Step 1: Understanding the Concept:
Self-incompatibility (SI) is a genetic mechanism in flowering plants that prevents self-fertilization, thereby promoting outcrossing and genetic diversity.
It is classified into homomorphic and heteromorphic systems based on floral morphology.
Step 2: Detailed Explanation:
Let us analyze both statements:
Statement (I):
The phenomenon of self-incompatibility was first scientifically reported by the German botanist Joseph Gottlieb Kölreuter in the late $18^{\text{th}}$ century while working with *Verbascum* species.
Physiologically, self-incompatibility occurs when viable pollen grains from a flower fail to germinate, grow, or fertilize the ovules of the same flower or other flowers on the same plant.
Thus, Statement (I) is correct.
Statement (II):
In a heteromorphic self-incompatibility system, different incompatibility groups produce flowers with distinct, visible morphological differences in their reproductive organs.
The classic example is distyly in primrose (*Primula vulgaris*), where some plants produce "pin" flowers (long styles and short stamens) and others produce "thrum" flowers (short styles and long stamens).
Fertilization can only occur between different floral morphs, physically preventing selfing.
Thus, Statement (II) is correct.
Step 3: Final Answer:
Both Statement (I) and Statement (II) are correct.
This corresponds to Option (A).