Download Sampling

Module VI – Biodiversity estimation – tools and techniques (4 hrs)
Sampling techniques Quadrate
Line transect
Measurements
Density
Abundance
Frequency
Biodiversity indices – concepts
Shannon-Weiner, Simpson
Sampling
Sampling is the process whereby a small proportion or subgroup of a population is
selected for analysis. Sample refers to the small subgroup which is thought to be representative
of the larger population.
Advantages of Sampling
i.
Sampling saves time and money
ii.
Sampling saves labor.
iii.
Sample coverage permits a higher overall level of adequacy than a full enumeration.
iv.
Complete census is often unnecessary, wasteful, and the burden on the public.
Types of sampling
1. Probability sampling: it is the one in which each sample has the same probability of being
chosen.
2. Purposive sampling: it is the one in which the person who is selecting the sample is who
tries to make the sample representative, depending on his opinion or purpose, thus being
the representation subjective.
3. No-rule sampling: we take a sample without any rule, being the sample representative if
the population is homogeneous and we have no selection bias.
Probability sampling:
1. Random sampling
Random sampling is usually carried out when the area under study is fairly uniform, very
large, and or there is limited time available. When using random sampling techniques, large
numbers of samples/records are taken from different positions within the habitat. A better
method of random sampling is to map the area and then to lay a numbered grid over the map. A
(computer generated) random number table is then used to select which squares to sample. For
example, if we have mapped our habitat, and have then laid a numbered grid over it as shown,
we could then choose which squares we should sample in by using the random number table.
2. Stratified sampling
Stratified sampling is used to take into account different areas (or strata) which are
identified within the main body of a habitat. These strata are sampled separately from the main
part of the habitat. The name 'stratified sampling' comes from the term 'strata' (plural) or stratum
(singular).
Individual habitats are rarely uniform throughout their extent. There are often smaller
identifiable areas within a habitat which are substantially different from the main part of the
habitat.
One of the problems with random sampling is that random samples may not cover all
areas of a habitat equally. Stratified random sampling would be used to avoid missing out on
important areas of the habitat.
Advantages:
We can have more precise information inside the subpopulations about the variables we
are studying.
We can raise precision of the estimators of the variables of the whole population.
Disadvantages:
The choice of the size of the samples inside each stratus to let the sample size be n.
It may be difficult in some populations to divide into strata.
As a general thing, stratified sampling provides better results than the random sampling
when the strata are more different among them and more homogeneous internally.
3. Cluster sampling.
In cluster sampling, population is divided into units or groups, called strata (usually they
are units or areas in which the population has been divided in), which should be as representative
as possible for the population, i.e., they should represent the heterogeneity of the population we
are studying and they should be homogeneous among them. The reason to make this sampling is
that sometimes it is too expensive to make a complete list of all the elements of the population
that we want to study, or that when we finish making the list it may have no sense to make the
study. The main disadvantage that we may have is that if the clusters are not homogeneous
among them, the final sample may not be representative of the population.
4. Systematic sampling
A systematic sample is one in which every Kth subject on a list is selected for inclusion in
the sample. The “K” refers to the sampling interval, and may be every 3rd (K=3) or 10th (K=10)
subject. The value of K is determined by dividing the population size by the sample size. Let’s
say that you have a list of 10,000 persons. You decide to use a sample of size 1000. K =
10000/1000 = 10. If you choose every 10th name, you will get a sample of size 1000. Systematic
sampling is equivalent to random sampling if the elements are numbered in a random way.
Advantages of this method are:
i.
Extends the sample to all the population.
ii.
It is very easy to apply it.
Disadvantages of the method are:
i.
Increase of the variance if there is periodicity in the numbering of the elements,
appearing a bias due to selection.
ii.
Problems when we want to estimate the variance.
Non-probability Sampling:
i. Availability/Accidental sampling is where the first available appropriate sample are used.
ii. Quota sampling begins with a matrix describing the characteristics of the target population.
The goal is to select people to reflect characteristics found in the population.
iii. Purposive/Judgmental sampling is where the sample is selected on the basis of knowledge of
the research problem to allow selection of "typical" persons for inclusion in the sample.
iv. Snowball sampling is appropriate when the members of a special population are difficult to
locate.
v. Dimensional sampling is a sampling technique for selecting small samples in a way that
enhances their representativeness. There are two steps to dimensional sampling. First, specify all
the dimensions or variables that are important, and second, choose a sample that includes at least
one case representing each possible combination of dimensions.
Biodiversity measurement
Whittaker (1972) described three terms for measuring biodiversity over spatial scales:
alpha, beta, and gamma diversity. Alpha diversity refers to the diversity within a particular area
or ecosystem, and is usually expressed by the number of species (i.e., species richness) in that
ecosystem.
Biologists use a variety of sampling methods depending on the type of organism and its
natural abundance and distribution. Samples are usually taken using a standard sampling unit of
some kind. This ensures that all of the samples represent the same area or volume (water) of the
habitat each time.
Quadrat methods
Quadrat is a sampling unit of definite area that is usually a square but it can also be a
rectangle or circle. Size and number of quadrats are determined based on the objective and
features of area under consideration. The purpose of using a quadrat is to enable comparable
samples to be obtained from areas of consistent size and shape.
The quadrat method has the following assumptions:
i. The number of individuals in each quadrat is counted.
ii. The size of the quadrats is known.
iii. The quadrat samples are representative of the study area as a whole.
Line Transect Method
Transect is the term used in cases where sampling unit is a strip of definite area. Transect
may be a line or belt depending upon the study area. In a line transect, sampling is usually done
across a line. In belt transect, an area (belt) of suitable size is selected where the sampling is
done. Belt transects are particularly used in forests and can be further divided into segments for
convenience.
A transect line can be made using a nylon rope marked and numbered at 0.5m, or 1m
intervals, all the way along its length. This is laid across the area you wish to study. The position
of the transect line is very important and it depends on the direction of the environmental
gradient you wish to study.
A line transect is carried out by unrolling the transect line along the gradient identified.
The species touching the line may be recorded along the whole length of the line (continuous
sampling). Alternatively, the presence, or absence of species at each marked point is recorded
(systematic sampling).
Mark-recapture method
These methods are used extensively to estimate populations of fish, game animals, and
many non-game animals. The approach was first used by Petersen (1896) to study European
plaice in the Baltic Sea and later proposed by Lincoln (1930) to estimate numbers of ducks.
Petersen's and Lincoln's method is often referred to as the Lincoln-Petersen Index, even though it
is not an index but a method to estimate actual population sizes. Their method involves capturing
a number of animals, marking them, releasing them back into the population. After the
individuals have mixed freely with unmarked individuals, new samples are taken, and for each
sample the ratio of marked to un-marked individuals is recorded. The key principle of sampling
applies to this method: the ratio of unmarked to marked individuals in a sample will be the same
as the ratio in the population as a whole. The population (P) is estimated by the formula:
P=
MC
R
where M is the number of animals marked in the first trapping session, C is the number of
animals captured in a second trapping session, and R is the number of marked animals recaptured
in the second trapping session. This is derived from the equation:
P
M
=
C
R
Species diversity
Each community is composed of taxonomically different species. Species diversity refers
to number of different species in the community including both abundant and rare species.
Species diversity is very high in natural communities like tropical rain forests or coral reefs in
oceans, whereas it is very low in physically or human controlled communities. Species diversity
has two components: species richness and species evenness. In simple words, species richness
refers to different types of species and their numerical strength. Technically, it refers to ratio
between different species (S) and total number of species (N). Species evenness refers to a
measure which qualifies as to how even species are in terms of their number. In a community, it
refers to the apportionment of each species. For example, a community is quite even if there are
10 species with 10 or 9 individuals of each species; whereas a community is uneven if there are
10 species of which one species has 90 individuals and the rest 9 species have only 10
individuals.
Species diversity can be measured by using various diversity indices-the mathematical
expressions based on species abundance data. Species diversity can be measured separately
either as species richness or evenness or diversity as a whole. Species richness is measured by
Index of richness (denoted by R) given by Margalef (1958). Species evenness can be measured
with evenness index (denoted by E) given by Hill (1973). Diversity of the species can also be
calculated directly with a variety of indices, of which two commonly used are Shannon-Weiner
Index or simply the Index of diversity or Shannon’s index (denoted by H ́; as given by Shannon
and Weaver, 1963) and Index of dominance (or λ) or Simpson’s index given by Simpson (1949).
Shannon‘s index has a direct relationship with the species diversity, whereas index of dominance
has an inverse relationship.
Density
Density of a species reflects the numerical strength of species in a given community.
Density =
Total number of species present in all Quadrats
Total number of Quadrats studied
Density can also be presented as relative density. Relative density is calculated based on
following formula:
Relative density of a species =
Individual density of a species
Total density of all species encountered
Abundance
Abundance is also calculated like density but in this case, only those quadrats are
considered for calculation where a species actually occurs. For example, if a species has occurred
in only 3 quadrats out of total 5 studied, then the total number of individuals of the species is
divided by 3 (instead of 5, as in case of density).
The formula for calculation of species abundance is:
Abundance of a species =
Total number of plants in all the Quadrats
Number of Quadrats of occurrence of plant species
Abundance is also presented on the basis of unit area, i.e. 1m2 especially in smaller areas
or grasslands. However, it is not much used as compared to density in ecological studies. It can
also be multiplied by 100 to get percent abundance.
Relative abundance of a species =
Individual abundance of the species
Total abundance of all species encountered
Frequency
Frequency is another important parameter of vegetation analysis, which reflects the
spread, distribution or dispersion of a species in a given area, and given in percent. For example,
a species is distributed uniformly in an area there is greater probability of its occurrence in all
quadrats and it would have maximum frequency. In another case, a species may be clustered or
present only in a part of the area. In this case, it will occur only in few quadrats and hence it
would have lesser frequency. The frequency of a species in a given area is studied by either
quadrat method or transects and is calculated by the following formula:
Number of Quadrats in which a species occurs
Frequency =
Total number of Quadrats studied
× 100
Thus, if a species occurs in 5 out of total 10 quadrats studied, its frequency would be
50%. If a species occurs in all the quadrats studied, its frequency would be 100%.
Evenness
Evenness is a measure of the relative abundance of the different species making up the
richness of an area. A community dominated by one or two species is considered to be less
diverse than one in which several different species have a similar abundance. As species richness
and evenness increase, so diversity increases.
Simpson's Diversity Indices
The term 'Simpson's Diversity Index' can actually refer to any one of 3 closely related
indices.
Simpson's Index (D) measures the probability that two individuals randomly selected from a
sample will belong to the same species (or some category other than species). There are two
versions of the formula for calculating D. Either is acceptable, but be consistent.
D=
(n / N)2
n = the total number of organisms of a particular species
N = the total number of organisms of all species
The value of D ranges between 0 and 1
With this index, 0 represents infinite diversity and 1, no diversity. That is, the bigger the
value of D, the lower the diversity. This is neither intuitive nor logical, so to get over this
problem, D is often subtracted from 1 to give:
Simpson's Index of Diversity 1 - D
The value of this index also ranges between 0 and 1, but now, the greater the value, the
greater the sample diversity. This makes more sense. In this case, the index represents the
probability that two individuals randomly selected from a sample will belong to different species.
Another way of overcoming the problem of the counter-intuitive nature of Simpson's Index is to
take the reciprocal of the Index:
Simpson's Reciprocal Index 1 / D
The value of this index starts with 1 as the lowest possible figure. This figure would
represent a community containing only one species. The higher the value, the greater the
diversity. The maximum value is the number of species (or other category being used) in the
sample. For example if there are five species in the sample, then the maximum value is 5.
Shannon Diversity Index
The Shannon index increases as both the richness and the evenness of the community
increase. The fact that the index incorporates both components of biodiversity can be seen as
both strength and a weakness.
s
H = ∑ - (Pi * ln Pi)
i=1
where:
H = the Shannon diversity index
Pi = fraction of the entire population made up of species i
S = numbers of species encountered
∑ = sum from species 1 to species S
Note: The power to which the base e (e = 2.718281828.......) must be raised to obtain a
number is called the natural logarithm (ln) of the number.
To calculate the index:
1. Divide the number of individuals of species #1 you found in your sample by the total number
of individuals of all species. This is Pi
2. Multiply the fraction by its natural log (P1 * ln P1)
3. Repeat this for all of the different species that you have. The last species is species “s”
4. Sum all the - (Pi * ln Pi) products to get the value of H
For example:
Birds
Ni Pi
Pigeon
96 .96 -.041 .039
Robin
1
.01 -4.61 .046
Starling
1
.01 -4.61 .046
Crow
1
.01 -4.61 .046
House sparrow 1
.01 -4.61 .046
H = 0.223
ln Pi
- (Pi * ln Pi)
High values of H would be representative of more diverse communities. A community
with only one species would have an H value of 0 because Pi would equal 1 and be multiplied by
ln Pi which would equal zero. If the species are evenly distributed then the H value would be
high. So the H value allows us to know not only the number of species but how the abundance
of the species is distributed among all the species in the community.