List of top Mathematics and Quantitative Ecology Questions on Ecology asked in GATE EY

A flask containing nutrient-rich media is seeded with 100 isogenic bacteria. Assuming that no bacteria die in the flask, after approximately how many generations will the population reach a size of \(10^5\)?

A bacterium can be approximated as a cylinder with a hemisphere capping each end, as shown in the figure. The cylinder has a height of 1 \(\mu m\) and a diameter of 1 \(\mu m\), so the two end hemispheres share the same radius as the cylinder.

Assuming that the density of the bacterium equals that of water, what is the approximate mass of this bacterium?
Given: density of water \(=10^3\ \text{kg/m}^3\); \(1\ \mu m = 10^{-6}\ m\).
Volume of a cylinder \(= \pi r^2 h\), where \(r\) is the radius and \(h\) is the height of the cylinder.
Volume of a sphere \(= \dfrac{4}{3}\pi r^3\), where \(r\) is the radius of the sphere.

Population growth of a species can be modelled as \[ \frac{dN(t)}{dt}=rN(t)\left(1-\frac{N(t)}{K}\right), \] where \(N(t)\) is the population size at time \(t\), \(r\) is the growth rate, and \(K\) is the carrying capacity of the environment. For \(K=9000\), \(\dfrac{dN(t)}{dt}\) is maximized at \(N=\) ______ (Answer in integer)

The Shannon-Weaver index 𝐻 is a measure of diversity and is calculated as H= -∑𝑝𝑖 𝑙𝑛(𝑝𝑖) where S is the total number of species and 𝑝𝑖 is the proportional abundance of a species i.The table below gives the abundance of different species in a community. The Shannon-Weaver index of reptile diversity in this community is ___________.(Rounded off to two decimal places)Species Abundance Indian gliding lizard 270 Malabar flying frog 325 Travancore tortoise 180 Malabar hornbill 160 Forest cane turtle 120 Malabar pit viper 30