For major fish stocks — cod, bluefin tuna, herring and anchovy — this tool computes Maximum Sustainable Yield (MSY), B_MSY and F_MSY using the Schaefer, Pella-Tomlinson and Fox surplus-production models. Enter the current biomass and fishing pressure to see the Kobe-plot quadrant (healthy / rebuilding / overfishing / overfished) and the precautionary TAC in real time.
Parameters
Target species
Preset r and K shown for reference
Carrying capacity K
t
Maximum biomass the habitat can sustain
Intrinsic growth rate r
1/y
Growth rate at low biomass
Current biomass B
t
Current estimated spawning biomass
Fishing mortality F
1/y
Instantaneous mortality from fishing
Surplus production model
Shape assumption for the surplus curve
Strategy
Reference point for TAC setting
Results
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MSY (t/y)
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B_MSY (t)
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F_MSY (1/y)
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B / B_MSY
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F / F_MSY
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Stock status
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Ocean & fish-school animation
The sea, the fish school, the logistic curve and the fishing-boat effort are shown. Colour shows stock status (green = healthy, yellow = rebuilding, orange = overfishing, red = collapsed).
Surplus production curve — Schaefer / Pella-Tomlinson / Fox
Schaefer logistic surplus production model. r: intrinsic growth rate; K: carrying capacity; MSY: maximum sustainable yield. Surplus is maximised when B = K/2, and that yield can be harvested indefinitely at F = r/2.
Time evolution of biomass B. First term: surplus production; second: removal by fishing. Steady-state (dB/dt = 0) defines the equilibrium biomass; once F exceeds F_MSY the equilibrium B drops below B_MSY.
I hear "MSY" all the time in fisheries news, but what number is it, really? Some kind of "do not exceed" line?
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Good question. MSY — Maximum Sustainable Yield — is "the largest catch you can take every year without depleting the stock". In a formula, MSY = rK/4, where r is the intrinsic growth rate and K is the carrying capacity. For the default Atlantic cod stock with r = 0.30 and K = 1 million tonnes, MSY = 75,000 t/year. Catch less than that and the stock can recover; catch more and you head toward collapse over the long run.
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Then why not just fish right up to MSY every year? Why bother with "precautionary 0.8 MSY"?
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Two reasons. First, r and K themselves are uncertain — ±30-50% is routine. If the true MSY is lower than estimated, fishing at "MSY" steadily depletes the stock. Second, environmental swings like El Niño can crash recruitment in a single year — the Peruvian anchoveta lost 99% of its biomass during the 1972 ENSO event. So FAO recommends a 70-90% cap on MSY — the precautionary approach.
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The Kobe plot on the right has four quadrants in green, yellow, orange and red. The default shows B/B_MSY = 1.20 and F/F_MSY = 1.00 in green. What happens if I push F up?
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Try setting F to 0.20: F/F_MSY = 1.33 and you flip into the orange quadrant — "biomass is still OK, but at this fishing pressure B will drop below B_MSY in a few years". Push F to 0.30 and B to 300,000 t and you land in red. That is exactly where Newfoundland cod was in 1992 — 30,000 jobs lost and the stock still hasn't fully recovered three decades later.
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Why are there three models — Schaefer, Pella-Tomlinson, Fox? Don't they all just compute MSY?
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Because life history changes the best shape. Schaefer assumes a symmetric bell with B_MSY = K/2 — good for long-lived steady stocks like cod. Pella-Tomlinson lets you tilt it with the m parameter — suitable for short-lived, fecund species like sardine and saury where MSY peaks below K/2. Fox reaches MSY earlier at B_MSY ≈ 0.37K, giving you a conservative estimate when the stock is fished hard at young ages. Switch the dropdown above and watch the surplus curve change shape.
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These surplus production models look simple. Do real assessments still use them, or have they moved on to more advanced methods?
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For the ICCAT bluefin and WCPFC bigeye assessments, age-structured methods like Statistical Catch-at-Age and Stock Synthesis are now standard. They use Beverton-Holt or Ricker stock-recruitment relationships to model how spawner biomass produces recruits. But for data-poor stocks, Schaefer-style biomass-dynamic models are still the international default. Treat this tool as the "first read" — and remember that the MSC (Marine Stewardship Council) sustainable seafood label, the blue one in the supermarket, ultimately runs on the same B/B_MSY and F/F_MSY behind the scenes.
Frequently Asked Questions
Under Schaefer's logistic surplus production model dB/dt = rB(1−B/K), surplus production peaks at MSY = rK/4, with the corresponding biomass B_MSY = K/2 and fishing mortality F_MSY = r/2. For an Atlantic cod stock with intrinsic growth r=0.30 and carrying capacity K=1,000,000 t, this gives MSY = 75,000 t/year, B_MSY = 500,000 t and F_MSY = 0.15/year. This tool computes them in real time from species presets.
A Kobe plot puts B/B_MSY on the x-axis and F/F_MSY on the y-axis and divides stock status into four quadrants. Green (B≥B_MSY and F≤F_MSY) is healthy; yellow (B<B_MSY and F≤F_MSY) is rebuilding; orange (B≥B_MSY and F>F_MSY) is overfishing-in-progress; red (B<B_MSY and F>F_MSY) is overfished AND overfishing. It is the standard visualisation used by ICCAT, WCPFC and other international RFMOs in TAC negotiations.
Schaefer is the simplest, assuming a symmetric dome with B_MSY = K/2. Pella-Tomlinson adds a shape parameter m to make the curve asymmetric, which fits short-lived, highly fecund species like sardine and anchovy whose MSY peak lies below K/2. Fox uses a Gompertz form with B_MSY ≈ K/e ≈ 0.37K, reaching MSY earlier — a conservative choice for stocks fished hard at young ages.
The precautionary approach sets the TAC below MSY itself to absorb estimation error in r and K and recruitment variability driven by climate. It was agreed internationally in the 1995 UN Fish Stocks Agreement, and FAO guidelines typically cap the limit at 70-90% of MSY. This tool offers 0.8 MSY (precautionary) and 0.5 MSY (rebuilding) options. The 1992 Newfoundland Atlantic cod collapse — 30,000 workers laid off, decades to recover — is the textbook cautionary tale of trusting raw MSY.
Real-World Applications
TAC setting at international RFMOs (ICCAT / WCPFC / NPFC): ICCAT for Atlantic bluefin, WCPFC for Pacific bluefin and NPFC for Pacific saury all run scientific committees that estimate B/B_MSY and F/F_MSY annually and produce Kobe plots. The next year's TAC is negotiated against those plots. Pacific bluefin was in the "red" quadrant in the 2010s; aggressive cuts and juvenile-fish protection moved it into "yellow" and it is now approaching "green".
Post-hoc analysis of historical collapses: The 1992 Newfoundland Atlantic cod collapse (30,000 jobs lost), the 1972 Peruvian anchoveta collapse (2 million t → 20,000 t), the 1947 California sardine collapse and the Newfoundland capelin crash — when reanalysed with Schaefer / Fox models, all show the stock sitting in the orange-to-red quadrant for an extended period before the crash. These cases are now staple references in modern fisheries textbooks.
MSC (Marine Stewardship Council) sustainability audits: MSC certification for sustainable seafood requires B/B_MSY ≥ 0.8 and F/F_MSY ≤ 1.0 for the source fishery. The blue MSC label you see on a salmon fillet in the supermarket is, under the hood, evidence that a Schaefer-style assessment classified that fishery as sustainable.
Climate-driven dynamic MSY scenarios: When carrying capacity K shifts long-term with sea-surface temperature, a fixed MSY no longer applies and a "dynamic MSY" is needed. Drop K to 70% of the default in this tool and you will see MSY drop proportionally. North Sea cod and Bering Sea pollock — cold-water species shifting north — are case studies where this dynamic-MSY conversation is happening right now.
Common Misconceptions and Pitfalls
The biggest pitfall is reading "MSY" as a "target catch". MSY is a theoretical ceiling — fishing at it every year means that the first time estimation error in r/K and an environmental downturn line up, the stock collapses. FAO and the 1995 UN Fish Stocks Agreement bound TACs to 70-90% of MSY, with a Harvest Control Rule (HCR) that automatically cuts catch the moment B drops below B_MSY. That is why this tool defaults to "Precautionary 0.8 MSY". Read MSY as a hard ceiling, never as the goal.
Second, do not over-trust the deterministic, instantly-equilibrium picture of surplus production models. Real stocks are dominated by recruitment variability (CV often 30-100%), so for short-lived species like anchovy and sand-eel a season at half the "expected MSY" is normal. Adding a Beverton-Holt or Ricker stock-recruitment function, or moving up to a Statistical Catch-at-Age model that resolves age structure, is often necessary. Use this tool for the first feel; for production assessments, switch to dedicated software like Stock Synthesis (SS3).
Finally, do not watch F alone and ignore B. Sitting in the orange quadrant (B ≥ B_MSY, F > F_MSY) for a long time eventually pushes B below B_MSY and slides you into yellow then red. Conversely, the yellow quadrant (B < B_MSY, F ≤ F_MSY) is "rebuilding": keep catch suppressed and you return to green in a few years. Modern stock management means watching B and F together on the Kobe plot, and tracking the trajectory of the point, not just one axis at a time.
How to Use
Enter carrying capacity K (tonnes) for your stock—cod typically 500,000–800,000 t; bluefin tuna 50,000–120,000 t depending on region.
Input intrinsic growth rate r (per year): herring and anchovy range 0.4–0.6/y; cod 0.1–0.2/y due to slower maturation.
Set current biomass B and fishing mortality F (1/year) from the latest stock assessment survey data.
Simulator computes MSY in tonnes/year, optimal F_MSY, and B_MSY harvest level, then displays depletion ratio B/B_MSY and stock status (healthy/overfished/collapsed).
Worked Example
North Atlantic cod stock: K=750,000 t, r=0.15/y, current B=280,000 t, observed F=0.35/y. Simulator yields MSY≈28,125 t/y at F_MSY=0.075/y and B_MSY=375,000 t. Current B/B_MSY ratio is 0.75 (moderately depleted). Since F=0.35/y exceeds F_MSY by 367%, stock status flags "overfished"—reducing catch to 28,125 t/y at F=0.075/y allows recovery to B_MSY within 8–12 years under stable environmental conditions.
Practical Notes
K estimates from historical catch records or acoustic surveys; use 3–5 year average to smooth recruitment variance in small pelagics (anchovy, herring).
Growth rate r is highly temperature-dependent; update seasonally for stocks in warming zones (e.g., Northeast Atlantic stocks shifting poleward).
Compare F/F_MSY ratio: values >1.0 indicate overharvesting; rebuilding plans typically target F/F_MSY=0.75–0.9 as precautionary approach per ICES guidelines.
B/B_MSY below 0.5 requires immediate catch reduction; most regional fishery bodies (ICCAT, NAFO) mandate rebuilding plans when depletion exceeds 50%.