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

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 − 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= -∑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

All else being equal, which one of the following population sizes (𝑁) and migration rates (𝑚) would result in the most genetic differentiation between populations (𝐹𝑠𝑡)? Note that 𝐹𝑠𝑡 is computed as 𝐹𝑠t=1/4𝑁𝑚+1

In a deer population, the male-to-female ratio is 1 : 2. The probability that a randomly formed group of size three has 2 males and 1 female is ________ (Round off to two decimal places).

The fitness \( f(n) \) of an individual in a group of size \( n \) is given by \[ f(n) = n(10 - n). \] At evolutionary equilibrium, groups are found in two different sizes. If one group size is 6, the other group size must be ________ (Answer in integer).

The prevalence of flu in a population is 1%. A diagnostic test has a false positive rate of 10% and a false negative rate of 10%. The probability that a randomly chosen person tests positive is ________ (Round off to three decimal places).

Which one or more of the following conditions can lead to an increase in tree densities in tropical savannas?

Gene conversion can lead to which one or more of the following evolutionary outcomes?

If the observed heterozygosity at a locus is 0.6, which one or more of the following could produce this outcome?

The genome of an organism has 60% GC (Guanine-Cytosine) content. The Adenine in this genome is ________% (Answer in integer).

In a linear regression with a single continuous predictor and 100 data points, the residual degrees of freedom are ________ (Answer in integer).

Which one or more of the following genes/markers is/are typically used for species identification?

A bee species forages for nectar on a plant species which has yellow flowers. To find out what cues the bees use to recognize the flowers, researchers performed the following experiment. They presented individual bees with the stimuli given below and examined the proportion of bees that approached and landed on the stimuli. The results are shown below.

Which one or more of the following interpretation(s) of the experiment is/are correct?

Which one or more of the following reason(s) explain(s) why whales use low frequencies (infrasound) for mate-finding and high frequencies (ultrasound) for hunting prey?

Which one or more of the following options represent(s) an evolutionary arms race?

The figure shows an \(F\) probability density function. The two dotted lines represent critical values corresponding to a two-tailed \(F\)-test at a level of significance of 0.05. The observed \(F\)-statistic for two samples is indicated by the solid line.

Which one of the following cladograms represents the correct phylogenetic relationships in the Kingdom Animalia?

Consider the logistic population growth model, given by \[ \frac{dn}{dt} = r n \left( 1 - \frac{n}{k} \right) \] where \(r\) is the intrinsic growth rate, \(n\) is the population size, and \(k\) is the carrying capacity. Which one or more of the following is/are assumption(s) of the model?

In a population of birds on an island, the average beak size reduced over one generation. A researcher estimated the association between beak size and relative fitness, shown in the graph. The estimated slope was \(-0.05\) with a 95% confidence interval of \(-0.15\) to \(0.09\).

Certain plants and animals rely on toxins such as cardiac glycosides for self-defense. Digitoxin and bufalin, structurally similar toxins produced by foxglove plants and bufonid toads, respectively, are one such example. Which one of the following statements about these toxins is correct?

All octopi dream every night, and sometimes change colour while dreaming. A student hypothesises that octopi change colour only when they dream about the food they ate that day. To test this hypothesis, the student conducts an experiment with two treatments that are randomly ordered, and separated by 2 days. In one treatment, she places 10 octopi in individual tanks in captivity and provides each one with a large crab to eat during the day. She then records the dream state colour of these octopi that night. Which one (or more) of the following would be an appropriate NEGATIVE control to test this hypothesis?

The table shows a list of analysis goals (i, ii, iii) and different statistical tests (P, Q, R).

In the graph shown, the solid line represents the best fit from an ordinary least-squares regression, where X is the predictor variable and Y is the response variable. In this case, which one of the following assumptions of the linear regression is violated?

A sample of heights of trees follows a normal distribution. In this sample, 68% of height measurements are expected to fall in the interval: \[ \text{mean} \pm \underline{\hspace{1cm}} \text{ standard deviation.} \] (Round off to the nearest integer.)

The frequency distributions of a trait in two populations, X and Y, are shown in the figure.

Which one of the following statements about the mean and standard deviation (SD) of the two populations is accurate?