Topic 14 -Exponential Growth Flashcards
Life tables can be used to determine if
a population grows from one generation to the next
Population growth models
are used to estimate population size over many generations in the future
N(later) equals
N (now) +births - deaths
Geometric model
assumes discrete breeding
population only grows during the breeding season
lambda
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
examples of species that use the geometric model
plants, salmon, birds
anything with a specific breeding season
Exponential Model
assumes continuous breeding
population grows continuously throughout the year
what is r in an exponential growth model
the exponential growth rate of the population between time 0 and time t (not the same as Ro)
how does population increase in an exponential model
population increases by a factor of e^r
the rate of change in population size over a specific time period (deltaN/deltaT which is approx dN/dt) is equal to the
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
dN/dt
slope of population growth curve (deltaN/deltat) at a particular point in time
r equals
b-d
dN/dt equals
(b-d)N which equals rN
Intrinsic Rate of increase
r is considered to be an instantaneous rate of increase
3 underlying principles for intrinsic rate on increase
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
curves depicting geometric and exponential relations can be super imposed, there is a direct relationship between lamba and r which is
Increase: r=+ lambda >1
Constant: r=0 lambda =1
decrease: r= - lambda <1
Exponential Model Assumptions (5)
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
typically observed pattern of growth when population size is low
no competition (resources are unlimited)
population grows at the intrinsic rate of increase, r (exponential growth= highest growth potential)
typically observed pattern of growth when population size is high
competition increases (resources become limited)
population size levels off and r=0
Violation for all individuals have the same average b and d rates
different age classes generally have different b and d rates (life table)
violation for b and d are constant through time
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
violation of no migration
populations are rarely closed except in lab
violation of resources are unlimited
resources are usually limited
Human Population growth
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
