In some of the cases children shows less mental ability as compared to their parents and vise-versa, this rule of heredity is known as what?

Heredity is responsible for the inheritance of genetic information which specifies their structure and functions similar to parents. 

Based on various theories on heredity certain laws have been propounded by psychologists and certain generalizations were led to these laws and generalization.

• The above-mentioned rule of heredity is known as the 'Law of Regression'. It was proposed by Sir Francis Galton.
• The Law of Regression tells heavily against the full hereditary transmission of any gift.
• Average parents tend to produce average offspring, but children of extreme parents inherit parental peculiarities to a lesser degree than they appear in their parents.
• For example, it is not compulsory that a child of gifted parents will inherit all their powers and a child of mentally retarded parents will inherit all their weaknesses and diseases.

Hence, it could be concluded that the above-mentioned rule of heredity is known as the 'Law of Regression'.

Additional Information

• The Law of Segregation: Organisms that sexually reproduce with meiosis have 2 copies of every gene and only one of these genes is passed to the next generation. 
• The Law of Independent Assortment: This law explains the inheritance of two separate genes from two different sets of chromosomes.
• The Law of Dominance: This principle of inheritance states that dominant alleles will mask recessive alleles, however, these recessive alleles still exist even though they are masked.