For my class, I was given a hypothetical situation that uses the concept of Maximum Sustainable Yield to see how much fish I should harvest. I am given an initial population, a growth rate, and a carrying capacity.

Then with these given values, I was supposed to use this information to calculate for next year's population which I easily did with the logistic growth formula. I got a population of 368 (which is obviously rounded to a whole number). From what I know, with this initial population of 368 that I calculated, it would a bit over the one-half capacity but not over the carrying capacity of the environment that was given to me.

At this point, I don't know how to apply the Maximum Sustainable Yield concept here. I am not sure on how much I should harvest this year if the current fish population is 368. I don't want to harvest all 368 fish because that would mean that I wiped out the entire population for this year, correct? So would it make sense if I harvested half this number while still have enough fish for next year?

I tried to look at this graph I found as a reference but I'm not too sure how to apply it:


If I am made a misstep in my process, please do share. Thank you!

  • I flagged the flag as off-topic because it is a mathematical homework question. Equally, the homework question "Albert earns 600 EUR per week and get's an annual bonus of 2000 EUR. Bart earns 2760 EUR per month. Who earns more per year?" does not fit to Economics.SE although it is about payment. – daniel.heydebreck Feb 12 '18 at 8:36
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    @daniel.neumann Personally I think it's on topic because the OP seems to be struggling with MSY concept and we can help with that. I do agree that the exact outcome has less relevance here. – THelper Feb 12 '18 at 13:26
  • @THelper: Thank you (for your answer below)! I think I understand how much I should harvest now since I do have the necessary values (K) to figure out how much there would be at K/2. From here, I believe I know the approximate number of fish to harvest without going below one-half capacity. – DistributionUnit Feb 12 '18 at 18:38

Since this is a homework question I will help you, but not give away the answer (which I cannot do anyway, because you didn't include the necessary information for that).

You are correct that you only want to harvest part of the population. Harvesting all fish will indeed wipe out the population and harvesting most of the fish will slow down population growth.

Quote from Wikipedia: "the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely"

The graph you added to your post already shows where the maximum growth point is; (Carrying Capacity / 2) because that's where the curve is the steepest. The population size at that point should be fairly easy to calculate. Note that I'm assuming here that the growth curve of the fish follows a similar pattern as the graph you found.

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