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A philosophical approach to model complexity Jim Smith

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Some types of environmental model Mechanistic Empirical Statistical/Stochastic Deterministic Bayesian Behaviour-based Dynamic Process-based Analytical Numerical Kinetic Matrix Predictive Neural network

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How do we judge good science? Publications High impact journals Citations Reputation Mechanistic or reductionist approach to studying complex systems. New processes New insight/understanding Complex models Detailed experiments

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Chernobyl

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Radioactive pollution of lakes

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Aquatic food webs

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Interaction of Cs-137 with lake sediments Cs + Burial of sediment AqueousSolid phases Lake water

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Fish sub-model

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Caesium-potassium model

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Empirical caesium- potassium model Vanderploeg et al. 1975

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Water Fish kfkf kbkb

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Any given set of empirical observations may be explained (fitted) by an infinite number of possible models (hypotheses). Historical explanation (curve fitting) is relatively easy. How do we decide which is the best model/explanation? Two key criteria: - Simplicity - Predictive power. Equifinality Ludwig von Bertalanffy (1901--1972)

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It is vain to do with more what can be done with less. - William of Ockham Ockhams razor

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If the consequences are the same it is always better to assume the more limited antecedent - Aristotle, Physics.

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We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances - Newton, Principia.

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Everything should be made as simple as possible, but not simpler." - Einstein, Autobiographical notes.

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Complexity and predictive power Conjecture and refutation

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Conjecture and Refutation Karl Popper Form a hypothesis (by any means you like) Test the hypothesis against empirical evidence The best theory is the simplest one which stands up to the most critical tests.

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Some types of environmental model Mechanistic Empirical Statistical/Stochastic Deterministic Bayesian Behaviour-based Dynamic Process-based Analytical Numerical Kinetic Matrix Predictive Neural network

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Does ecology work like this? - Very rarely (Peters) Vague and/or untestable general theories –Density dependent relationships and population models –Evolutionary ecology –Ad-hockery and historical explanation Quantified but trivial mini-hypotheses –Detailed studies of model systems –Tractable mini-questions How many blind tests of predictive models do we see? How many failures?

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Physics is simpler than environmental science

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Some characteristics of useful predictive environmental models Simple in structure Few driving variables Ignore many processes Strong empirical basis Applied to many systems Well tested

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Some predictive models in ecology Phosphorus in lakes – Wollenweider model Lake Phosphorus inflow Phosphorus sedimentation Phosphorus outflow

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Some predictive models in ecology Radiocaesium in rivers and lakes Lake Cs-137 inflow Cs-137 sedimentation Cs-137 outflow Fish

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Conclusion The central purpose of environmental science is not to understand or simulate complex ecosystems, but to provide practical solutions to real environmental problems. "All models are wrong, but some are useful." - George Box

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