5. Quantitative inheritance are due to
(1) Variation in phenotype
(2) Variation in genotype
(3) Variation in environment
(4) Variation in both genotype and environment

Quantitative inheritance is due to variation in both genotype and environment. It involves traits that show continuous variation rather than discrete categories because these traits are controlled by multiple genes (polygenes) and are influenced by environmental factors.

Explanation of each option:

1. Variation in phenotype: Phenotypic variation refers to the observable traits of an organism. This variation is a result, not the cause, of quantitative inheritance. So, this option alone does not explain the cause.

2. Variation in genotype: Genotypic variation (differences in genetic makeup) is a major component of quantitative inheritance, as multiple genes contribute to the trait.

3. Variation in environment: Environmental factors also contribute significantly to quantitative traits by modifying the expression of genotypes.

4. Variation in both genotype and environment: This is the most comprehensive and accurate explanation. Quantitative inheritance results from the combined effect of multiple genes and environmental influences on the phenotype.

Hence, the correct answer is option (4): Variation in both genotype and environment.

Introduction:
Quantitative inheritance refers to the inheritance pattern of traits controlled by multiple genes and influenced by environmental factors. Unlike qualitative traits, quantitative traits show continuous variation, such as height, weight, or crop yield. Understanding the causes of variation in these traits involves examining both genetic differences (genotype) and environmental effects. This article explains the components of quantitative inheritance and why variation in both genotype and environment leads to continuous phenotypic variation.

Detailed Explanation:
Quantitative traits are controlled by many genes, often called polygenes or quantitative trait loci (QTL), each contributing a small additive effect to the phenotype. The genetic variation among individuals occurs due to different combinations of alleles at these multiple loci. However, the environment in which an organism develops also influences these traits, modifying how genetic potential is expressed. Examples include how nutrition affects height or how soil quality impacts crop yield.

Phenotypic variation in quantitative inheritance is modeled by the equation:
Phenotype (P) = Genotype (G) + Environment (E) + (Genotype × Environment Interaction)
This means that observed traits are the result of genetic factors, environmental conditions, and the interaction between the two. To fully understand and predict quantitative traits, both sources of variation must be considered.

In summary:

• Variation in genotype provides the genetic basis for differences in traits.

• Variation in environment influences the expression of these genetic differences.

• Their combined effect results in the continuous variation seen in quantitative traits.

This explains why quantitative inheritance cannot be attributed to genotype or environment alone but to the variation in both.