Lec 17 - Modeling Populations 2 Flashcards
Ro
average number of daughters produced by female in lifetime (overlapping gen)
Generation time (T)
average age at which female gives birth to her offspring or average time from mother to daughter
per capita rate of increase (r)
birth rate - death rate (b-d)
- measure of pop growth
- calculated from Ro and T
r < 0
b < d
declining
(neg)
r = 0
b = d
stable
r > 0
b > d
increasing
population growth
- 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
geometric and exponential
unlimited environment (overabundant resources, density independent)
logistic
limited environment (depleted resources, density dependence)
growth rate
rate of pop growth (“steepness” of curve)
dN/dt = change on # of individuals per time
population size
population size at t
geometric rate of increase (lambda)
ratio of population size at 2 points in time
- growth increases by constant proportion where repro pulsed and generation are non-overlapping (discrete)
geometric population growth
size of population growing at t modeled as : Nt = No x lambda^t
- J shaped curve
- increases by constant ratio
exponential population growth
each successive generation differs in size based on constant times population size at moment in time
- non-pulsed repro and overlapping generations
- J-shaped
rate of population growth for exponential
dN/dt = rN
Nt = Noe^rt
do geometric and exponential growth happen?
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
Scots pine
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)
exponential population growth in phytoplankton Daphnia and algae
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
why doesn’t exponential growth continue indefinitely?
resources aren’t unlimited
logistic population growth
if resources become limited, population growth rate will slow down and eventually stop
carrying capacity (K)
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
why does K exist?
all resources are limited so environments can only support so many individuals of a given species
“idealized” logistic population curve
initially population will show exponential growth first but will slow down and eventually will stop growing and stabilizing at a population size (= carrying capacity)
model for log growth
dn/dT = r(max) N [K-N/K] or dn/dT = r(max)N[1- (N/K)]
what happens when N is small
the second term is closer to one so N/K is small
- growth characterized most by r(max)N
what happens when N increases
second term will be close to 0
growth will be slowed
N = K
dN/dT = 0
logistic growth (humans)
pop is increasing but growth is slowing down due to lower female fertility
