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

A population subject to the Allee effect will decrease when population numbers are either very low (due to inability to find a mate) or very high (due to overcrowding), but will increase when population numbers are at intermediate levels (due to successful reproduction and not too much overcrowding). A model for a population subject to an Allee effect is given by

x_t+1= (4x²_t)/(3+x²_t), x_t is greater than and equal to 0

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

(a) Determine the equilibria.

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

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

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

Expert Solution

Pls, give thumbs up.

Colby Messinger answered 2 years ago

Show the effect on price (increase, decrease, no effect): Show the effect on price (increase, decrease,...

Show the effect on price (increase, decrease, no effect): Show the effect on price (increase, decrease, no effect) for each of the following situations under three form of market efficiency Situations Situations Weak Semi-Strong Strong The WSJ publishes that Landmark Inc. declared a dividend of $1 per share Landmark Inc. board members decide in a closed door meeting to open a new factory in Taiwan Your broker in NYSE tells you that Landmark Inc. CEO is going to declare retirement

When demand is very elastic then if price rise then the quantity demanded will decrease in...

When demand is very elastic then if price rise then the quantity demanded will decrease in a big amount. When supply is very inelastic then if the sellers' received amount fall due to tax then the quantity supplied will not decrease too much. Hence if demand is very elastic and supply is very inelastic then consumers will bear a small amount of whole tax burden where producers will bear a large amount of whole tax burden. Now, if demand is...

Many drivers operate vehicles either without insurance or with very low liability insurance limits. They often...

Many drivers operate vehicles either without insurance or with very low liability insurance limits. They often are in no position to pay for the damage they cause. Is this fair and should society take any action in this area?

When wage changes, the amount of hours worked can either increase or decrease depending on the...

When wage changes, the amount of hours worked can either increase or decrease depending on the relative strengths of the income and substitution effects. a) Define the income and substitution effects. b) Suppose you initially work 8 hours. Your wage increases and you decide to work 7 hours. Which effect dominates? c) State the range of values that the substitution effect could be in part (b) in terms of hours of leisure. In other words, what is the largest and...

Do retirees always get hurt more when interest is very low?

According to the Fisher effect, a decrease in _____ inflation causes an equal decrease in the...

According to the Fisher effect, a decrease in _____ inflation causes an equal decrease in the _____ interest rate. Question 3 options: expected, nominal expected, real unexpected, nominal unexpected, real Because most loans are specified in nominal terms, low _____ inflation hurts _____. Question 4 options: expected, debtors expected, creditors unexpected, debtors unexpected, creditors If the demand for real money balances depends on nominal interest rate, then lower inflation can Question 5 options: reduce the quantity of real money balances....

Discuss the substitution effect and the real-income effect of a price decrease.

when talking to another person either stand very close within a foot or else maintain a...

when talking to another person either stand very close within a foot or else maintain a distance of 3 feet. does your proximity affect the other person's conversation or other reactions to you? is there an ''ideal distance within which you are expected to approach a close friend? an acquaintance? or stranger? does violating the person's personal space of others disturb you? if so, why? you might precede this experiment by first establishing through observation the personal space or "buffer...

1. The multiplier effect magnifies the effect of a decrease in spending, resulting in a bigger...

1. The multiplier effect magnifies the effect of a decrease in spending, resulting in a bigger decrease in real GDP. True/False 2. What is the likely result from a depreciation of a nation's currency when its economy is already operating at its full-employment level of output? A. Net exports would fall, but equilibrium GDP would rise. B. Net exports would fall and contribute to demand-pull inflation. C. Net exports would rise and contribute to demand-pull inflation. D. Net exports would...

What are the possible consequences a salesperson might experience when using low-price tactics? Be very specific...

What are the possible consequences a salesperson might experience when using low-price tactics? Be very specific and give detailed examples.

Question