Ecology: From Quantitative Foundations to Artificial Intelligence VOLUME I of III (The Scottish Science Companion Books)

Product Description

This treatise begins from a proposition about the present character of ecology. Ecology remains biological in its object: its objects are organisms, populations, communities, ecosystems and the relations among them. But its explanatory core is no longer adequately described as a collection of qualitative biological observations. In its mature quantitative form, the core of ecology is applied mathematics. Rates of birth and death become differential and difference equations; age and stage structure become matrices; continuous traits become projection kernels; interactions become coupled dynamical systems; uncertainty becomes probability and likelihood; adaptation becomes optimisation and evolutionary dynamics; spatial structure becomes stochastic geometry and dispersal theory. The organism is still there, but the explanatory object has become the mathematical structure connecting observations. The architecture of this work is deliberate. The first volume establishes foundations, population ecology and the mathematical core. The later volumes carry the same logic into interactions, communities, ecosystems, spatial ecology, global change, conservation, computation and artificial intelligence. The movement is not from biology towards mathematics and then away from it. It is the progressive discovery that biological questions are often most sharply stated, tested and criticised through mathematical models. A further principle governs the exposition. Formulae are not introduced merely because they are standard. Where the derivation is short enough, it is given. Where a model is structurally limited, the limitation is made explicit. Where empirical evidence is ambiguous, the ambiguity is retained rather than repaired by rhetoric. A model is valuable not because it resembles nature in every detail, but because its assumptions can be exposed and its consequences tested. The reader should consequently expect a treatise rather than a catalogue. The objective is not to memorise isolated models, but to recognise the mathematical operations that recur under different ecological names: balance, feedback, averaging, projection, optimisation, inference and stability. Richard Murdoch Montgomery