Unit 4 Lecture 19

Question 1

Explain the study with the black footed ferrets

Answer 1

• Black footed ferrets are located in Wyoming and primarily ate prairie dogs (pest species to farmers)
• Because of this prairie dogs declined, but as they started to decline, this caused the black footed ferrets to decline (nearly went extinct)

Question 2

What do population ecologists do?

Answer 2

They want to be able to describe this dynamic of population growth (i.e. formulate a model) and predict what will happen to the population in the future

Question 3

How do you find the rate of population growth between two years?

Answer 3

Take Nt+1/t

Question 4

How do you find the annual population growth rate?

Answer 4

Nt+1 (population size at the next year) / Nt (population at size t) = lambda

Question 5

How do you solve for the population size at a time next year?

Answer 5

Nt+1 = 𝜆𝑁𝑡

Question 6

When a population grows with a constant 𝜆 for multiple step what equation do you use?

Answer 6

Nt = N0𝜆^t
n0: initial population size
nt: population size at time t

Question 7

If 𝜆>1 why would the graph be curved linear and not linear?

Answer 7

Because our initial population size is low, even with a high rate of increase, our population size is going to grow slowly until it reaches a certain point then it’ll grow rapidly

Question 8

If lambda ‘𝜆’ is constant, then we get a _____ population growth

Answer 8

Geometric: initially growing slowly, but as population size grows is speeds up
- Use this when we measure in discrete time steps

Question 9

What is the main difference between exponential growth and geometric growth?

Answer 9

In exponential growth, we are no longer talking about time in discrete time intervals

Question 10

1. Nt = N0 λt
2. Nt+1 = λNt

When do we use each of these

Answer 10

1. Use the top one when finding the population size at time t+1
2. When a constant 𝜆 in multiple steps use this to find population at time t

Question 11

Geometric and exponential growth happens when?

Answer 11

When we have a constant population growth rate

Question 12

Explain exponential population growth?

Answer 12

Is the same as geometric growth, but for case where reproduction occurs continuously

dN/dt = rN
- dN/dt: Change in N over change in time
- r: exponential growth rate

Question 13

During what specific times should you use geometric population growth?

Answer 13

When we have organisms that have a very defined breeding time during the year; you can also have organisms that’ll d their reproduction then die

You should use geometric population growth for these scenarios because breeding happens during a very discrete time/time steps

Question 14

Give an example of when we use exponential growth in organisms

Answer 14

Humans; we are fertile once a month and at different times

Question 15

Whats another equation do we use for exponential growth?

Answer 15

Nt = N0e^rt

Question 16

Show the connection between the geometric growth equation and the exponential growth equation
1. Nt = N0 λ^t
2. Nt = N0 e^rt

Answer 16

1. λ = e^r
2. r = ln(λ)

Question 17

The defining feature of geometric/exponential population growth is what?

Answer 17

Population growth rate is constant across time
- when the population grows whether geometric or exponential growth rate (λ or r) is constant

Question 18

When does dN/dt increases when?

Answer 18

There’s a larger population size

Question 19

When population growth rate is constant its a _______ on a log scale

Answer 19

straight line; because geometric/exponential growth is multiplicative

Question 20

What is population regulation?

Answer 20

There is a limit to population growth, this idea is population regulation

Question 21

What are density-independent factors?

Answer 21

Effects on birth and death rates are independent of the number of individuals in the population like:
- Drought
- Extreme weather
- Flood
- Pollution

Question 22

Give an example of density-independence in a study with thrips

Answer 22

Guys in Australia went out into their rose garden and counted the number of thrips on their roses for several years. They then looked to see what factor correlated with the number of thrips per year
- The main reason for population size to be fluctuating was due to weather changes across years

Question 23

What are density-dependent factors?

Answer 23

Birth, death, and dispersal rates change as the density of the population changes
- most often there is a negative density dependence (deaths increase when population is crowded)

Question 24

As density of a population increases, birth rates _____ and death rates ______ and emigration _______

Answer 24

1. decrease
2. increase
3. increase

Question 25

What factors might cause a negative density dependence?

Answer 25

Disease and Fewer resources per capita
- things that cause negative density dependence are things that CHANGE as a function of the population size
- As population size increases, this could cause diseases to spread easier

Question 26

Explain the study with the sparrow

Answer 26

There was a graph of the number of independent young per female as a function of number of breeding females recorded over a bunch of years
- In long sparrows, the number of eggs laid per female decreased with density, as did the number of young that survived
- Limited food supply at high density

Question 26

Explain the study with the owl/bird

Answer 26

There was a graph of the number of independent young per female as a function of number of breeding females recorded over a bunch of years
- In long sparrows, the number of eggs laid per female decreased with density, as did the number of young that survived
- Limited food supply at high density

Question 27

What is density dependent mortality?

Answer 27

When density-dependence can reduce birth rate AND death rate

Question 28

What is carrying capacity (K)?

Answer 28

Maximum population size that can be supported indefinitely by the environment

Question 29

Under logistic growth what happens?

Answer 29

Population increases rapidly looking like geometric or exponential growth but then stabilizes
- What we are plotting for is the number of individuals under a function of time

Question 30

Carrying capacity can be determine by the amount of what?

Answer 30

Resource

Question 31

Carrying capacity is where birth rate is:
1. > death rate
2. < death rate
3. = death rate

Answer 31

3.

Question 32

Carrying capacity is where per-capita growth rate is ___ or when R passes the _____

Answer 32

1. 0
2. x axis

Question 33

What is the logistic equation?

Answer 33

dN/dt = rmax N(1-n/k)

Question 34

As Logistic growth –> growth rate

Answer 34

1. Declines through time
2. Declines linearly with population size N

Question 35

When N is small relative to K N«K then…

Answer 35

N/K = 0 or 1-N/K = 1
So dN/dt = rN

Question 36

When N is close to K (N=K)

Answer 36

dN/dt = 0
N/K = 1
1- N/K = 0

Question 37

Overall population growth rate (dN/dt) is the ________

Answer 37

Slope of the tangent line

Question 38

K is where dN/dt = what

Answer 38

0