the stock per year. For each, find the equilibrium (or equilibria) and explain which rule is safer if the stock is overestimated.
(a) Solve 0.4N(1 − N/50 000) = 4800: N² − 50 000N + 600 000 000 = 0, N = [50 000 ± √(2 500 000 000 − 2 400 000 000)] ÷ 2 = [50 000 ± 10 000] ÷ 2, so N = 30 000 (stable) and N = 20 000 (unstable). (b) Harvest = 0.1N. Set 0.4N(1 − N/50 000) = 0.1N, so 1 − N/50 000 = 0.25, N = 37 500, a single stable equilibrium. The harvest-rate rule is safer: as the stock falls, the catch falls automatically, so there is no unstable collapse point; a fixed quota keeps taking 4800 even when the stock has shrunk.
2Design a co-management plan for a declining moose population in a region shared by a First Nation, hunters and a provincial ministry. Include the data you would collect, how you would include Indigenous knowledge, and how harvest decisions would be made.
Sample: Form a joint committee with equal representation of the First Nation and the ministry, plus hunter representatives. Data: aerial surveys and calf-to-cow ratios (science); harvesters' and Elders' observations of moose condition, ticks, habitat change and predator activity over decades (Indigenous knowledge); collected and interpreted together (Two-Eyed Seeing). Decisions: agree on population goals and precautionary harvest limits below estimated sustainable yield; respect constitutionally protected Aboriginal and treaty rights to harvest for food, social and ceremonial purposes as a priority; review annually and adjust when monitoring shows change; address causes such as habitat loss, roads, parasites (meningeal worm, winter ticks) and predation.
3Choose one career from this lesson. Describe a typical day using at least four techniques or concepts from this unit, and outline a realistic education pathway from Grade 12.
Sample (fisheries stock assessment biologist): In the morning, check mark-recapture and tagging data from a lake survey and calculate Chapman estimates; build a life table from fish ages read from ear bones; fit a logistic model to estimate r and K; calculate sustainable yield under different harvest rules; meet with an Indigenous fisheries committee to compare results with harvesters' observations. Pathway: Grade 12 biology, chemistry and calculus; B.Sc. in biology, ecology or environmental science with statistics and programming; summer field jobs as a technician; an M.Sc. in fisheries or quantitative ecology; then a position with a government agency, Indigenous organization, university or consulting firm.
Check your understandingQuiz
1. In the logistic model, maximum sustainable yield is taken when the population is kept at:
2. For r = 0.5 and K = 8000, the MSY is:
3. The northern cod moratorium was declared in:
5. A constant harvest that is less than MSY has two equilibrium population sizes. The lower one is:
6. Which career mainly studies human births, deaths and migration?
7. Clam gardens built by Indigenous peoples on the Pacific coast:
For parents and teachersBig idea (F1.2, F1.1, F3.3, A2): the logistic model shows that the maximum sustainable yield (rK/4 at K/2) is a knife-edge: overestimates or bad years can tip a population into collapse, as happened to the northern cod in 1992. First Nations, Métis and Inuit knowledge and co-management (Two-Eyed Seeing, Inuit Qaujimajatuqangit, Haida co-management, clam gardens, Guardians) contribute long-term observation and practices that help sustain populations. Many careers use these ideas.
How to help: play the harvest game with the family; the conversation afterward is the lesson. If your family has a connection to fishing, hunting or a First Nation, Métis or Inuit community, your teen may value hearing about it, if you are comfortable sharing.
Respectful learning: Indigenous peoples and knowledge systems are diverse and living. Encourage your teen to name the specific nation and to use sources written by or with Indigenous communities.
Common difficulties:
- Quadratic algebra when solving for the two equilibria.
- Thinking MSY is a safe target (it is the maximum, not a safe level).
Sources: Fisheries and Oceans Canada (northern cod moratorium, 2 July 1992; precautionary approach framework); Bartlett, Marshall and Marshall (2012) on Two-Eyed Seeing; Nunavut Wildlife Management Board; Parks Canada and the Haida Nation (Gwaii Haanas); Groesbeck and colleagues (2014), PLOS ONE, on clam gardens; Myers and Worm (2003), Nature.