Numerical Problems/ISC/Class 12
Created by Titas Mallick
Biology Teacher • M.Sc. Botany • B.Ed. • CTET (CBSE) • CISCE Examiner
BioNotesBioNotesCreated by Titas Mallick
Biology Teacher • M.Sc. Botany • B.Ed. • CTET (CBSE) • CISCE Examiner
Online
Numerical Problems - Biodiversity
Biodiversity and its conservation involve understanding species richness, area relationships, and various indices used to measure the diversity of ecosystems. The numerical problems here will focus on the Species-Area Relationship, Simpson's Diversity Index, and Shannon-Wiener Index.
The relationship between species richness () and area () is a rectangular hyperbola on a normal scale, but a straight line on a logarithmic scale.
Species-Area Relationships:
Steps to Calculate Simpson's Index of Diversity:
The species-area relationship for frugivorous birds in a tropical forest region is given by the equation . The regression coefficient () for this entire continent is typically steep, recorded at 1.15. If rampant deforestation reduces the original forest area by 90%, what percentage of these bird species is expected to go extinct from the region?
Solution:
Step 1: Understand the initial and final states.
Step 2: Express the new species richness in terms of the original.
Step 3: Calculate the multiplier.
Step 4: Calculate the percentage of species lost (extinction).
Answer: Approximately 92.92% of the frugivorous bird species will go extinct.
An ecologist samples a local pond and records the following number of individuals for four different fish species:
Calculate Simpson's Index of Diversity (1 - D) for this pond ecosystem.
Solution:
Step 1: Calculate the total number of individuals (N).
Step 2: Calculate the proportion () and its square () for each species.
Step 3: Sum the squared proportions to find Simpson's Dominance Index (D).
Step 4: Calculate Simpson's Index of Diversity.
Answer: Simpson's Index of Diversity is 0.675. (A higher value closer to 1 indicates greater diversity).
You are given data for two communities, A and B. Both have exactly two species, but their relative abundances differ:
Calculate the Shannon-Wiener Diversity Index () for both communities and determine which is more diverse. (Use natural logarithm, ). (Formula: )
Solution:
Step 1: Calculate H for Community A (Maximum Evenness).
Step 2: Calculate H for Community B (High Dominance).
Step 3: Compare.
Answer: Community A is significantly more diverse because it has higher species evenness (individuals are distributed equally), which is directly reflected by the higher Shannon-Wiener index.
The Trap: Assuming that the regression coefficient is always the same across different scales. The Reality: In the species-area relationship, typically lies between 0.1 and 0.2 for small areas (like a state or a country). However, if you analyze the species-area relationship for very large areas like entire continents, the slope becomes much steeper, and values typically range between 0.6 and 1.2. Always read the question carefully to see if it specifies a localized or continental scale!
The Trap: A question asks for "Simpson's Diversity Index," and you calculate and stop there. The Reality: The term by itself is actually the Dominance Index. It measures the probability that two individuals randomly selected from a sample will belong to the same species.
The Trap: Mixing up and (natural log). The Reality: The Species-Area relationship usually uses standard base-10 logarithms (). The Shannon-Wiener index traditionally uses natural logarithms ( or ), though base-2 () is sometimes used in information theory. If calculating Shannon's Index, explicitly verify which log base you are applying on your calculator to avoid completely wrong final values.