Life tables Flashcards
populations have a spacial structure which includes:
- their range
- spatial arrangement of individuals within and among the range
- density
- patterns of movement among individuals
Populations also have genetic variation
among individuals throughout the population
… or represented in
subpopulations
Another component of populations is
associated with age structure
and the
rates at which births and deaths occur
within a population
who invented life tables and why
the Insurance and Health Care Industry to monitor mortality and survivorship in human populations
When was the first life table developed
in 1921 by Pearl and Parker
In order to construct a life table in the first place,
one must have some knowledge of the
age structure within a population
the first column of the life table is
x
x usually represents
age (could be in days, weeks, years, hours, etc.)
individuals that make up x are referred to as a
cohort
two inherent weaknesses in life tables
- only age is considered when allocating individuals to classes (not size, social status, and genotype)
- life tables almost always include only females for species having distinct males and females. This is because one of the key parameters in a life table is the rate of production
the male’s contribution to sexual reproduction
difficult to measure in terms of the numbers of young produced
how is birth accounted for in life tables
by counting the number of female offspring produced per breeding season or age interval per female in the population (fecundity)
Life tables
tables that contain class-specific survival and fecundity data
x
age class
nx
the number of individuals in each age class immediately after the population has produced offspring
sx
the survival rate from one age class to the next age class
bx
the fecundity of each age class
what is the fecundity of each age class denoted by
bx (b for birth)
what does the column bx indicate
new offspring cannot reproduce, but 1-year-olds can each produce one offspring, 2-year-olds can each produce three offspring, and 3-year-olds can each produce two offspring
Number surviving to next age class
(nx) x (sx)
Number of new offspring produced
(nx) x (sx) x (bx)
if we do these calculations for every age class…
we can find the number of individuals that we will have after one time interval
the number of individuals in a population after one time interval divided by the initial number of individuals provides…
lambda
A POPULATION WITH A FIXED LIFE TABLE
ASSUMES A STABLE AGE DISTRIBUTION AND
GROWS
at a constant rate
When age-specific birth bx and survival, sx, rates remain
unchanged for a sufficient length of time, a population
will assume
a stable age distribution
Under such conditions, each age class in the population grows or declines at the same rate; and so, therefore, does the
total size of the population
lambda
the growth rate of the population
Under stable age distribution conditions, each age class grows at the
same rate from year to year
Stable age distribution
when the age structure of a population doesn’t change over time
when does a stable age distribution occur
when survival and fecundity of each age class stays constant over time
survivorship
the probability of surviving from birth to any later age class (lx); survivorship in the first age class is always set at 1
survivorship to the second year (l2) is calculated as
l1s1
net reproductive rate (R0)
the total number of female offspring that we expect an average female to produce over the course of her life
R0 =
Sigmalxbx
lx is the number at the beginning of a particular age class divided by
the number at the beginning of the cohort
Generation time (T)
the average time between the birth of an individual and the birth of its offspring
T =
Sigma X x X lx X bx / Sigma X lx X bx
When λ or r is estimated from a life table, it is assumed that the life table has
a stable age distribution
Age distributions fluctuate due to environmental conditions, so any approximation of λ or r is restricted to
the environmental conditions that the population experiences at the time of measurement
To calculate an approximate (denoted as a) λ
λa =
R0^(1/T)
to calculate an approximate r
ra = logeR0 / T
populations grow when
R0 > 1
populations decline when
R0 < 1
Net reproductive rate (R0)
the total number of
female offspring that we expect an average female to
produce over the course of her life
Generation time (T)
the average time between the birth
of an individual and the birth of its offspring.
We can provide close approximations, denoted as λa and ra (where the letter “a”
indicates an approximation), based on our estimates of net reproductive rate (R0 )
and generation time (T):
λa = R0^(1/T)
Kinds of Life Tables
- cohort/dynamic life tables
2. static/time-specific life table
Cohort life table
a life table that follows a group of individuals born at the same time from birth to the death of the last individual
Cohort life tables are readily applied to
sessile organisms that can be tracked over the course of their life
Environmental changes can affect survival and fecundity of a cohort
it is difficult to separate the effects of age and the environment
Rosemary and Peter Grant
1978 marked 210 cactus finch fledglings and followed them for 15 years
The cohort life table does not work well for
species that
are highly mobile or for species with very long life spans,
such as trees
One of the problems in using a cohort life
table is that
a change in the environment during one year
can affect survival and fecundity of the cohort that year.
This makes it difficult to disentangle the effects of age from
the effects of changing environmental conditions
Static life table
a life table that quantifies the survival and fecundity of all individuals in a population during a single time interval
age is not confounded with
time
Static life tables can be applied to
highly mobile organisms, and species with long life spans
Life tables may not be representative of years with different environmental conditions
tables for multiple years should be constructed
A life table may also be constructed from the
distribution of the ages at death in a population
For example, one could obtain the age of death for
each person in a local cemetery by examining the
headstones. Using the total number of occupants of
the cemetery, we could determine the number of
individuals surviving at the beginning of each age
interval, and from that, survivorship
Some biases though (life table)
For example, it assumes that an
equal number of newborns forms the basis for each
age class. This assumption is violated in expanding
and declining populations in which younger and older
age classes, respectively, are over-represented.
Sea turtle populations have declined by more than
99% over the past several centuries
Once life tables were created, population modelers realized that
few hatchlings survive in nature anyway, so protecting eggs would not benefit the population
Instead, life tables indicated that
improving the survivorship of adult turtles would grow the population
what has been proven to be a tremendous success in conserving the sea turtles
turtle excluder devices on fish trawling nets
