Harvesting Fish: Examining Population Models

In summary, the conversation includes a question about the long-term behavior of a fish population in a lake, using a logistic population model with a growth-rate parameter of k = 0.3 and a carrying capacity of N = 2500. The model is adjusted to account for different harvesting scenarios, such as harvesting 100 fish per year or one-third of the population annually. The correct differential equation is questioned and a possible typo is identified.
  • #1
GreenPrint
1,196
0

Homework Statement



I only need help with problem 16 but included problem 15 because it is referenced in problem 16.

16.
Suppose that the growth-rate parameter k = 0.3 and the carrrying capacity N = 2500 in the logistic population model of Excercise 15. Suppose p(0) = 2500.

(a) If 100 fish are harvested each year, what does the model predict for the long term behavior of the fish population? In other words, what does a qualitative analysis of the model yield?

(b) If one-thrid of the firs are harvested each year, what does th emodel predict for the long-term behavior of the fish population?

15.
Suppose a species of fish in a paricular lake has a population that is modeled by the logistic opulation model with growth rate k, carrying capacity N, and time t measured in years. Adjust th emodel to account for each of the following situations.

(a) 100 fish are harvested each year.

(b) One-third of the firsh population is harvested annually.

(c) The number of fish harvested each year is proportional to the square root fo the number of fish in the lake.

Homework Equations





The Attempt at a Solution



16.
(a)
I thought that this would be the correct differential equation
dP/dt = 3/10(1-P/2500)-100

but I guess this is wrong because I found this question and answer here on google search
http://www.math.uga.edu/~azoff/courses/2700notes.pdf [Broken]
and it claims that the correct equation is
dP/dt = 3/10(1-P/2500)-300

I'm not exactly sure as to why it's minus 300 and not minus 100
thanks for any help that anyone can provide.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2


I think that's a typo. It should be -100.
 

1. How do population models help in harvesting fish?

Population models use mathematical equations and data to estimate the size and growth of fish populations. This information can help scientists and fishery managers make informed decisions on sustainable harvesting practices.

2. What factors are considered when creating population models for fish?

Population models take into account factors such as reproduction rates, mortality rates, and environmental conditions that affect the growth and survival of fish populations. They also consider human activities, such as fishing, that may impact the population.

3. How does overfishing affect fish populations?

Overfishing occurs when the rate of fishing exceeds the rate at which fish can reproduce and replace themselves. This can lead to a decline in fish populations, negatively impacting the ecosystem and the fishing industry. Population models can help predict when a population is at risk of overfishing and inform management strategies to prevent it.

4. Can population models accurately predict fish population sizes?

Population models are based on scientific data and assumptions, so they can provide a good estimate of population size and growth. However, they are not 100% accurate and can be affected by changes in environmental conditions or unexpected events. It is important for scientists to continually update and refine these models to improve their accuracy.

5. How can population models be used to promote sustainable fishing practices?

Population models help scientists and fishery managers determine the maximum amount of fish that can be harvested while still maintaining a healthy population. By using these models, sustainable fishing practices can be implemented to ensure that fish populations are not overexploited and can continue to support the ecosystem and fishing industry in the long term.

Similar threads

  • Calculus and Beyond Homework Help
Replies
7
Views
5K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
Replies
8
Views
3K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
5
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
3K
  • Calculus and Beyond Homework Help
Replies
6
Views
2K
Replies
2
Views
3K
  • Calculus and Beyond Homework Help
Replies
4
Views
3K
Back
Top