Topic 14 -Exponential Growth

Question 1

Life tables can be used to determine if

Answer 1

a population grows from one generation to the next

Question 2

Population growth models

Answer 2

are used to estimate population size over many generations in the future

Question 3

N(later) equals

Answer 3

N (now) +births - deaths

Question 4

Geometric model

Answer 4

assumes discrete breeding

population only grows during the breeding season

Question 5

lambda

Answer 5

average number of offspring left by an individual during one time interval (same as Ro)

if lamba 1=lamba 2 and so on….

population increases by lambda ^t

Question 6

examples of species that use the geometric model

Answer 6

plants, salmon, birds

anything with a specific breeding season

Question 7

Exponential Model

Answer 7

assumes continuous breeding

population grows continuously throughout the year

Question 8

what is r in an exponential growth model

Answer 8

the exponential growth rate of the population between time 0 and time t (not the same as Ro)

Question 9

how does population increase in an exponential model

Answer 9

population increases by a factor of e^r

Question 10

the rate of change in population size over a specific time period (deltaN/deltaT which is approx dN/dt) is equal to the

Answer 10

average birth rate (b) minus the average death rate (d) multiplied by the number of individuals in the population (N) at the start of the time period t0

Question 11

dN/dt

Answer 11

slope of population growth curve (deltaN/deltat) at a particular point in time

Question 12

r equals

Answer 12

b-d

Question 13

dN/dt equals

Answer 13

(b-d)N which equals rN

Question 14

Intrinsic Rate of increase

Answer 14

r is considered to be an instantaneous rate of increase

Question 15

3 underlying principles for intrinsic rate on increase

Answer 15

1) r is the individual or “per capita” contribution to population growth
r equals average birth rate (b) minus average death rate (d)

2) dN/dt varies in direct proportion to N at that instant
3) r is consistant through time

Question 16

curves depicting geometric and exponential relations can be super imposed, there is a direct relationship between lamba and r which is

Answer 16

Increase: r=+ lambda >1
Constant: r=0 lambda =1
decrease: r= - lambda <1

Question 17

Exponential Model Assumptions (5)

Answer 17

All individuals have the same average b and d rates

b and d are constant through time

b and d occur continuously (not discrete)

No migration (I or E) the population is closed

Resources are unlimited

Question 18

typically observed pattern of growth when population size is low

Answer 18

no competition (resources are unlimited)

population grows at the intrinsic rate of increase, r (exponential growth= highest growth potential)

Question 19

typically observed pattern of growth when population size is high

Answer 19

competition increases (resources become limited)

population size levels off and r=0

Question 20

Violation for all individuals have the same average b and d rates

Answer 20

different age classes generally have different b and d rates (life table)

Question 21

violation for b and d are constant through time

Answer 21

populations rarely have constant b and d because

age distribution of a population changes through time

environmental conditions change through time continuously and influence b and d and r(=b-d)

consider r the highest growth rate that a population has potential to achieve if the population has a stable age distribution and b and d remain constant over time

Question 22

violation of no migration

Answer 22

populations are rarely closed except in lab

Question 23

violation of resources are unlimited

Answer 23

resources are usually limited

Question 24

Human Population growth

Answer 24

a large population with low growth rate can still greatly increase by size

dN/dt =rN

1600-rapid growth 
1800-1 billion 
1930-2billion 
1975-4billion
2000-7billion
2050-10billion