Age and stage structured population growth -7 Flashcards
Bx
age specific birth rates (average number of live births per female in age class x)
mx
age specific FEMALE birth rates (average number of live female births per female in age class x)
Why does Bx=2mx
because assume sex ratio of 50:50 at birth
R0
net reproductive rate
measure of whether a population is reproducing at a greater or lesser rate than needed for its replacement
sum of lxmx
R0 is related to ____
the multiplication rate (lambda) per generation
When R0 =1…
the population just replaces itself but does not grow or shrink
When R0 <1…
the population shrinks
When R0>1…
the population grows (exponentially while R0 is constant)
rc
capacity for increase, simply way of calculating the growth rate
rc = ln(R0)/Tc
Tc
cohort generation time, is the average age at which a female gives birth to her female offspring
sum of xlxmx/sum of lxmx
rm
intrinsic rate of natural increase
populations grow at a rate of rm once they have reached a stable age distribution
(dont need to know how to calculate)
most consider ____ to be an approximation of ___
rc
rm
Explain how maple trees can be an example of how stages can be more important for reproduction than age
maple trees start from seeds and germinate in forest floor under a canopy of other maple trees. They are shade tolerant and remain short until by chance a gap arises and they can grow big. So size is not tightly correlated with age because of the gap dynamics, therefore looking at stage is more beneficial
Define Leslie matrix `
a generic transition matrix
discrete, age structured model of population growth
fertility coefficients of the age class on the top
and probabilities of surviving each age
p in transition matrix
probability of surviving from one age class to the next
px = lx+1/lx
F in transition matrix
the average fertility of an age class
Fx = mx+1/px or Fx = mxp0
Why are there two equations for F
post-birth pulse sampling (birth then census)
and pre-birth pulse sampling (census then birth)
In a grid, where are Fx values and Px located
Fx (fertility) top row
Px is diagonal
The transition matrix applied 200 times quickly leads to…
a stable population distribution among age classes with the population growing exponentially
Define population pyramids
way of visualizing age structure within a population at a certain point in time (used to compare populations and infer population history and underlying processes)
Describe the 4 types of population pyramids
Stage 1 Expanding = high birth rate, rapid fall due to high death rate and short life expectancy (squeezed triangle)
Stage 2 Expanding = high birth rate, fall in death rate, slightly longer life expectancy (triangle)
Stage 3 Stationary = declining birth rate, low birth rate, more people living to old age
Stage 4 Contracting = low birth rate, low death rate, longer life expectancy
