Biology takes a special place among the other natural sciences because biological units, be they pieces of DNA, cells or organisms, reproduce more or less faithfully. As for any other biological processes, reproduction has a large random component. The theory of branching processes was developed especially as a mathematical counterpart to this most fundamental of biological processes. This active and rich research area allows us to make predictions about both extinction risks and the development of population composition, and also uncovers aspects of a population's history from its current genetic composition. Branching processes play an increasingly important role in models of genetics, molecular biology, microbiology, ecology and evolutionary theory. This book presents this body of mathematical ideas for a biological audience, but should also be enjoyable to mathematicians.

This book was first published in 2004. Unraveling the origin of biodiversity is fundamental for understanding our biosphere. This book clarifies how adaptive processes, rather than geographic isolation, can cause speciation. Adaptive speciation occurs when biological interactions induce disruptive selection and the evolution of assortative mating, thus triggering the splitting of lineages. Internationally recognized leaders in the field explain exciting developments in modeling speciation, together with celebrated examples of rapid speciation by natural selection. Written for students and researchers in biology, physics, and mathematics, this book is a groundbreaking treatment of modern speciation science.

As anthropogenic environmental changes spread and intensify across the planet, conservation biologists have to analyze dynamics at large spatial and temporal scales. Ecological and evolutionary processes are then closely intertwined. In particular, evolutionary responses to anthropogenic environmental change can be so fast and pronounced that conservation biology can no longer afford to ignore them. To tackle this challenge, areas of conservation biology that are disparate ought to be integrated into a unified framework. Bringing together conservation genetics, demography, and ecology, this book introduces evolutionary conservation biology as an integrative approach to managing species in conjunction with ecological interactions and evolutionary processes. Which characteristics of species and which features of environmental change foster or hinder evolutionary responses in ecological systems? How do such responses affect population viability, community dynamics, and ecosystem functioning? Under which conditions will evolutionary responses ameliorate, rather than worsen, the impact of environmental change?

Emerging diseases pose a continual threat to public health. Short multiplication time and high variability allow pathogens to evolve very rapidly. It is therefore imperative to incorporate evolutionary considerations into longer-term health management plans. The evolution of infectious disease is also an ideal test-bed for theories of evolutionary dynamics. This book combines both threads, taking stock of our current knowledge on the evolutionary ecology of infectious diseases, and setting out the goals for the management of virulent pathogens. Throughout the book, the fundamental concepts and techniques underlying the modelling are carefully explained in a unique series of integrated boxes. The book ends with an overview of novel options for virulence management in humans, farm animals, plants, wildlife populations and biological control schemes. Written for graduate students and researchers, Adaptive Dynamics of Infectious Diseases provides an integrated treatment of mathematical evolutionary modelling and disease management.

The field of theoretical ecology has expanded dramatically in the last few years. This volume gives detailed coverage of the main developing areas in spatial ecological theory, and is written by world experts in the field. Integrating the perspective from field ecology with novel methods for simplifying spatial complexity, it offers a didactical treatment with a gradual increase in mathematical sophistication from beginning to end. In addition, the volume features introductions to those fundamental phenomena in spatial ecology where emerging spatial patterns influence ecological outcomes quantitatively. An appreciation of the consequences of this is required if ecological theory is to move on in the 21st century. Written for reseachers and graduate students in theoretical, evolutionary and spatial ecology, applied mathematics and spatial statistics, it will be seen as a ground breaking treatment of modern spatial ecological theory.