List of top Mathematics and Quantitative Ecology Questions

A researcher estimates the relationship between reproductive success (𝑁, number of offspring) and horn length (𝐻, in cm) in a wild goat as 𝑁 = 40 βˆ’ 2.2𝐻 + 0.04𝐻 2 Horn length typically varies from 10 cm to 50 cm in this species. Which one of the following graphs correctly represents this relationship?
The Shannon-Weaver index 𝐻 is a measure of diversity and is calculated as H= -βˆ‘π‘π‘– 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
All else being equal, which one of the following population sizes (𝑁) and migration rates (π‘š) would result in the most genetic differentiation between populations (𝐹𝑠𝑑)? Note that 𝐹𝑠𝑑 is computed as 𝐹𝑠t=1/4π‘π‘š+1