3.
Mortality
In a given population,
mortality can be defined as the rate of organism’s deaths.
Mortality is majorly
categorized into two types:
a.
Minimum
mortality
Under
idealistic condition, the death rate is termed as Minimum or Theoretical
mortality. It’s a constant component of population statistical factors. Under
ideal conditions also organism dies because of natural process of senescence or
ageing.
b.
Realized
mortality
Under
realistic or non idealistic conditions, the rate of death is defined as
Realized or ecological mortality. It varies with the prevailing conditions of
population and environment, eg. epidemic, predation etc.
Mortality
generally expressed as death rate at a given time difference is the number of
deaths divided by average population. For instance at the beginning of the time
400 people constitute the population size but at the end of time period only
350 people are alive, means total 50 are dead. Thus, the average size of
population is 400+350/2= 375 and the death rate will be 50/375=0.133
Death rate=Dead people/
Average population
To
calculate the probability of people dying divided the “dead people” at a given
time with the alive people present at the beginning of time intervals. For
example by assuming above data, probability of dying= 500/400=0.125. Probability
of dying is complementary to probability of surviving given by = 350/400=0.875
i.e. people alive at a given time divided by population size at the beginning
of time interval. Here, we do not consider average population size as in case
of calculated death rate.
Life Expectancy
An
average number of years a member of a given age is expected to live in future
in a population define Life expectancy.
In
1921, under laboratory conditions, Raymond Pearl was the first who introduced
and used life table for Drosophila population.
Life
stable is a set of records of mortality and survival at a given time intervals
in a population. It gives a systematic order to population characteristics
recorded overtime varying with size, developmental stages and with age.
Ecologist found the applicability of life table in natural population for
understanding the cause and pattern of mortality and predicting the possibility
of survival and future growth of population. A life table describes an age
specific mortality aspects of people and represented in a form of subsequent
columns.
“Cohort” is group of people born at the
same time. It’s the life expectancy and reproductive rate on which the increase
or decrease in population size depend on. Reproductive rate specially depends
on the female age at which she starts producing young one and also possible age
of female to which she can reproduce in future.
Applications of life
tables
1. The
rate of premium by life insurance companies was determined by using life tables
to determine the possibility of client survivorship.
2. Life
tables are used to predict wildlife population growth decline and management.
3. Conservation
biologists use life tables in species conservation.
4. Comparing
the life history trends within and between populations.
Three types of life stable
are there:
1.
Cohort/
Horizontal/Dynamic life tables
Use
of this life tables is for short lived species and short generation time. This
table records the survival and reproduction of cohort of individuals from birth
to death. Cohort is group of individuals born and hatched together during a
defined time interval. Dynamic/ Cohort life tables start with 1000 initial
members of cohort and they are followed till the population is exhausted.
Cohort
can be defined on daily, weekly, monthly or annual basis such as Ursus americanus, all black bear cubs
born in Ozarks in 2014. The cohort life table record two important aspects (A)
fecundity schedules and (B) survivorship schedules.
2.
Static/
Vertical/Time specific life tables
Static
life table is based on assumption that the population is stable and the
Natality and mortality fecundity rate etc characteristic of population are
constant too. It measure all the individuals each age and reproduction in a
population and ages at death. In short, all living members of each age counted
at a given time.
3.
Dynamic
composite life tables
In
1986, Begon and Mortimur define this form of life table. It is similar to
cohort life table but here the members of cohort are counted on annual basis rather
than birth timings. It’s a time specific technique allowing natural variability
in survival rates.
Life
tables whether static or cohort if classified the members on age basis are
termed as age based life tables.
Representation of age is by “x” and age specific life expectancy as “ex” for each age. Life
tables classifying the members on the basis of size and developmental stages
are termed as size-based life tables
and stage based life tables
respectively.
To determine ecological
life tables, the following type of data have been used:
1.
Laboratory
animals
Laboratory
animals are used to prepare life tables as their specific stages are known to
us. We observe the number of animals/members at regular intervals and record
their death arte till the population dies off.
2.
Direct
observation of Survivorship
In
1961, Connell constructed life table of Chthamalus
stellatus growing on rocks in autumn season in Scotland. He observed and
recorded the mortality at regular intervals. Hence, survival data of cohort at
regular intervals were followed till its existence.
3.
Direct
observation of Age structure
By
observing several physiological features of individual, the age structure
information can be observed. For example observation of the annular rings on
fish scales, horns of sheep, growth rings in trees etc. Although, this type of
data is not preferred for table construction yet some age structure ecological
information can be collected.
Table
1: Different columns of life table are:
S. no
|
Abbreviation
|
Meaning
|
1
|
x
|
Age
interval
|
2
|
nx
|
Number
of survivors at start of age interval x
|
3
|
lx
|
Proportion
of organisms surviving to start age interval x
|
4
|
dx
|
Number
dying during age interval x to x+1
|
5
|
qx
|
Rate
of mortality during age interval x to x+1
|
6
|
Lx
|
Average
number of live individuals during age interval x to x+1
|
7
|
Tx
|
Total
years lived by individuals of age x
|
8
|
ex
|
Life
expectancy for individuals alive at age x
|
Table
2: Life table of Baranus glandula (Barnacle)
on pile points at the upper shore levels, San Juan Island, Washington (Connell
1970).
Age (yr)
(x)
|
Observed No. Barnacles Alive Each Year
(nx)
|
Proportion Surviving at start of age interval
x
(lx)
|
No. dying within age interval x to x+1
(dx)
|
Range of mortality
(qx)
|
Average Live individuals within age
interval x to x+1
(Lx)
|
Total years lived by individual of
age x (Tx)
|
Mean expectation of further life for
animals alive at start of age x (Tx/lx=ex)
|
0
|
1000000
|
1
|
999938.0
|
0.9999
|
0.500031
|
0.500153
|
0.5002
|
1
|
62
|
0.00006
|
28.0
|
0.4516
|
0.000048
|
0.000122
|
1.9613
|
2
|
34
|
0.00003
|
14.0
|
0.4118
|
0.000027
|
0.000074
|
2.1647
|
3
|
20
|
0.00002
|
4.9
|
0.2450
|
0.000018
|
0.000047
|
2.3300
|
4
|
15.1
|
0.00002
|
4.1
|
0.2715
|
0.000013
|
0.000029
|
1.9238
|
5
|
11
|
0.00001
|
4.5
|
0.4091
|
0.000009
|
0.000016
|
1.4545
|
6
|
6.5
|
0.00001
|
4.5
|
0.6923
|
0.000004
|
0.000007
|
1.1154
|
7
|
2
|
0.00000
|
0.0
|
0.0000
|
0.000002
|
0.000003
|
1.5000
|
8
|
2
|
0.00000
|
2.0
|
1.0000
|
0.000001
|
0.000001
|
0.5000
|
9
|
0
|
0.00000
|
0
|
0.0000
|
0.0000
|
0.0000
|
0.0000
|
Calculations
Life
expectancy is calculated in following steps.
Step 1: We first calculate (lx)
as:
(i)
For the first age group its always 1.
For example for the age (x)=0, and nx
=1,000,000 the (lx)=1.
(ii) For the next interval, (x) =1, and nx+1=
62, the (lx+1) is calculated by unitary method, i.e. if 142
individuals are 1 in proportion, 62 will have how many?
(lx)
for 1000000 = 1
(lx+1) for 62…..??
(lx+1) for 62 = 1x62/1000000
= 0.00006
Step 2: Now we calculate dx
as: [nx-(nx+1)]
For example, (x) =0, and nx =1000000;
and (x) =1, and nx+1= 62
dx as: [nx-(nx+1)]
= 100000-62= 999938.0.
Step
3: Now we calculate qx as: {dx/ nx}
For example, (x) =0, and nx =1000000;
dx = 999938.0,
qx = 999938.0/1000000= 0.9999
Step
4: Now we calculate Lx as: {lx + lx+1/2}
For example, (x) =0, and nx =1000000;
(lx) for 1000000 = 1
(x) =1, and nx+1 =62, (lx+1)
for 62= 0.00006,
Therefore, Lx = {lx + lx+1/2}
= {(1+0.00006)/2}= 0.500031
and,
Lx+1 = {lx+1 +
lx+2/2} = {(0.00006+0.00003)/2}= 0.000048
Step
4: Now we calculate Tx as: {Tx(n) + Lx(n-1)}
To calculate Tx, start from
bottom,
for (x9)=9, nx+8 =0,
Tx is also 0, i.e. Tx9=0
For (x8) =8, nx8 =2,
Tx8 = {Tx9 + Lx8}
i.e. Tx8 = (0 + 0.00001) =
0.00001
Let’s take another reading,
For (x7) =7, nx7 =2,
Tx7 = {Tx8 + Lx7}
i.e. Tx8 = (0.00001 + 0.00002)
= 0.00003 and so on.
Step 5: Calculate life
expectancy as 𝑒x = (𝑇𝑥/ l𝑥)
For
example for the age (x) =0, (lx) =1 and Tx1= 0.5015
𝑒x
= (𝑇𝑥/
l𝑥) = (0.5015/1) = 0.502
Step 6: Proceed further
for calculations similar to this and then draw survivorship curve graph on the
semi-log graph by plotting Age (years) on X-axis and lx on Y-axis.
The
graph plotted against the lifespan (Age or Years) and lx on X-axis
and Y-axis respectively has represented the life table of Barnacle and depicted
a Type III or Concave type curve. Hence, by using the data of life tables we
can predict the history pattern, size or developmental stages of the species.
Life
insurance companies and state government municipal communities collect birth
and death records of humans and with the collected data construct the Human
life tables.
A
very potential application of life table is the comparison of history trends
between the population and within the population is possible.
Life tables illustrate
three types of survivorship curves which help in understanding the mortality,
pattern of survival in the observed population and also the growth and decline
of future population.
Survivorship
curve
Survivorship
curves are generally produced from the data of cohort life tables for a
particular population and these curves depicts the age specific mortality.
These curves represent that in each phase of life cycle what are the number of
surviving individuals per thousand of a population.
Survival
curves are drawn on semi-log graph where X and Y axis represents the Lifespan
(age, years) and number of surviving individuals per thousand of population on
algorithm scale respectively. Generally these survivorship curves are in
frequent use by ecologists- Type I, Type II and Type III. These curves are standards
and used to compare with the real life survivorship curves of different
organisms: (a) Convex type curve, (b) linear curve and (c) Concave type curve.
a.
Convex
type curve or Type I
Populations
capable of living their physiological life span are Type I or convex type of
curve. They show high survivorship rate throughout life and low survivorship
curve in later stages when upto 75% of life span is complete i.e. high
mortality in old ages. It’s a characteristic pattern in many mammals, like
humans, and sheep.
Figure
2: Convex type or Type I survivorship curve obtained from the life table data
between age (x) and (lx).
b.
Linear
curve or Type II curve
These
curves represent uniform age specific survival throughout life in organism.
Adult stages of many birds and rodents show this type of curve. In mice,
rabbits and many birds the high mortality rate in young one but constant rate
in adults attributed to slightly sigmoid or slightly concave curve. A staircase
survivorship curve is an indication of different survival rates at different
stages by homometabolous insects.
Figure
3: Linear type or Type II survivorship curve obtained from the life table data
between age (x) and (lx).
c.
Concave
type curve or Type III curve
Concave
curve is a survivorship curve represented by many organisms such as fishes,
oysters, many insects and shellfishes. It is curve for organisms with high
reproduction rate in early life and dies off quickly after reproduction. Those
individuals who sustain 25% of their lifespan tend to have slow death rate. For
example in oyster, the early larval stages are more prone to predation therefore
high mortality rate is there initially but those who survived reaches their
adult stages and live longer.
Figure
4: Concave type or Type III survivorship curve obtained from the life table
data between age (x) and (lx).
Mortality
curve
The
rate of mortality plotted against age during age intervals gives mortality
curve. Plotted graph has time/year/age on X-axis and “qx” on Y-axis. It has two phrases in Type I a high
mortality phase or juvenile phase and a post juvenile phase where rate of
mortality first decreases as age increase and then increases with age. It forms
a J-shaped curve.
Figure
5: J-shaped Mortality curve obtained from the life table data between age (x)
and (qx).
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