Lecture 17

Question 1

what is a population

Answer 1

collection of individuals living in an area
population size = N
N0 = initial population when t = 0

Question 2

population density

Answer 2

N/area
pop size - pop abundance

Question 3

why do we care about the population size

Answer 3

• natural resource management - how much food we have
• conservation
• heath - viruses, bacteria, understanding the risk
• predicting human population growth - is there enough resources

Question 4

what did Malthus say about human population growth

Answer 4

an essay on the principles of population
- The human population cannot grow faster than food production

Question 5

the population bomb book

Answer 5

saying that with explosive population growth, the human population will have catastrophic social and environmental consequences

Question 6

what is the goal of population models

Answer 6

to predict the population growth through time using equations
Nt = individuals in a population now
Nt+1 = f (Nt)

Question 7

what are time steps

Answer 7

t+1
using differential equations - makes time steps very small = smooth growth = continuous reproduction
using difference equations - makes time as discrete units like days, years - growth is stepwise and bump = episodic reproduction = discrete-time approaches

Question 8

birth and immigration rate

Answer 8

both are added to the population
- ignore immigration

Question 9

death and emigration

Answer 9

both are leaving the population
- they are equivalent so we can ignore emigration
the model = only birth and death rates = fixed constants

Question 10

what does green lambda mean

Answer 10

multiplicative factor by which population changes over one-time unit = finite rate of increase
lambda = Nt+1 / Nt
when Lambda > 1 = births exceed deaths = pop growth
when lambda < 1 = deaths exceed births = pop decline

Question 11

what is the geometric growth model

Answer 11

discrete-time, step function, days, years
Nt = N0 L^t
when L > 1

Question 12

what is the exponential function

Answer 12

instantaneous per capita rates of birth and death
b - d = r = constant = intrinsic rate of increase
Nt = N0 e ^rt
- smooth function

Question 13

what happens when lambda increases and decreases in a geometric growth model

Answer 13

1.5 = growing very fast
below 1
0.8 = very steep decline
at 1 = straight horizontal line

Question 14

what happens to the r when lambda increases in an exponential model

Answer 14

L = 1.5, r = 0.405 = increasing rapidly
L = below 1, r = negative value = rapidly decreasing

Question 15

T/F both geometric and exponential have the same outcome and can be simplified to just exponential because the L and the r are constants

Answer 15

true
- both constants
- grow to +/- infinity

Question 16

T/F species are able to sustain exponential growth and decline for long periods of time

Answer 16

false
- something has to limit population growth

Question 17

density dependant regulation

Answer 17

the GROWTH of a population depends on N - the individuals in a population
- stress, predation, disease from high number of individuals - crowded

Question 18

density-independent reduction

Answer 18

a DECREASE in the number of individuals in a population because of other factors that are not dependent on the density
- random events, natural disasters, reverse weather, human impact

Question 19

what is a logistic growth model

Answer 19

S-shaped curve (sigmoid) that will eventually slow down = running out of food or resources
- only s-shaped when the initial N0 is low, if it is not low it will not be S-shaped but it will still level off at K
dN/dt = rN(1/N/K)
first part = exponential = GO
second part = braking term = STOP
- makes pop density slow down when it is very close to the carrying capacity (1-1 = 0)

Question 20

carrying capacity

Answer 20

the inflection point of the curve = K/2 = max growth rate
- the HA limit of the graph where it can not go above = K value

Question 21

Pros of the logistic model

Answer 21

1. a good model for intraspecific competition for resources (individuals in the same species fighting over food, shelter)
2. simple
3. can be used to consider multispecies competition

Question 22

Cons for the logistic model

Answer 22

1. too simple - only shows density dependence regulation
2. gradual approach to the carrying capacity
3. K is used as a constant but it may fluctuate