8.14. (10/16) Population Dynamics & Growth Flashcards
What is birth rate?
- 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
What do we need to know to track birth rates?
- number of individuals (females) per age class
- average number of births per individual
what is a fecundity schedule?
summary of the number of individuals (females) being born at different age classes through time
What does a life table do?
how many individuals are surviving to each age class
What can we find out with fecundity schedules and life tables?
estimates like how fast this population is growing
What is the net reproductive rate?
avg number of offspring produced per individual in the population
*R0
What is the geometric rate of increase?
the estimated rate at which a population with pulsed reproduction is increasing
*λ
What is pulsed reproduction?
- no overlapping generations
- individuals are born, reproduce, and die
What is generation time?
average time it takes for an individual to move from one birth to the next
*T
what is per capita rate of increase?
- birth rate minus death rate
- the best way to express how quickly a population is growing or declining
*important for rate of growth
*r
What information is in a life table?
age, number of surving to day x, proportion surviving to day x (lx survivorship)
What information is in a fecundity table?
average number of seeds per individual during time interval (mx fecundity), lxmx
How do we calculate net reproductive rate?
the sum of the proportion of individuals surviving to each age class multiplied by average number of seeds produced
*R0=Σlxmx
What does the calculation for net reproductive rate mean?
each individual leaves an average of __ offspring
How do we calculate the total number of seeds produced by the population cohort?
- population multiplied by the average number of seeds produced per individual
- seeds produced by the end of a year
- R0*N1
How do we calculate geometric rate of increase?
- 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
When might λ=R0?
the geometric rate of increase is equal to the net reproductive rate when organisms have pulsed reproduction (like annual plants)
What do we need to calculate net reproductive rate (R0)?
- fraction of females reproducing during each time interval
- average clutch size
- number of reproductive events per time interval
What does clutch size mean?
number of offspring produced by an average female per reproductive event
What is the trend for a stable population?
R0=1
each female is producing on average one other female
What is the trend for a declining population?
R0<1
What is the trend for an increasing population?
R0>1
How do we calculate generation time?
the sum of the years times survivorship times fecundity divided by the net reproductive rate
* τ=(Σxlxmx)/R0
How do we calculate per capita rate of increase?
r= ln(R0)/T
What does natural log do?
gives us the amount of time needed to reach a certain level of growth
What does r=0 mean?
stable population
What does r<0 mean?
declining population
What does r>0 mean?
growing population
When would we have positive growth?
birth or immigration
When would we have negative growth?
death or emigration
When do we have a stable population?
births + immigration = deaths + emigration
What is a discontinuous model?
geometric population growth model for populations with non-overlapping generations and no limits to growth
*bamboo, cicadas, salmon, annual plants, insects, spiders
How do we calculate the size of a population that grows geometrically for any given time interval?
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
What is exponential population growth?
- for populations with overlapping generations
- no limits to growth
- continuous model
- smooth curve
What is the exponential model?
dN/dt= rN
- dN/dt: change in numbers with changes in time
r: per capita rate of increase
N: population size
In the exponential growth model what happens as N increases?
the rate of population change increases
How do we calculate the size at any given time (t) for a population growing at an exponential rate
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
What does e^x do?
gives you the amount of continuous growth that you would have after a certain amount of time
What did Malthus do?
described the logistic growth model
What is carrying capacity?
the number of individuals in our population that an environment at some time can support
*K
What is an s-shaped curve?
growth appears exponential at first, but the rate of increase slows and levels off after some time
What factors cause populations to slow their growth rates and eventually stop at their carrying capacity?
- yeast –> alcohol waste
- barnacles –> available space
- paramecium –> food resources
*determined by a complex interplay of factors
What is the equation for logistic growth?
dN/dt= rmaxN(1-N/K)
What does (1-N/K) do in the logistic growth equation?
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
What is maximum per capita rate of increase?
- 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?
What is another way to write the logistic model in terms of r and rmax?
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
What is happening to r and rmax when a population size is small?
the realized is equal to the maximum
What is happening to the r and rmax when population size increases?
realized decreases until the population size equals the carrying capacity
* r=0 (no growth)
what is the relationship between realized and population size in a logistic model?
r decreases as N increases
What happens to r if N<K?
r is positive and the population grows
What happens to r if N=K?
r=0 and population growth stops
What happens to r if N>K?
r is negative and the population declines
How are organism size and rmax correlated?
- inversely
- the intrinsic rate of increase declines with increasing size
What are the two factors that limit population growth?
density dependent and independent factors
What are density-dependent factors?
- product of increasing number of individuals
- food
- predation
- available space
- nest sites
- parasitism
- disease*
- biotic factors
*could be density-independent
What are density-independent factors?
- affects on growth rate that have nothing to do with the number of individuals on the landscape
- drought/flood
- storms
- fire
- abiotic factors
