Determination of Population density in a natural/hypothetical community by quadrate method and calculation of Shannon-Weiner diversity index for the same community

 Principle:

In ecological field surveys, the quadrat sampling technique serves as a fundamental method for estimating community composition. Some sample must be collected in a given area by this method. According to the Law of Probability, the study's margin of error is minimized as the number of quadrats used for sampling increases. Based on population density, one can calculate the species diversity of the community using the Shannon Diversity Index.

Requirement: The investigation utilizes an optimized quadrat dimension applied to a hypothetical community model, which comprises seven distinct species exhibiting a stochastic (random) spatial distribution across the study area.

Procedure:

1. Choice of sample area which contain randomly four species a, b, c, d, r, s & t.
2. Chosen quadrate size is 1cm x1cm & number of quadrate is given to the area is as 1,2,3,4.....,10.
3. Calculation of total number of each species in the sample.
4. Tabulate all the figures for calculating population density & Shannon-Weiner diversity index.

Calculation:

 Density is the average number of individuals per unit area.

Density= Total number of individuals of each species / total number of sample

The Shannon diversity index is calculated by H’  or Hs =  -∑(niN)ln(ni/N)

Or H’  or Hs =  - ∑pi ln pi

where ,

ni= number of individuals of i th species.

N= Total for all the species.

Pi=Relative abundance (proportion) of the i th species.

ln =Natural logarithm.

Hypothetical community data

A forest floor area  was sampled using 10 quadrates of 1m² each 

Species:

a = Black-kneed Meadow Katydid [Conocephalus melaenus]

b  = Weaver ant [Oecophylla smaragdina ]

c = Red Pumpkin beetle [Aulacophora foveicollis ]

d =Hover fly [Episyrphus sp]

r = Fire ant  [Solenopsis geminata]

s = Indian Black ant [Camponotus compressus ]

t = Common Cricket [Acheta domesticus]

Species No:	Sampling number										Total Number Of Individual	Total Number Of Sample	Quadrates present	Density [/m2]
	1	2	3	4	5	6	7	8	9	10
a	4	2	0	0	1	0	1	3	7	2	20	10	7	20/10=2.0
b	0	2	5	6	3	2	2	5	3	3	31	10	9	31/10=3.1
c	7	5	5	0	2	0	2	0	3	1	25	10	7	25/10=2.5
d	0	1	2	0	0	0	0	4	0	0	7	10	3	7/10=0.7
r	4	0	0	0	2	0	10	22	0	0	38	10	4	38/10=3.8
s	0	0	1	6	0	0	0	0	15	0	22	10	3	22/10=2.2
t	1	3	2	0	0	2	0	0	0	2	10	10	5	10/10=1.0

Overall Community Density: D=153/10=15.3 individuals/m²

Species	Number of Individual	Pi	Pi  ln	Pi ln Pi
a	20	20/153=0.13	-0.886	0.13(-0.886) = -0.11518
b	31	31/153=0.20	-0.698	0.20 (-0.698) = -0.1396
c	25	25/153=0.16	-0.7958	0.16 (-0.7958) = -0.127328
d	7	7/153=0.045	-1.346	0.045 (-1.346 )=  -0.06057
r	38	38/153=0.25	-0.602	0.25 (-0.602)= -0.1505
s	22	22/153=0.14	-0.853	0.14(-0.853)= -0.11942
t	10	10/153=0.065	-1.1870	0.065(-1.1870)= -0.077155
Total	153			( Σ)= -0.789753

The Shannon Diversity Index (H') is: 0.78975

Result:

Diversity Level: (H') value of 0.790 is relatively low. In most natural ecosystems, the Shannon Index typically falls between 1.5 and 3.5.

Community Structure: This lower value suggests that either the species richness (number of species) is low, or the evenness is poor (meaning one or two species might be dominating the area while others are rare).

Ecological Health: As a "hypothetical community," this result serves as a baseline. In a real-world sanctuary, a higher index would indicate a more stable and complex food web.

Species evenness:

The Evenness Index is calculated as:

J' = H'/H max

Where H max = ln(S), and S=  total number of species.

Here, S= 7 , so H max = ln(7)=0.8450

J' =  0.78975/0.8450= 0.9346

Conclusion:

This heterogenous community shows different density for species.

r > b > c > s > a > t > d

So, species r has highest density & species d has the lowest density. The (-) in Shannon Diversity index exists to give us a positive index.

[0-1:Low Density,1-2: Moderate Density,2-3 :High Density, 3:Very high density.]

An evenness value approaching 1.0 indicates that the community is almost perfectly balanced.

 This indicates a near-homogeneous distribution of individuals across the identified taxa.

• No single species is dominating the environment.

• Lack of competitive exclusion, i.e. low level of future community & ecosystem service disruption.

• The individuals are distributed very equally among the different species present.

• The habitat in this hypothetical model  provides stable, shared resources that support all seven species nearly equally.