(1) Which of set of predator-prey equations listed below is the correct set?
(a) Nt+1 = (1.0 +Bzt)Nt + CNtPt &Pt+1 = QNtPt
(b) Nt+1 = (1.0 +Bzt)Nt - CNtPt &Pt+1 = QNtPt
(c) Nt+1 = (1.0 -Bzt)Nt + CNtPt &Pt+1 = QNtPt
(d) Nt+1 = (1.0 -Bzt)Nt - CNtPt &Pt+1 = QNtPt
You chose "(a) Nt+1 = (1.0 +Bzt)Nt + CNtPt &Pt+1 = QNtPt".
No. Let’s look at what the prey equation is saying. The terms within the () function as a density dependent control of population growth (intraspecific competition). We want the value within the () to be closer to 1.0 the closer we get to K, and remember that zt = Nt - K. So, as the population size increases zt gets closer to zero but it does so from below, that is with negative numbers. B is the slope of the density dependent change in net reproductive rate, so it has to be negative. If it were positive as it is in (a) it means the population growth rate continues to increase with population density, an unstable situation correct? So putting the two of these together it would mean that when the population is below carrying capacity the term Bzt would be negative so the population would actually be decreasing when the population size is below K.
Click here to return to question 1.
You chose "(b) Nt+1 = (1.0 +Bzt)Nt - CNtPt &Pt+1 = QNtPt".
No. Let’s look at what the prey equation is saying. The terms within the () function as a density dependent control of population growth (intraspecific competition). We want the value within the () to be closer to 1.0 the closer we get to K, and remember that zt = Nt - K. So, as the population size increases zt gets closer to zero but it does so from below, that is with negative numbers. B is the slope of the density dependent change in net reproductive rate, so it has to be negative. If it were positive as it is in (b) it means the population growth rate continues to increase with population density, an unstable situation correct? So putting the two of these together it would mean that when the population is below carrying capacity the term Bzt would be negative so the population would actually be decreasing when the population size is below K.
Click here to return to question 1.
You chose "(c) Nt+1 = (1.0 -Bzt)Nt + CNtPt &Pt+1 = QNtPt".
No. The terms CNtPt relate to how many prey each predator takes out. This number needs to be subtracted from the prey population size, not added to it.
Click here to return to question 1.
You chose "(d) Nt+1 = (1.0 -Bzt)Nt - CNtPt &Pt+1 = QNtPt".
Yes! Let’s take a look at why. First we look at what the prey equation is saying. The terms within the () function as a density dependent control of population growth (intraspecific competition). We want the value within the () to be closer to 1.0 the closer we get to K, and remember that zt = Nt - K. So, as the population size increases zt gets closer to zero but it does so from below, that is with negative numbers. B is the slope of the density dependent change in net reproductive rate, so it has to be negative. If it were positive it means the population growth rate continues to increase with population density, an unstable situation correct? So if B were not negative it would mean that when the population is below carrying capacity the term Bzt would be negative so the population would actually be decreasing when the population size is below K.
Click here to go to question 2.
(3) In the figure above, what factor(s) are limiting the predator population?
(a) Intraspecific competition for things other than prey
(c) Intraspecific competition for prey
You answered "(a) Intraspecific competition for things other than prey".
No. In this graph the predator zero growth isocline is vertical. When this is the case it means that the only thing limiting the predator population size is the prey population size. If the number of prey is limiting the number of predators it must be because the predators are competing for the prey.
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Question 3
You answered "(b) Interspecific competition". No. Remember interspecific competition occurs between two different species competing for the same resource. In this
graph it only shows one prey species and one predator species thus it gives you no indication of the strength of interspecific
competition.
You answered "(c) Intraspecific competition for prey".
Yes! In this graph the predator zero growth isocline is vertical. When this is the case it means that the only thing limiting the predator population size is the prey population size. If the number of prey is limiting the number of predators it must be because the predators are competing for the prey.
Click here to go to question 4.
(5) In which of the these graphs would the equilibrium prey density change if the zero growth isocline changed?
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You said the equilibrium prey population size would change in this graph,
No, in this graph it doesn’t matter what the zero growth isocline looks like for the prey, the equilibrium value for the prey will be the same. This is because the predator population size depends only on the prey size, thus when the zero growth isocline changes shape it changes how many predators there are but it won’t change how many prey there are at equilibrium. When the zero growth isocline rises it just means that there will be more predators so they will keep the prey population at the same level.
Click here to return to question 4.
Question 4
You said the equilibrium prey population size would change in this graph, Yes. In this graph the predators are experiencing ratio dependent predation. That is they are predating at a constant rate
depending on the current population size. As the prey increase the predators eat more of them, but only so that they remove a
constant percentage, thus the prey population size will change as well as the predators population size. However, this is not
the only correct answer.
You said the equilibrium prey population size would change in this graph,
Yes. In this graph the prey equilibrium population size will change if their zero growth isocline changes, providing the left side of the curve moves. However, the predator equilibrium population size will not change in this case. It may eventually change if the prey zero growth isocline shifts far enough left so that it intersects with the vertical part of the curve, but other wise it will remain constant. This is because the predator population size is being limited by something other than the prey population size. For example, it might be limited by the number of territories open. However, this is not the only correct answer. Make sure you see which others are also correct.
Click here to return to question 4. Click here to go to question 5.
(5) What would happen between these two species (1 and 2) if they sympatric (i.e. coexistence or would one species win out in competition)?
K1 = 10,000 b = 0.33
K2 = 5,000 a = 0.75
(d) It’s an unstable equilibrium and so we can’t tell who will win
You answered "(a) Species 1 will win".
No. Remember for only species 1 to win it must limit its own population size by intraspecific competition more than it is limited by interspecific competition of species 2. We use the inequalities we talked about in class to determine if species 1 will win. The conditions for species 1 to win would be,
K1 > aK2
b
K1 > K2If we do the math we see that both of these are not true.
10,000 > (0.75)5,000
10,000 > 3,750 True so we know species 1 will survive with species 2 around because species 1 is limiting its own population more than it is being limited by interspecific competition from species 2.
(0.33)10,000 > 5,000
3,300 > 5,000 False, so species 2 will not lose in competition to species 1 because species 2 is not being more limited by interspecific competition from species 1.
Click here to return to question 5.
If we do the math we see that both of these are not true.
5,000 > (0.33)10,000
5,000 > 3,300 True so we know species 2 will survive with species 2 around because species 2 is limiting its own population more than it is being limited by interspecific competition from species 1.
(0.75)5,000 > 10,000
3,750 > 10,000 False, so species 1 will not lose in competition to species 2 because species 1 is not being more limited by interspecific competition from species 2.
Click here to return to question 5.
You answered "(c) Coexistence".
Yes! Remember the conditions for coexistence are,
K1 > aK2
K2 > bK1
We can see that this is true by putting the values in.
10,000 > (0.75)500
10,000 > 3,750 True so we know species 1 will survive with species 2 around because species 1 is limiting its own population more than it is being limited by interspecific competition from species 2.
and
5,000 > (0.33)10,000
5,000 > 3,300 True so we know species 2 will survive with species 2 around because species 2 is limiting its own population more than it is being limited by interspecific competition from species 1.
Since both species are more limited by intraspecific competition than interspecific competition coexistence will occur.
Click here to go to question 6.
You answered "(d) It’s an unstable equilibrium and so we can’t tell who will win".
No. Let’s look at the inequalities for Lotka-Volterra competition and see why.
For it to be an unstable equilibrium both species have to be more limited by interspecific competition than by intraspecific competition. For that to be true both of the following inequalities would have to be true,
a
K2 > K1b
K1 > K2If we put the numbers in we can see that this is not true.
(0.75)5,000 > 10,000
3,750 > 10,000 False, so species 1 will not lose in competition to species 2 because species 1 is not being more limited by interspecific competition from species 2.
and
(0.33)10,000 > 5,000
3,300 > 5,000 False, so species 2 will not lose in competition to species 1 because species 2 is not being more limited by interspecific competition from species 1.
Click here to return to question 5.
(7) Click on the graph which represents a type II function response.
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You clicked on this graph.
No. This is a type I functional response. A type I functional response occurs when predators consume increase the consumption of their prey at a constant ratio with its abundance in the environment. The plateau occurs when handling time prevents them from eating any faster.
Click here to return to question 7.
Question 7
You clicked on this graph. No. This is a type II functional response. A type II functional response occurs when predators consume increase the
consumption of their prey but the rate at which they increase consumption is slower than the rate at which the prey population
is increasing. The plateau occurs when handling time prevents them from eating any faster.
You clicked on this graph.
Yes. This is a type III functional response. A type I functional response occurs when predators initially consume prey at a rate below their frequency in the environment but quickly start to increase their rate of consumption above the rate of increase of the prey. At the inflection point the predators while still increasing their feeding on the prey do so at a slower rate than at which the prey are increasing. The plateau occurs when handling time prevents them from eating any faster.
Congratulations you have finished the predatition tutorial.