Introduction to Fish Populations and Ecosystems

Quick note: no files came through on my end this time, so I've built this study note straight from the core content of "Introduction to Fish Populations and Ecosystems" — the concepts every intro fisheries course covers. If you upload the images again, I can fold in anything specific from your slides.

TL;DR

Fish populations grow, shrink, and shift based on birth (recruitment), death (natural and fishing mortality), and movement. Ecosystems tie populations to habitat, food webs, and other species, all bounded by a carrying capacity. Master recruitment, mortality, carrying capacity, and estimation methods (mark-recapture) and you'll cover 80% of exam questions.

1. The Mental Model

A fish population is just a bucket: fish flow in through births and immigration, and flow out through deaths and emigration. The ecosystem is the container that decides how full that bucket can get — food, oxygen, predators, and space all set the limit. A fish population's size at any moment is a running balance between how fast new fish enter and how fast old ones leave.

2. The Core Material

2.1 Population Dynamics: The Four Forces

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Every fish population changes size due to exactly four processes. Exam questions almost always trace back to one of these:

• Recruitment (R): new fish entering the population — usually meaning young fish surviving long enough to be counted or caught (they "recruit" to the fishery or to adulthood).
• Growth (G): individual fish getting bigger, which matters because biomass (total weight) can rise even if fish numbers don't.
• Natural mortality (M): death from predation, disease, old age, starvation — anything not caused by fishing.
• Fishing mortality (F): death caused by harvest.

Put together, the change in population biomass over a year looks like this:

$$B_{t+1} = B_t + R + G - M - F$$

where $B_t$ is biomass at time $t$. This is the core "population balance" equation. If $R + G > M + F$, the population grows. If it's the reverse, the population shrinks. Fisheries scientists spend entire careers trying to measure each of these four terms accurately, because you can't directly count fish in the ocean — you estimate.

2.2 Carrying Capacity and Density Dependence

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A population can't grow forever. Food, space, oxygen, and predators impose a ceiling called carrying capacity (K). The classic model for this is the logistic growth equation:

$$\frac{dN}{dt} = rN\left(1 - \frac{N}{K}\right)$$

Here $N$ is population size, $r$ is the intrinsic growth rate (how fast the population would grow with unlimited resources), and $K$ is carrying capacity. Notice what happens at the extremes:

• When $N$ is small (population way below capacity), $\left(1-\frac{N}{K}\right) \approx 1$, so growth is close to its maximum rate $rN$ — this is why small, recovering populations often grow fast.
• When $N \approx K$, the term $\left(1-\frac{N}{K}\right) \approx 0$, so growth stalls — the population plateaus.

This curve produces the classic S-shaped (sigmoid) growth curve. The point where growth rate is fastest (not where population is biggest) is at $N = K/2$. This is a critical fact for fisheries management: harvesting is most sustainable near $K/2$, because that's where the population can replace losses quickest. This is the logic behind Maximum Sustainable Yield (MSY) — the largest catch you can take indefinitely without depleting the stock.

2.3 Ecosystems: Food Webs and Trophic Structure

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Fish don't exist in isolation — they sit inside a food web with defined trophic levels:

1. Primary producers — phytoplankton, algae (convert sunlight to energy).
2. Primary consumers — zooplankton, small grazers (eat producers).
3. Secondary consumers — small fish (eat zooplankton).
4. Tertiary/apex predators — large predatory fish, sharks (eat other fish).

Energy transfer between trophic levels is inefficient — roughly only 10% of energy passes from one level to the next (the "10% rule"). This is why apex predators are always far less abundant than the producers at the base — there simply isn't enough energy to support large numbers of them.

Fish ecosystems also depend on abiotic factors: temperature, dissolved oxygen, salinity, pH, and habitat structure (reefs, seagrass beds, estuaries). Changes in any of these — say, warming water reducing oxygen — can shift carrying capacity down even if fishing pressure stays the same.

flowchart LR
    A["Recruitment (new fish)"] --> B["Population Biomass"]
    G["Individual Growth"] --> B
    B --> C{"Compare to Carrying Capacity K"}
    C -->|"N << K"| D["Fast population growth"]
    C -->|"N approx K"| E["Growth stalls / plateau"]
    B --> F["Natural Mortality"]
    B --> H["Fishing Mortality"]
    F --> B
    H --> B
    D --> B
    E --> B

2.4 Estimating Population Size: Mark-Recapture

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You can't line up fish and count them, so scientists use indirect methods. The most common intro-level method is the Lincoln-Petersen mark-recapture estimator:

$$\hat{N} = \frac{n_1 \times n_2}{m_2}$$

where:
- $n_1$ = number of fish caught, marked, and released in the first sample
- $n_2$ = total number of fish caught in the second sample
- $m_2$ = number of marked fish recaptured in the second sample
- $\hat{N}$ = estimated total population size

The logic: if marked fish mix randomly back into the population, the proportion of marked fish in your second catch should mirror the proportion of marked fish in the whole population. This method assumes: no births/deaths between samples, marks aren't lost, and marked fish redistribute randomly — assumptions examiners love to ask about.

3. Worked Example

Scenario: You're studying a trout population in a small lake for a fisheries course project.

Step 1 — Mark-recapture population estimate.
You catch and tag 50 trout, then release them back into the lake ($n_1 = 50$). A week later (enough time for mixing, but short enough that births/deaths are negligible), you catch 60 trout ($n_2 = 60$), and 12 of them have tags ($m_2 = 12$).

$$\hat{N} = \frac{n_1 \times n_2}{m_2} = \frac{50 \times 60}{12} = \frac{3000}{12} = 250$$

Your estimated population is 250 trout. Sanity check the assumptions: was a week long enough for tagged fish to mix evenly through the whole lake? If tagged fish stayed clustered near the release point, your second sample would be bi