The idea not related to the Darwinian evolutionary theory is: Inheritance of acquired characters.

Explanation:
Charles Darwin's theory of evolution by natural selection is a fundamental concept in biology. It explains how species evolve and adapt to their environment over time. However, the idea of "inheritance of acquired characters" is not related to Darwinian evolutionary theory.

Darwinian Evolutionary Theory:
Darwin's theory of evolution by natural selection can be summarized as follows:

1. Struggle for Existence:
In any population, more individuals are born than can survive due to limited resources. This leads to competition for resources and a struggle for existence.

2. Variation and Inheritance:
Individuals within a population exhibit natural variations, such as differences in size, color, or behavior. These variations are heritable, meaning they can be passed on to offspring through genes.

3. Survival of the Fittest:
Individuals with variations that are advantageous in their environment are more likely to survive and reproduce. This is often referred to as "survival of the fittest."

4. Natural Selection:
Over time, the favorable variations accumulate in the population, while less advantageous traits are gradually eliminated. This process, known as natural selection, leads to the adaptation of species to their environment.

5. Origin of Species by Natural Selection:
The cumulative effects of natural selection can eventually lead to the formation of new species. This occurs when populations become reproductively isolated from each other and accumulate enough genetic differences to be considered separate species.

Inheritance of Acquired Characters:
The idea of "inheritance of acquired characters" was proposed by Jean-Baptiste Lamarck, an early evolutionary biologist. According to Lamarck's theory, organisms can acquire new traits or characteristics during their lifetime through use or disuse of certain organs or behaviors. These acquired traits are then passed on to their offspring.

For example, Lamarck suggested that giraffes acquired their long necks by stretching to reach leaves on tall trees. According to his theory, this acquired characteristic would be passed on to future generations, resulting in longer necks in giraffes.

However, the concept of inheritance of acquired characters has been largely discredited and is not supported by modern genetics. The passing on of acquired characteristics is not a mechanism for evolutionary change in Darwinian theory. Instead, Darwinian evolution relies on the principles of variation, heritability, and natural selection to explain the adaptation and diversity of species.

In conclusion, the idea of "inheritance of acquired characters" is not related to Darwinian evolutionary theory. Darwin's theory is based on natural selection, while the concept of inheritance of acquired characters was proposed by Lamarck and is not supported by modern scientific evidence.