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Calcimator

Fish Stock Assessment Calculator

Stock status from catch data and abundance indices.

About this calculator

This calculator applies the Leslie-DeLury depletion method, a classic fisheries technique -- formalized by Leslie and Davis (1939) and DeLury (1947) -- for estimating population size from how catch-per-unit-effort (CPUE) declines as fish are removed over a season. The core idea: if you know your catchability coefficient (how efficiently your gear removes fish relative to the population size), the drop from Initial CPUE to Final CPUE over a known Total catch tells you how large the starting population must have been. From that initial population estimate, the calculator derives Remaining stock (population minus catch) and Exploitation rate (the percentage of the stock removed), then classifies the fishery as healthy, fully exploited, or overfished using standard exploitation-rate thresholds.

Total effort (units) does not feed into the depletion estimate at all -- it is used only to compute the separate Avg CPUE figure, a simple catch-per-effort summary rather than part of the population model. The Leslie-DeLury method assumes a closed population (no recruitment, immigration, or natural mortality during the assessment period) and constant catchability throughout -- assumptions that hold reasonably well for a short, intensive fishing season but break down for long seasons, migratory stocks, or fisheries with strong recruitment pulses. The method also requires CPUE to have actually declined from start to end of season -- if Final CPUE is equal to or higher than Initial CPUE (for example because recruitment offset removals, or the two figures were entered in the wrong fields), the depletion math cannot produce a valid estimate, and the calculator reports Stock Status as undeterminable rather than a misleadingly reassuring result.

Inputs

lb

Results

Initial population (N0)

12,500

Remaining stock7,500
Exploitation rate (%)40
Catchability (q)0.01
Stock StatusFully Exploited
Avg CPUE50

Figures current as of 1947. Source: Leslie PH, Davis DHS. An attempt to determine the absolute number of rats on a given area. J Anim Ecol. 1939;8(1):94-113; DeLury DB. On the estimation of biological populations. Biometrics. 1947;3(4):145-167.

How to Use This Calculator
  1. Enter Initial CPUE (kg/effort), Final CPUE (kg/effort), and Total catch (kg).
  2. Set Total effort (units).
  3. Review the Initial population (N0) result.
  4. Use Remaining stock and Exploitation rate (%) to inform your decision.

How the result changes with Initial CPUE (kg/effort)

Initial CPUE (kg/effort)Initial population (N0)
500
7525,000
1508,333
2506,579

What each input means

Initial CPUE (kg/effort)
Catch per unit effort at start of season.
Final CPUE (kg/effort)
Catch per unit effort at end of season.
Total catch (kg)
Total catch during the assessment period.
Total effort (units)
Total fishing effort in standardized units.

What each result means

Initial population (N0)
Estimated initial stock size (depletion method).
Remaining stock
Estimated remaining population after harvest.
Exploitation rate (%)
Percentage of stock removed by fishing.
Catchability (q)
Catchability coefficient (efficiency of fishing effort).
Stock Status
Healthy (under 30% exploitation), Fully Exploited (30-50%), or Overfished (over 50%), based on exploitation rate. Reports Undeterminable if Final CPUE did not come in lower than Initial CPUE.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Initial CPUE (kg/effort) = 100, Final CPUE (kg/effort) = 60, Total catch (kg) = 5000, Total effort (units) = 100 = 4 input(s) provided
  2. Calculate Initial population
    Initial population (N0)
    12500 = 12500
  3. Calculate Remaining stock
    Remaining stock
    7500 = 7500
  4. Calculate Exploitation rate
    Exploitation rate
    40 = 40

Figures and sources

Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.

Frequently Asked Questions

What is the Leslie-DeLury depletion method estimating?

It estimates the initial population size (N0) of a fish stock from how catch-per-unit-effort declines as cumulative catch accumulates over a season. The underlying logic is that a larger starting population declines more slowly in CPUE for the same amount of catch than a smaller one does, so the rate of CPUE decline reveals the population size. The method traces back to two foundational papers -- Leslie and Davis's 1939 study estimating a rat population from trapping removals, and DeLury's 1947 formalization of the same logic for fisheries -- and is still taught and applied today as one of the classic closed-population depletion estimators.

Does Total effort (units) change my population estimate?

No. Total effort only feeds into the separate Avg CPUE output, a simple catch-divided-by-effort summary reported alongside the results. The Initial population, Remaining stock, and Exploitation rate all come from the CPUE-decline calculation, which does not use Total effort at all.

What counts as an overfished stock in this calculator?

This calculator flags a stock as Healthy below 30% exploitation rate, Fully exploited between 30% and 50%, and Overfished above 50%. These are common rule-of-thumb thresholds in fisheries management, though actual regulatory thresholds vary by species, jurisdiction, and stock assessment method.

What assumptions does this depletion method depend on, and why might it be unreliable for a long fishing season?

It assumes a closed population during the assessment period -- no new fish entering through recruitment or immigration, and negligible natural mortality alongside the fishing removals -- plus constant catchability, meaning your gear removes a consistent fraction of the remaining population per unit of effort throughout the season. Over a long season, new fish can enter the population through recruitment or immigration, which violates the closed-population assumption and makes the CPUE decline look smaller than the true fishing pressure would otherwise produce -- so the method is most reliable over a short, intensive season where the population can reasonably be treated as fixed.

What happens if Final CPUE is the same as or higher than Initial CPUE?

The Leslie-DeLury method depends on CPUE declining as fish are removed, so if Final CPUE does not come in lower than Initial CPUE -- whether from recruitment offsetting the catch or the two figures being entered in the wrong fields -- the depletion math has no valid solution. Rather than reporting a misleading population estimate, this calculator flags Stock Status as undeterminable in that case; Avg CPUE still reports a real figure since it is computed directly from your catch and effort, independent of the depletion model.

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