8.14. (10/16) Population Dynamics & Growth

Question 1

What is birth rate?

Answer 1

• the number of young born per female (individual) per unit of time
• refers to the addition of new individuals to a population
• number of individuals being born

Question 2

What do we need to know to track birth rates?

Answer 2

• number of individuals (females) per age class
• average number of births per individual

Question 3

what is a fecundity schedule?

Answer 3

summary of the number of individuals (females) being born at different age classes through time

Question 4

What does a life table do?

Answer 4

how many individuals are surviving to each age class

Question 5

What can we find out with fecundity schedules and life tables?

Answer 5

estimates like how fast this population is growing

Question 6

What is the net reproductive rate?

Answer 6

avg number of offspring produced per individual in the population
*R0

Question 7

What is the geometric rate of increase?

Answer 7

the estimated rate at which a population with pulsed reproduction is increasing
*λ

Question 8

What is pulsed reproduction?

Answer 8

• no overlapping generations
• individuals are born, reproduce, and die

Question 9

What is generation time?

Answer 9

average time it takes for an individual to move from one birth to the next
*T

Question 10

what is per capita rate of increase?

Answer 10

• birth rate minus death rate
• the best way to express how quickly a population is growing or declining
  *important for rate of growth
  *r

Question 11

What information is in a life table?

Answer 11

age, number of surving to day x, proportion surviving to day x (lx survivorship)

Question 12

What information is in a fecundity table?

Answer 12

average number of seeds per individual during time interval (mx fecundity), lxmx

Question 13

How do we calculate net reproductive rate?

Answer 13

the sum of the proportion of individuals surviving to each age class multiplied by average number of seeds produced
*R0=Σlxmx

Question 14

What does the calculation for net reproductive rate mean?

Answer 14

each individual leaves an average of __ offspring

Question 15

How do we calculate the total number of seeds produced by the population cohort?

Answer 15

• population multiplied by the average number of seeds produced per individual
• seeds produced by the end of a year
• R0*N1

Question 16

How do we calculate geometric rate of increase?

Answer 16

• comparing the population size at two points in time
• ratio of population at some future time divided by size of population at some earlier time
• slope
• Nt+1 future time
• Nt earlier time
  *λ=Nt+1/ Nt

Question 17

When might λ=R0?

Answer 17

the geometric rate of increase is equal to the net reproductive rate when organisms have pulsed reproduction (like annual plants)

Question 18

What do we need to calculate net reproductive rate (R0)?

Answer 18

• fraction of females reproducing during each time interval
• average clutch size
• number of reproductive events per time interval

Question 19

What does clutch size mean?

Answer 19

number of offspring produced by an average female per reproductive event

Question 20

What is the trend for a stable population?

Answer 20

R0=1
each female is producing on average one other female

Question 21

What is the trend for a declining population?

Answer 21

R0<1

Question 22

What is the trend for an increasing population?

Answer 22

R0>1

Question 23

How do we calculate generation time?

Answer 23

the sum of the years times survivorship times fecundity divided by the net reproductive rate
* τ=(Σxlxmx)/R0

Question 24

How do we calculate per capita rate of increase?

Answer 24

r= ln(R0)/T

Question 25

What does natural log do?

Answer 25

gives us the amount of time needed to reach a certain level of growth

Question 26

What does r=0 mean?

Answer 26

stable population

Question 27

What does r<0 mean?

Answer 27

declining population

Question 28

What does r>0 mean?

Answer 28

growing population

Question 29

When would we have positive growth?

Answer 29

birth or immigration

Question 30

When would we have negative growth?

Answer 30

death or emigration

Question 31

When do we have a stable population?

Answer 31

births + immigration = deaths + emigration

Question 32

What is a discontinuous model?

Answer 32

geometric population growth model for populations with non-overlapping generations and no limits to growth *bamboo, cicadas, salmon, annual plants, insects, spiders

Question 33

How do we calculate the size of a population that grows geometrically for any given time interval?

Answer 33

Nt= N0λ^t - Nt: number in population at some time t - N0: number in population at some initial time - λ: average number of offspring left by an individual during a time interval (geometric rate of increase) t: number of time intervals

Question 34

What is exponential population growth?

Answer 34

- for populations with overlapping generations - no limits to growth - continuous model - smooth curve

Question 35

What is the exponential model?

Answer 35

dN/dt= rN - dN/dt: change in numbers with changes in time r: per capita rate of increase N: population size

Question 36

In the exponential growth model what happens as N increases?

Answer 36

the rate of population change increases

Question 37

How do we calculate the size at any given time (t) for a population growing at an exponential rate

Answer 37

Nt=N0e^rt Nt: number of individuals at time t N0: initial number of individuals e: base of the natural logarithms (constant 2.72) rt: per capita rate of increase*number of time intervals

Question 38

What does e^x do?

Answer 38

gives you the amount of continuous growth that you would have after a certain amount of time

Question 39

What did Malthus do?

Answer 39

described the logistic growth model

Question 40

What is carrying capacity?

Answer 40

the number of individuals in our population that an environment at some time can support *K

Question 41

What is an s-shaped curve?

Answer 41

growth appears exponential at first, but the rate of increase slows and levels off after some time

Question 42

What factors cause populations to slow their growth rates and eventually stop at their carrying capacity?

Answer 42

- yeast --> alcohol waste - barnacles --> available space - paramecium --> food resources *determined by a complex interplay of factors

Question 43

What is the equation for logistic growth?

Answer 43

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

Question 44

What does (1-N/K) do in the logistic growth equation?

Answer 44

as the population approaches the carrying capacity the growth slows down * as soon as population equals carrying capacity it'll go to one giving you a zero value that means there is no more growth

Question 45

What is maximum per capita rate of increase?

Answer 45

- rmax - occurs at very low population sizes - birth rate, death rate, and age structure are *constant* - under ideal conditions - intrinsic rate of increase - if everything was perfect for a species how high would their r value be?

Question 46

What is another way to write the logistic model in terms of r and rmax?

Answer 46

r= rmax- rmax(N/K) r: realized per capita rate of increase *r is being modified by how close the population size is to K

Question 47

What is happening to r and rmax when a population size is small?

Answer 47

the realized is equal to the maximum

Question 48

What is happening to the r and rmax when population size increases?

Answer 48

realized decreases until the population size equals the carrying capacity * r=0 (no growth)

Question 49

what is the relationship between realized and population size in a logistic model?

Answer 49

r decreases as N increases

Question 50

What happens to r if N

Answer 50

r is positive and the population grows

Question 51

What happens to r if N=K?

Answer 51

r=0 and population growth stops

Question 52

What happens to r if N>K?

Answer 52

r is negative and the population declines

Question 53

How are organism size and rmax correlated?

Answer 53

- inversely - the intrinsic rate of increase declines with increasing size

Question 54

What are the two factors that limit population growth?

Answer 54

density dependent and independent factors

Question 55

What are density-dependent factors?

Answer 55

- product of increasing number of individuals - food - predation - available space - nest sites - parasitism - disease* - biotic factors *could be density-independent

Question 56

What are density-independent factors?

Answer 56

- affects on growth rate that have nothing to do with the number of individuals on the landscape - drought/flood - storms - fire - abiotic factors