How to use Maximum Sustainable Yield concept with given a given population, growth rate and carrying capacity? [closed]

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: MSY GRAPH HERE

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

• Unfortunately your question isn't really in line with the topics typically considered to be the core of earth science, which is centered more around the physical processes of the earth than biological subjects. Sustainable Living SE may cover some of that area. Or your best bet is to get involved in the Agiculture SE proposal, which would be great to see take off. – JeopardyTempest Feb 10 '18 at 4:29
• Also could maybe try Gardening and Landscaping? If you wish to move it to one of those sites, flag the question for moderator attention and indicate where you would like it moved. Otherwise it may well end up closed or lacking good answers here :-( – JeopardyTempest Feb 10 '18 at 4:30
• Okay! Thank you so much for pointing me in other directions! – DistributionUnit Feb 11 '18 at 0:02
• Population dynamics research is done by a lot of earth scientist and physicists. Also the questions seems to fit better into biology.SE on the first look, it is actually and mathematical question. Therefore, I am in favor of not closing the question because of it being off-topic (complicated sentence ...). However, the Wikipedia article on the maximum sustainable yield has an example on logistic growth, which answers this question nicely. – daniel.heydebreck Feb 11 '18 at 11:14
• @DistributionUnit : You can obtain the maximum sustainable yield if you harvest when the growth rate is highest. In the case of the logistic growth, it happens when half of the carrying capacity is reached. You harvest as much as would be produced. In your case: you calculate how much would be produced within one year starting from 275 (kg biomiass???). This is your maximum sustainable yield. – daniel.heydebreck Feb 11 '18 at 11:17