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

Correlation and its computation. Correlation is a statistical measure indicating the direction and degree of association between two variables. If both variables tend to rise or fall together, correlation is positive; if one rises while the other falls, it is negative; if no systematic association exists, it is zero. It may be linear, where points lie near a straight line, or non-linear, where association follows a curve. It is also classified as simple, involving two variables; partial, measuring the effect of one variable while holding another constant; and multiple, where one variable is related to several others simultaneously.

The scatter diagram is the first method: plotting paired values shows whether the relation is positive, negative, linear or curved, though it does not give an exact coefficient. Pearson’s product-moment coefficient, r, is used for interval or ratio data and is computed as r = [nΣxy − ΣxΣy]/√{[nΣx²−(Σx)²][nΣy²−(Σy)²]}. In practice, one calculates means, deviations, products of deviations and sums of squares, or uses covariance divided by the product of standard deviations. The coefficient ranges from −1 to +1 inclusive; +1 and −1 denote perfect linear association, while 0 denotes no linear association. The magnitude indicates strength, and the sign indicates direction. It can be computed without assuming bivariate normality; normality is mainly relevant for significance tests and confidence intervals. Spearman’s rank correlation, ρ, is used for ordinal data or when Pearson’s assumptions are unsuitable. Ranks are assigned to each variable, differences are squared and summed; for no tied ranks, ρ = 1 − 6Σd²/[n(n²−1)]. With tied ranks a tie correction is applied, for example ρ = 1 − [6Σd² + Σ(t³−t)/12]/[n(n²−1)]. If n=5 and Σd²=10, ρ=1−60/120=0.5. The coefficient of concurrent deviations gives a rough estimate: r=(c−d)/(c+d), where c and d are the numbers of concordant and discordant deviations from the means; it is less precise and is affected by zero deviations.

Ecological pyramids. An ecological pyramid graphically represents trophic levels and energy flow, based on Lindeman’s trophic-dynamic theory, which emphasises unidirectional energy flow and heat loss. The pyramid of numbers shows the count of organisms at each level; in Terai grassland it is usually upright, with many grasses, fewer grazers and fewer predators, but it can be inverted in a parasitic chain where one host supports many parasites. The pyramid of biomass shows standing crop; in grassland it is upright, while in many aquatic ecosystems it may be inverted because phytoplankton have low standing biomass but high turnover. The pyramid of energy is always upright because energy transfer is inefficient, typically about 10% from one trophic level to the next; a pond ecosystem illustrates this, with phytoplankton fixing solar energy, zooplankton using less, small fish less still, and large carnivores least. Thus, pyramids summarise trophic structure, but their shape depends on the unit used and the time of sampling.

Pheromones. Pheromones are species-specific semiochemicals released by insects that modify the behaviour of conspecifics, often detected by antennae at very low concentrations. Sex pheromones attract mates, as in Bombyx mori where bombykol guides male moths to females. Aggregation pheromones gather individuals, as in Tribolium beetles. Alarm pheromones warn and mobilise defence, and trail pheromones mark routes, as in Lasius niger ants. In Apis mellifera, queen substance maintains colony organisation and suppresses worker ovary development. In applied entomology, pheromones are used in IPM through mass trapping, monitoring and mating disruption, for example against fruit flies and bollworm, reducing pesticide dependence and improving pest control. Their specificity makes them valuable for monitoring pest populations without broad-spectrum chemicals.

Thus, correlation provides the statistical basis for quantifying ecological relationships, while pyramids and pheromones explain the structure and behavioural regulation of insect populations.