Darwin's ideas are really important for the concept of Modern Synthesis, which came about in the early to mid-1900s. This idea combines Darwin’s thoughts on evolution with Mendelian genetics, helping us understand how evolution works.

Key Contributions of Darwin’s Theories:

1. Natural Selection:

   • Darwin introduced natural selection. This is the idea that animals and plants with helpful traits are more likely to survive and have babies.
   • For example, researchers studied finches, a type of bird, and found that their beak sizes changed depending on what food was available. During dry times, finches with bigger beaks could eat better, leading to a 20% rise in their population.

2. Variation and Adaptation:

   • Darwin pointed out how important it is for there to be differences among individuals in a species. These differences allow natural selection to happen.
   • The tortoises in the Galápagos Islands had different shell shapes depending on where they lived. This showed how they adapted to their surroundings.

3. Common Descent:

   • Darwin suggested that all species come from common ancestors. This idea helps us understand how different species are related.
   • Genetic studies have shown that humans share about 98.8% of their DNA with chimpanzees, supporting the idea of common ancestry.

Integration with Genetics:

The Modern Synthesis came about when scientists like R.A. Fisher and J.B.S. Haldane brought Mendelian genetics into the study of evolution. This combination led to:

• Population Genetics: This looks at how gene variations exist in groups of living things, helping to predict how evolution may happen.

• Statistical Models: One example is the Hardy-Weinberg principle, which is written as $p^2 + 2pq + q^2 = 1$. This shows how gene frequencies in a group can stay the same unless something changes evolutionarily.

Conclusion:

Darwin's theories set up the foundation for Modern Synthesis by introducing important ideas about evolution. Later, these ideas were combined with genetic research. The mathematical approach from genetics gives us a better understanding of how adaptation and new species happen. So, Darwin's thoughts not only changed biology in his time but also shaped our current understanding of evolution.