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K/2

Constant Quota fishing at levels approaching the MSY shortens the biomass range the population will recover, and the likelihood of entering the danger zone increases. Once the danger zone is entered fishing must stop or be severely curtailed. Danger zone. Stable biomass range. Catch rate. B.

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K/2

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  1. Constant Quota fishing at levels approaching the MSY shortens the biomass range the population will recover, and the likelihood of entering the danger zone increases. Once the danger zone is entered fishing must stop or be severely curtailed Danger zone Stable biomass range Catch rate B K/2 K Maximum Sustainable Yield (MSY)

  2. What would happen to a population at K/2 subjected to a harvest rate of C B K/2 K is called the Maximum Sustainable Yield (MSY)

  3. The logistic model * C B K/2 K

  4. An operational example A lake that hasn’t been fished for 20 yr is opened for fishing and annual creel surveys show that CPUE is declining rapidly CPUE Kg/hr • The estimated total catch varies from year to year but the trend rapidly becomes apparent and the lake is closed • After a 9-yr moratorium the population has gradually bounced back, and the fishery is opened again with more restrictive limits Catch Kg/yr • After signs of tapering off limits are tightened even further. Year

  5. How can such a population be managed with the logistic model? We don’t know B, K or r0 We can assume that CPUE is a linear function of Biomass (eg B=q*CPUE Where q is called the “catchability” factor We can also assume that the population is at K to start with CPUE Kg/hr Catch Kg/yr Year

  6. The catch (C) in the first year was 1020 kg, at the rate of 1.0 kg/fisherman hr. • The following year the CPUE went down to 0.9 kg/fisherman hr. • Assuming that the population was at its K, and that the CPUE reflects the biomass linearly, B=q *CPUE, then dB/dt at K will be 0, and the entire catch will be subtracted from the biomass present. • That is we assume that there will be no significant recruitment or growth response to compensate for thinning within the first season • The response to the first year’s thinning will be reflected in the next year’s catch data • assume the change in CPUE reflects the change in B, • (D CPUE)/CPUE = (D B)/B, 0.1/1=1000/K. Therefore K =10,000 kg • And CPUE =q B, that is 1.0 kg/hr =q * 10,000 kg, • so q =1kg/hr/10000 kg = 0.0001kg/hr/kg • The next year the catch rises to 1050 kg, and the CPUE falls to 0.83 kg/hr. This catch appears to be unsustainable at this B level, but how much would have been sustainable?

  7. The next year the catch rises to 1050 kg, and the CPUE falls to 0.83 kg/hr. • This catch appears to be unsustainable at this B level, but how much would have been sustainable? • Using the catchability estimate q we can translate the drop in CPUE and estimate that the biomass dropped from 9000 to 8300 kg (a drop of 700), and reason that if a catch of 1050 caused a drop of 700, then a catch of 350 would have been sustainable at that level of biomass. • We can then repeat this for every year, including the years where the fishery is closed • CPUE can still be estimated from catch and release fishing if the fishery is closed. • In this way each year’s catch combined with the change that takes place in CPUE the following year can allow you to estimate the sustainable catch for that year

  8. Actual catches in kg/yr Estimates of sustainable catch By comparing the catch for each year to the change in biomass (estimated from change in CPUE) we can estimate the catch that would have been sustainable each year For the first 10 yr catches were unsustainably high and the population crashed, After the new limits were put in they tended to oscillate around the estimated catch. Catch Kg/yr CPUE Kg/hr

  9. Fit to the logistic curve from the lake time series dB/dt MSY (r0K)/4=990 K/2 = 5000 Biomass If (r0K)/4 = 990 kg/yr and K=10000 kg, then r0=0.39 kg*kg-1yr-1

  10. Suppose we have a lake with a population of 10,000 kg of pike where fishing has not been allowed for at least 20 years. Fishing is then opened up for several years and the population is knocked back to 5,000 kg. Assume that growth follows the logistic curve. (a) What would the biomass be after 10 yr if r0 were 0.2 kg/kg/yr (b) If after closure it recovers to 9,800 kg in 10 years. Find r0?

  11. (c) What should be the maximum sustainable yield of this fishery? (d) If the population were reduced to 2,000 kg, would a catch of 500 kg/yr be sustainable?, 1000kg?

  12. Constant Quota fishing at levels approaching the MSY shortens the biomass range the population will recover, and the likelihood of entering the danger zone increases. Once the danger zone is entered fishing must stop or be severely curtailed Danger zone Stable biomass range Catch rate B K/2 K Maximum Sustainable Yield (MSY)

  13. The red zone is much bigger if the curve is strongly skewed right

  14. Solutions that are being considered by fish managers

  15. What if we consider a fishery based on constant effort rather than constant quota The catch isn’t as great but the likelihood of entering the red zone is lower Catch = qB Slope=q Stable range C B K/2 K

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