Lecture 5: Population ecology

Question 1

What is population density?

Answer 1

individuals per unit area.

Question 2

Why does N matter?

Answer 2

1) Natural resource management.

(Size of fish stock, or abundance of outbreaking insect pests)

2) Conservation: Population decline of species

3) Health: Monitoring population of virus in humans

4) Understanding and predicting human growth.

Question 3

What is time-series?

Answer 3

It is a type of data plotted, in which the X-axis represents the time and Y-axis has the population size, N

Question 4

Why did the number of bats (Myotis lucifugus) decrease in 2006?

Answer 4

-Due to WNS: white-nose syndrome which is a fungal disease.

Question 5

How was HIV plotted?

Answer 5

The x-axis has time in weeks and years

The y-axis has the count of CD4+ lymphocytes. (Which has the viruses)

The larger the count of CD4+, the more the person is sick.

Question 6

What happens to CD4+ cells as the HIV virus increase?

Answer 6

CD4+ cells decreases.

Question 7

What did Paul Ehrlich say or do?

Answer 7

Wrote the book ‘population bomb’

Said that explosive population growth would have catastrophic social and environmental effects

Question 8

What is depopulation?

Answer 8

Rapid fall in the population size.

Question 9

What is the goal of population models?

Answer 9

To model N against time T, N is a function of time T.

Question 10

What is N subscript t?

Answer 10

The number of individuals in a population at time T

Question 11

What is N subscript t+1

Answer 11

It is the number of individuals as time advances one step.

Question 12

What is the general model for population?

Answer 12

N subscript (t+1) = f(N subscript t)

where f is a function, and N is the number of individuals at time T.

Question 13

What is a challenge in coming up with function in predicting future population?

Answer 13

coming up with f, in simple but accurate parameters, which should show a relationship between current and future population.

Question 14

When do you use differential equations in population modeling?

Answer 14

If you are modeling population growth, calculus is the best approach because the data is changing continuously, and the growth is smooth and time steps are incredible small.

it is also called continuous-time approach.

Question 15

What is difference equation? When do you use it?

Answer 15

It is a simple math equation used when the population changes episodically, and time steps are discrete units ( months, years)

It is also called a discrete-time approach

N1 = lambda* N(0)
N2 = N(o) * lambda^t

Question 16

What is the equation for simple house keeping for population?

Answer 16

N(t+1) = N(T) - D + B - E + I
But just model birth and death

D: # of death in a population
B: # popualtion born
E: # Emmigration
I: # Immigration

But mostly ignore Emmigration and assume it to be equal to death

Assume Immigration and Birth to be equivalent

Question 17

What is treated as per-capita rates?

Answer 17

The birth and death rates are treated as fixed constants, and birth rate is the likely hood of a specie reproducing in that time frame, and death rate is the likeyhood of that specie dying in that time frame.

Question 18

If population changes by a constant rate, write the formula for population changes.

Answer 18

N( t+1) = lambda*(N(t))

Where lambda is the rate at which the population changes over one unit of time or it is ‘finite rate of change’

Question 19

According to geometric growth, how do you know if a population is growing or shrinking?

Answer 19

If lambda > 1: Growth is more than death hence the population grows (step function with growth)

if lambda < 1 : Death rate is more than birth rate, hence the population is shrinking.

Question 20

What was r in continuous population model? or differential equations?

Answer 20

Birthrate-deathrate = r

r is the intrinsic rate of increase
if r > 0 : smooth function with exponential growth.

Question 21

What is the differential equation?

Answer 21

It is exponential.

dN/dt = rN

where N(t) = N(o) e^rt

Question 22

What does graphing geometric function show?

Answer 22

X: axis: time
Y-axis: z, which is the number of individuals

if lambda = 1: population is neither growing nor decreasing

if lambda < 1: population is decreasing

if lambda < 1: population is increasing

Question 23

What does graphing exponential function for population show?

Answer 23

X: axis: time
Y-axis: z, which is the number of individuals

if ln(lambda) = 0: population is neither growing nor decreasing

if ln(lambda) < 0: population is decreasing

if ln(lambda) < 0: population is increasing

Question 24

What is common in geometric growth and exponential growth?

Answer 24

Both have a constant, lambda or r

and if both are positive it means that they keep growing exponentially.

Question 25

What happens in bad, good conditions to species?

Answer 25

good: species grow, birth exceeds death (lambda > 1)

bad: species shrink, death exceeds birth (lambda < 1)

but it can never be equal, because nothing can ever go to infinity, population cannot grow infinitely.

Question 26

Why can’t lambda > 1 or < 1 over a long period of time?

Answer 26

No species can grow exponentially, cause population is limited by something.

No extant specie can shrink exponentially, because it should have gone extinct. (if a specie is not extinct, it means that it has not had lambda <1 in a long time)

Question 27

What is density-dependent regulation?

Answer 27

-If there are less species or individual, the population will grow faster (similar to what Maltus said) because the resources are available more if individuals are few.

Question 28

What is density-independent reduction?

Answer 28

-Reduction of species due to storm etc is not dependent on the density of a population.

Question 29

What is logistic growth?

Answer 29

s- shaped model: initially population growth exponentially, but then slows down bc it runs out of food.

It is density dependent.

Question 30

What is the equation for logistic growth?

Answer 30

dN/dt = rN ( 1 - N/K)

Where dN/dt = rN is the ‘go’ term, it makes populations grow.

and the rest is the stop term.

Question 31

What is ‘K’ in logistic growth?

Answer 31

K: Called the carrying capacity of the population.

constant, it is the size of resources the environment can support.

Question 32

How does the S-shape reflect what N is?

Answer 32

if N in the logistic growth is almost K, the eqauation becomes

dN/dt = rN (1-1) == 0

Then there will no longer be any growth.

There is no breaking of the population if N is small, but if N approaches K then there is complete breaking.

Question 33

What sort of curve does this produce:

N(t) =( KN(o)e^rt)
———————–
K + N( e^rt - 1)

Answer 33

It produces the sigmoid graph

The s-shape curve: Initially (when the population size is small) the population grows very large, then starts to level off as the population gets large and then becomes constant, when N reaches K

Question 34

When does inflection point occur in the sigmoid graph?

Answer 34

at K/2: population starts to slow down.

Question 35

When is s-shaped graph not applicable?

Answer 35

When the population modelled starts off from value closer to K

Question 36

What happens to the sigmoid graph if N(o) > K?

Answer 36

It declines and becomes constant at K

Question 37

Where is the maximum growth (at which point) in the sigmoid graph?

Answer 37

At the inflection point (K/2)
as it is the highest slope for the growth of the population.

Question 38

What are pros and cons for logistic model?

Answer 38

pros:
1) Simple (only K is added)
2) Mathematical eqn for INTRAspecific competition (shows how population competes for food)
3) Can be expanded to consider multi-specie competition.

Cons:
1) too simple (only one density dependence is shown)

2) Always gradual approach to carrying capacity

3) In reality K might be overshot, it is usually non-linear

NONE of the graphs look like s in reality.

Question 39

When is the population growing the fastest?

Answer 39

When the population is small