Lec 17 - Modeling Populations 2

Question 1

Ro

Answer 1

average number of daughters produced by female in lifetime (overlapping gen)

Question 2

Generation time (T)

Answer 2

average age at which female gives birth to her offspring or average time from mother to daughter

Question 3

per capita rate of increase (r)

Answer 3

birth rate - death rate (b-d)
- measure of pop growth
- calculated from Ro and T

Question 4

r < 0

Answer 4

b < d
declining
(neg)

Question 5

r = 0

Answer 5

b = d
stable

Question 6

r > 0

Answer 6

b > d
increasing

Question 7

population growth

Answer 7

• increase in number of individuals within a population over time
• studying population growth can help to understand factor associated with pop increase/decrease
• helps us to make predictions about population in future

Question 8

geometric and exponential

Answer 8

unlimited environment (overabundant resources, density independent)

Question 9

logistic

Answer 9

limited environment (depleted resources, density dependence)

Question 10

growth rate

Answer 10

rate of pop growth (“steepness” of curve)
dN/dt = change on # of individuals per time

Question 11

population size

Answer 11

population size at t

Question 12

geometric rate of increase (lambda)

Answer 12

ratio of population size at 2 points in time
- growth increases by constant proportion where repro pulsed and generation are non-overlapping (discrete)

Question 13

geometric population growth

Answer 13

size of population growing at t modeled as : Nt = No x lambda^t
- J shaped curve
- increases by constant ratio

Question 14

exponential population growth

Answer 14

each successive generation differs in size based on constant times population size at moment in time
- non-pulsed repro and overlapping generations
- J-shaped

Question 15

rate of population growth for exponential

Answer 15

dN/dt = rN
Nt = Noe^rt

Question 16

do geometric and exponential growth happen?

Answer 16

yes but for short period of time when resources are abundant
- both unrealistic over long periods, per capita death rates will increase as densities increases, birth rates will decrease as resources decrease

Question 17

Scots pine

Answer 17

exponential growth is rare
- growth occurring naturally
- grew as the glaciers of last ice age retreated in Britain and new habitat was available to be occupied
- studied pollen content in sediment cores
- scientist can recontsruct pollen accumulation rates (proxy for pop size)
- could expand without much competition (abundant resources after ice age)

Question 18

exponential population growth in phytoplankton Daphnia and algae

Answer 18

spring: after snowmelt, high amounts of resources available
both algae and Daphnia grow exponentially
populations crash in summer, resources are limited
fall: lake turnover brings up nutrients from bottom to surface

Question 19

why doesn’t exponential growth continue indefinitely?

Answer 19

resources aren’t unlimited

Question 20

logistic population growth

Answer 20

if resources become limited, population growth rate will slow down and eventually stop

Question 21

carrying capacity (K)

Answer 21

population size at whoch growth stops
- generally number of individuals of a species that local environment can support
- usually reaches when per capita: b + i = d + e

Question 22

why does K exist?

Answer 22

all resources are limited so environments can only support so many individuals of a given species

Question 23

“idealized” logistic population curve

Answer 23

initially population will show exponential growth first but will slow down and eventually will stop growing and stabilizing at a population size (= carrying capacity)

Question 24

model for log growth

Answer 24

dn/dT = r(max) N [K-N/K] or dn/dT = r(max)N[1- (N/K)]

Question 25

what happens when N is small

Answer 25

the second term is closer to one so N/K is small
- growth characterized most by r(max)N

Question 26

what happens when N increases

Answer 26

second term will be close to 0
growth will be slowed
N = K
dN/dT = 0

Question 27

logistic growth (humans)

Answer 27

pop is increasing but growth is slowing down due to lower female fertility