(a) Define correlation. Explain its types and methods of computing coefficient of correlation. (20 marks) (b) Write a note on…

(a) Correlation: types and methods of computing the coefficient

Correlation is a statistical measure of the direction and degree of association between two variables. It is positive if both rise and fall together, negative if one rises as the other falls, and zero if there is no systematic relation. Types: linear (points near a straight line) and non-linear (along a curve); simple (two variables), partial (the effect of one variable with another held constant) and multiple (one variable related to several others together).

Methods of computing:

• Scatter diagram. Plotting the paired values shows whether the relation is positive, negative, linear or curved. It gives no exact coefficient.
• Karl Pearson's product-moment coefficient for interval or ratio data: r = [nΣxy − ΣxΣy]/√{[nΣx² − (Σx)²][nΣy² − (Σy)²]}, equal to the covariance divided by the product of the standard deviations. It lies between −1 and +1; ±1 is perfect linear association, 0 is no linear association, and the sign gives the direction. Normality is needed only for significance tests.
• Spearman's rank correlation for ordinal data or when Pearson's assumptions fail: rank each variable, find the differences d, and ρ = 1 − 6Σd²/[n(n² − 1)]. With tied ranks the correction Σ(t³ − t)/12 is added to Σd². For n = 5 and Σd² = 10, ρ = 1 − 60/120 = 0.5.
• Coefficient of concurrent deviations, a rough measure: r = ±√[±(2c − n)/n], where c is the number of pairs of deviations with the same sign and n the number of such pairs.

The correlation shows association, not causation.

(b) Ecological pyramids

An ecological pyramid is a graphic representation of the trophic structure of an ecosystem, with producers at the base and successive consumers above (Charles Elton). There are three kinds.

• Pyramid of numbers shows the number of individuals at each level. It is upright in a grassland (many grasses, fewer grazers, fewer carnivores) and in a pond. It is inverted in a tree ecosystem, where one tree supports many insects, and in a parasite chain, where one host carries many parasites.
• Pyramid of biomass shows the standing crop of each level. It is upright in forests and grasslands, but inverted in many ponds and seas, because phytoplankton have a small standing biomass that is renewed very fast and supports a larger biomass of zooplankton and fish.
• Pyramid of energy shows the energy flow per unit area per unit time at each level. It is always upright, since only about 10% of the energy passes to the next level (Lindeman's ten percent law) and the rest is lost as heat in respiration. A pond or Silver Springs shows this.

Limitations: pyramids ignore decomposers, seasonal change and organisms feeding at several levels. The energy pyramid is the most informative.

(c) Pheromones in insects

Pheromones are chemicals released by an individual into the environment that cause a specific behavioural or physiological response in another individual of the same species, often detected by the antennae at very low concentrations. Their roles in insects are:

• Sex pheromones: attract mates, as the bombykol of the female silk moth (Bombyx mori) attracting males.
• Aggregation pheromones: bring individuals together for feeding or mating, as in bark beetles and flour beetles (Tribolium).
• Alarm pheromones: warn the group and mobilise defence, as in bees and ants.
• Trail pheromones: mark the way to food, as in ants and termites.
• Queen substance (9-oxodecenoic acid) in honey bees: inhibits ovary development in workers and keeps the colony organised.
• Primer pheromones: cause lasting changes in physiology or development, such as caste determination in termites.

Applications: pheromone traps are used to monitor pests, for mass trapping and for mating disruption in pest management, for example in fruit flies and bollworms, reducing pesticide use.