There are several recommended books for mathematical ecology for the UPSC Mathematics Optional exam. These books not only provide a comprehensive understanding of mathematical ecology but also help in developing problem-solving skills and analytical thinking. Here are some of the recommended books:

1. "Mathematical Ecology" by J.D. Murray:
- This book is considered a classic in the field of mathematical ecology.
- It covers various topics such as population dynamics, competition, predation, disease, and spatial ecology.
- The book provides a rigorous mathematical treatment of ecological models and their analysis.
- It includes numerous examples, exercises, and applications to real-world ecological problems.

2. "Mathematical Models in Population Biology and Epidemiology" by Fred Brauer and Carlos Castillo-Chavez:
- This book focuses on the mathematical modeling of population dynamics and disease spread.
- It covers topics like population growth, harvesting, competition, predator-prey interactions, and the spread of infectious diseases.
- The book provides a solid foundation in mathematical techniques used in population biology and epidemiology.
- It includes numerous exercises and examples to reinforce the concepts.

3. "Mathematical Ecology of Populations and Ecosystems" by John Pastor:
- This book provides an introduction to mathematical ecology with an emphasis on populations and ecosystems.
- It covers topics such as population growth, competition, predation, mutualism, and community dynamics.
- The book combines mathematical theory with ecological examples and empirical data.
- It includes exercises and problems to test the understanding of the concepts.

4. "Introduction to Mathematical Ecology" by Simon A. Levin:
- This book provides a broad introduction to mathematical ecology.
- It covers topics such as population dynamics, competition, predation, spatial ecology, and evolutionary ecology.
- The book emphasizes the integration of mathematical models with empirical data and experimental observations.
- It includes exercises and problems to enhance the understanding of the concepts.

These books are highly recommended for the UPSC Mathematics Optional exam as they cover the important topics in mathematical ecology and provide a solid foundation in the subject. They are written in a clear and concise manner, making them accessible to both beginners and advanced learners.