cohort
group of same aged young that grow & survive at similar rates.
used to determine survival & mortality of individuals in a population
age class
consists of individuals of a particular age
life table
provides data on the number of individuals alive in different age classes & the age specific survival & mortality rates in these age classes
survivorship curve
graphical representation of the numbers of individuals alive in a population at various ages
2 types of life tables
cohort life table
static life table
cohort life table
follows a cohort of individuals from birth to death.
used to estimate the age specific probabilities of survival
static life table
data is gathered on the age structure of a given population at one point in time.
for long lived organisms, a snapshot approach is used.
age distribution
reflects survival & mortality patterns.
do not include males in calculating population growth
imbalance in age classes influences population's future: increasing has large number of young, decreasing has few young.
static life tables
provide snapshot of population's age structure from a sample at a given time
Static life table calculations
dx = (nx-1) - nx
nx = number alive at start of previous year
dx = number dying in a given age class or year
survivorship calculation
lx = nx / n0
lx = survivorship
nx = number surviving this year
n0 = number born
mortality rate calculation
qx = dx / nx
qx = mortality rate within each age class
dx = number dying this year
nx = number alive this year
Average number alive calculation
Lx = [nx + (nx+1)] / 2
Lx = average number alive in each age class
nx = number alive this year
(nx+1) = number alive next year
Total years lived calculation
Tx = sum of Lx (L1+L2+L3+.....Lx)
Tx = total years lived
Lx = average number alive in each age class
Life expectancy calculation
ex = Tx / nx
ex = life expectancy - average number of additional age classes an individual can expect to live at each age
Tx = total years lived
nx = number alive this year
limiting factors of static life tables
accuracy limited by assuming that equal numbers of offspring are born each year b/c there's no independent method for estimating birth rate of each age class
methodology difficulties = difficult to accurately assess age structure of population
constructing cohort life table
conduct population censuses frequently but for limited time
use log to express number of individuals
survivorship curve
graphical representation of numbers of individuals alive in a population at various ages.
plot the number of surviving, nx, from any given cohort of young (log scale) against age
determining population loss with log
express nx on log scale to examine rates of change with time not in absolute numbers.
shows difference between starting & ending population sizes
type I curve
rate of loss for juveniles relatively low
most lost later in live b/c older & prone to sickness & predators
few offspring but invest time & resources in raising young
ex:
large mammals
humans
type II curve
fairly uniform death rates over time
ex:
birds
small mammals
reptiles
some annual plants
type III curve
rate of loss for juveniles is relatively high
survivorship curve flattens out for organisms that have avoided early death
most juveniles die or are eaten; few reach favorable habitat & thrive
ex:
fish
marine invertebrates
accuracy in static vs cohort
cohort:
always more accurate b/c in natural world & environmental variation includes years of good & bad climate or food supply
do not have time & resources to follow populations of organisms from birth to death
static:
quicker & cheaper method to get rough idea of how the individuals of a population are distributed among age classes
age specific fertility rate
the proportion of female offspring that are born to females of reproductive age
age specific fertility rate calculation
mx = number of offspring/ number of females at age x
mx = age specific fertility rate
lxmx
represents the contribution of each age class to the overall population growth rate
average number of offspring per female
age specific fertility rate X average number alive in age class
net reproductive rate
overall growth rate per generation is the number of offspring born to all females of all ages
net reproductive rate calculation
R0 = sum of lxmx
R0 = net reproductive rate (overall growth rate)
lx = average number alive in age class
mx = age specific fertility rate
how to tell with Net reproductive rate if population is growing
R0 < 1, population is in decline
R0 = 1, population is at equilibrium
R0 > 1, population will grow
future size of population calculation
N(t+1) = NtR0
N(t+1) = net population size in next generation
Nt = number at generation t
R0 = net reproductive rate
Generation time calculation
T = sum of xlxmx / R0
x = age class
lx = average number alive in age class
mx = age specific fertility rate
R0 = net reproductive rate
generation time vs body size
generally, generation time increases as organismal size increases
Which of the following is true concerning static life tables?
they provide a snapshot a population's age structure at a specific point in time
why do survivorship curves typically express the number of individuals alive during each age class as log10nx, rather than simply nx?
because ecologists are more interested in rate of mortality, rather than the absolute number of survivors
which type of organism is most likely to exhibit a type III survivorship curve?
butterfly
age specific fertility rates are typically based only on females in the population because
it is easier to accurately assess their fecundity compared to males
which of the following is a characteristic of type II survivorship curves?
constant mortality across age classes
which of the following was found to affect the survivorship of fox populations in england?
hunting
which of the following represents the net reproductive rate (R0) of a population?
R0 = sum of lxmx
adolf murie found which of the following to be responsible for the relatively high mortality of both young and old age classes of all mountain sheep in alaska?
predation by wolves
which of the following is generally true regarding cohort life tables?
they are more accurate than static life tables
a population is said to be at its equilibrium size when which of the following is true?
R0 = 1
which of the following was not found by joe connell in his study of barnacle?
R0>1 for barnacle population
how much is a population of mice for which R0 = 1.15 growing?
15%
what is the yearly net reproductive rate for a pack of wolves if the pack contained 62 wolves last generation & consists of 51 individuals this generation?
0.823
dx
number of individuals dying during age class x
px
proportion of individuals surviving age class x
ex
average life expectancy of an individual alive at start of age class x
nx
number of individuals alive at start of age class x
lx
proportion of individuals surviving to the start of age class x
qx
proportion of individuals dying during age class x
Lx
average number of individuals alive during age class x
___ survivorship curves are usually associated with organisms that have high mortality rates in early stages of life
type III
if the net reproductive rate (R0) is equal to .5, what assumptions can we make about the population?
in decline
in population of beavers, in n2=500, n3=300 & n4=200, what is d3?
100
if nt = 100 & r0 = .5, what is n(t+1)?
50
type 1 survivorship cures include
large mammals