GATE — Ecology and Evolution (EY) · India · IITs and IISc on rotation
Original practice questions written to the published syllabus · not past papersThe mathematics and statistics needed for every numerical question in this track: calculus and differential equations for growth and decay, probability and risk, regression and hypothesis tests, and sampling designs for field data. Experimental design and survey sampling in depth live in the Agricultural Statistics track; this subject covers the environmental applications.
In the exams: GATE ES Section 1 (Mathematics Foundation); ICAR AICE subject 71 Unit 7; UGC NET Environmental Sciences Unit 9
How our questions for GATE spread across the units of Mathematics & Statistics for Environmental Science. Difficulty: 3 easy, 9 medium, 4 hard.
| Diversity indices: Shannon, Simpson and evenness | 7 | |
| Probability distributions: binomial, Poisson, normal, log-normal | 4 | |
| Linear algebra: matrices, linear systems, eigenvalues | 2 | |
| Ordinary differential equations and first-order decay and growth | 2 | |
| Calculus: limits, derivatives, maxima and minima, integrals | 1 |
Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.
A two-stage Leslie matrix is [[0, 4], [0.5, 0]]. What is its dominant eigenvalue, the asymptotic growth rate per time step?
B. 1.41
λ² = 4 × 0.5 = 2, so λ = √2 ≈ 1.41, a 41% increase per step. 2.00 forgets the square root; 4.50 adds; 0.50 is survival only.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Counts of an insect per quadrat have a variance much larger than the mean. This suggests a spatial pattern that is
A. clumped (aggregated)
Variance/mean > 1 indicates aggregation, often modelled with the negative binomial.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
A sample has 20 species among 500 individuals. What is Margalef's richness index, (S − 1)/ln N?
B. 3.06
19/ln 500 = 19/6.215 ≈ 3.06. 0.89 is Menhinick's index; 0.04 is S/N.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
In a sample of 500 individuals, the most abundant species has 200. What is the Berger–Parker dominance index?
A. 0.4
Berger–Parker d = Nmax/N = 200/500 = 0.4. 2.5 is its reciprocal, 1/d, and 300 is the count of the remaining individuals.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
A community has three species with proportions 0.5, 0.3 and 0.2. What is Simpson's index D = Σp²?
D. 0.38
0.25 + 0.09 + 0.04 = 0.38; 1 − D = 0.62; 1.03 is Shannon's H′.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Why can high diversity index values be misleading for site health?
C. Invaders and generalists raise diversity too
Disturbed sites can score high on diversity indices because invasive or generalist species add to richness and evenness; interpretation needs species identity, sampling effort and context. High diversity does not prove a pristine ecosystem.
Further reading: See the manual sources: Kreyszig; Zar; Gilbert; Gomez & Gomez; Chow et al.; Magurran
Ten here, 16 in the app. The Laisha app has every practice question we have written to GATE in this subject, marked as you go, with timed papers, a jump-to-unanswered list and a certificate when you pass at 70 per cent.
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