Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. advance math
  3. a population subject to the allee effect will decr

A population subject to the Allee effect will decrease when population numbers are either very low...

50.1K

Verified Solution

Question

Advance Math

A population subject to the Allee effect will decreasewhen population numbers are either very low (due to inability tofind a mate) or very high (due to overcrowding), but will increasewhen population numbers are at intermediate levels (due tosuccessful reproduction and not too much overcrowding). A model fora population subject to an Allee effect is given by

xt+1=(4x2t)/(3+x2t),xt is greater than and equal to 0

where ?t is the population number in year t (measuredin hundreds of individuals.

(a) Determine the equilibria.

(b) Use the Stability Criterion to classify the equilibria asasymptotically stable or unstable.

(c) Use cobwebbing to illustrate the dynamics of the differenceequation for ?0=0.5, ?0=0.5,?0=1.5 and ?0=4(it is OK to plot all three onthe same diagram).

(d) Explain the significance of all equilibria and theirstability in terms of the population size in the long run.

Answer & Explanation Solved by verified expert
3.6 Ratings (481 Votes)
Pls    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Mechanical Engineering
1.2K views

A small quantity of n-octane is placed in a wide test tube at 20 degrees C...

Physics
1.2K views

A plane mirror 50 cm long is hung on a vertical wall of a room...

Basic Math
1.2K views

Consider the function f x log z a Graph the function Tool help First click...

Calculus
1.2K views

x 1 What is the first derivative of g x ln 1 Select the correct...

Algebra
1.2K views

Name the rational numbers from the list below 1 3 10 0 74 1 04...

Accounting
1.2K views

Accounting
1.2K views

After thinking about all the interest paid over a 30-year span, you begin considering a...

Accounting
1.2K views

Pearl Products Limited of Shenzhen, China, manufactures and distributes toys throughout Southeast Asia. Three cubic...

Accounting
1.2K views

Exercise 11-30 (Algo) Impairment; property, plant, and equipment [LO11-8] General Optic Corporation operates a manufacturing...

Accounting
1.2K views

Please analyze at least 8Profitability ratios of TET in 2013 and make conclusions. Add step...

Accounting
1.2K views

nswer question no 2 only, Answer within 1 hours 30 mint , i will give...

Finance
1.2K views

The risk-free rate of return is equal to the real rate plus the inflation premium....