Principles and Practice of Phylogenetic Systematics. Biol Rich Strauss

Transcription

1 Principles and Practice of Phylogenetic Systematics Biol Rich Strauss 1

2 Phylogenetics Phylogenetics: the attempt to infer how organisms are related historically in terms of their evolutionary paths of descent and divergence. = Phylogenetic estimation = Phylogenetic inference = Phylogenetic analysis = Phylogeny reconstruction ti = Tree building Trees describe evolutionary relationships von Baer, 1837 Darwin, 1837 Haeckel, 1870 Darwin,

3 But first: some philosophy of science The scientific method is usually portrayed strictly in terms of cycles of hypothesis-testing. Has been criticized for not sufficiently recognizing the role of creativity in science. Leaves no room for exploration and description. Alternative view: scientists create and modify models. Man tries to make for himself, in the fashion that suits him best, a simplified and intelligible picture of the world; he then tries to some extent to substitute this cosmos of his for the world of experience, and thus to overcome it. This is what the painter, the poet, the speculative philosopher and the natural scientist do, each in his own fashion. Albert Einstein, Essays in Science, 1934 Models Models: simplified representations of objects, patterns, or processes. Models are (dark, distorted) windows into the real world, and form the basis for thinking and communicating about it. Many kinds of models: 2D representations of 3D objects (maps). Space-filling molecular models (mechanical models). Growth equations (mathematical models). Simulations (computer algorithms). Natural selection (original verbal, later mathematical). Extrasensory perception (verbal, lacking evidence). Stories, poems, artistic representations, religions. 3

4 Scientific model A mental construct that summarizes a large number of observations and provides novel predictions about new observations. Useful simplification of some aspect of the world. Provides: (1) Explanation: explain (account for) observations, and help make sense of the world. (2) Prediction: consequences of models (=hypotheses) tested by comparison to new (perhaps prior) observations. The more novel and explicit the predictions, the better. If consequences are falsified, then the model is falsified (or must be adjusted to account for the problem). Models that account for the past but fail to predict the future (e.g., many economic and ecological models) are of limited utility in science. Models provide creativity and beauty in science. Scientific models Where do models come from, and how are they used? First you guess. Don t laugh, this is the most important step. Then you compute the consequences. Compare the consequences to experience. If it disagrees with experience, the guess is wrong. In that simple statement is the key to science. It doesn t matter how beautiful your guess is, or how smart you are, or what school you graduated from, or what your name is. If it disagrees with experience, it s wrong. That s all there is to it. Richard Feynman 4

5 Scientific models Model is a compromise between simplicity and reality. Incorporate the important aspects of a process and omit the unimportant aspects. Models differ with respect to what s important and what s unimportant. All models invoke assumptions. A model: Gives meaning to facts (observations). Assigns more importance to some facts that others. Integrates existing facts. Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house. Jules Henri Poincaré, 1883 Just as the same stones can be used to make different houses, so can a set of facts be given different meaning by different theories by organizing them differently, emphasizing different behaviors, and inferring different hypothetical constructs. P.H. Miller, 1993 More interesting quotations about models Make things as simple as possible, but no simpler. Albert Einstein Science may be described as the art of systematic over-simplification. Karl Popper Nothing is less real than realism. Details are confusing. It is only by selection, by elimination, by emphasis, that we get the real meaning of things. Georgia O Keeffe There are surely no true models in the biological sciences. David R. Anderson All models are wrong; some models are useful. George E. P. Box 5

6 Why mathematical models? If you know a thing only qualitatively, you know it no more than vaguely. If you know it quantitatively grasping some numerical measure that t distinguishes i it from an infinite number of other possibilities you are beginning to know it deeply. You comprehend some of its beauty and you gain access to its power and the understanding it provides. - Carl Sagen Testing scientific models Two concepts are important in the comparison and testing of scientific models: Parsimony Falsification 1) Parsimony (Occam s razor): William of Ockham ( ), English philosopher: Pluralitas non est ponenda sine necessitate. Explanations should not be multiplied needlessly. Simpler models are always preferred over more complicated models that explain the same observations, other things being equal. Simpler models require fewer assumptions or fewer pieces of information than complicated models, and thus are more likely to generalize. 6

7 Testing scientific models Use of parsimony as a criterion for choosing among models does not imply a belief that the world is simple. Simplicity relates to the predictive value of a model. Implemented by methods such as: Bayesian theory: rewards simpler models for sharper predictions. Information theory: quantifies degrees to which simplicity it (number of parameters) and goodness-of-fit fit contribute to the expected predictive accuracy of a model. Testing scientific models Simpler models require fewer assumptions or fewer pieces of information than complicated models, and thus are more likely to generalize. E.g., in statistics, linear regression is parsimonious: (Random points were generated from a linear relationship.) 7

8 Testing models 2) Falsification: Scientific models are falsified rather than proven. Falsification is much more efficient than proof. Deduction vs. induction. Proof or confirmation : Based on data that are consistent with a model. But many observations can agree with an incorrect or insufficient model. Takes only one critical piece of contradictory evidence to falsify a model. Scientists don t prove models, they attempt to falsify them. Testing models It is a good morning exercise for a research scientist to discard a pet hypothesis every day before breakfast. It keeps one young. Konrad Lorenz It is the tentative nature of science and the ability of future evidence to prove current theories wrong that constitutes its great strength. Robert Ehrlich The great tragedy of Science: the slaying of a beautiful hypothesis by an ugly fact. Thomas Huxley 8

9 Scientific models Scientific models are always provisional. Scientists are constantly creating new models and refining old ones. Both activities are imaginative, dynamic, and often artistic processes. Often involves hypothesis testing, but not necessarily. New simpler or more consistent models sometimes replace older models in the absence of any new data. New models are tested against current models in terms of their explanatory and predictive power. Successful models are kept (at least temporarily), while unsuccessful models are modified or discarded. The models that are most successful win out in the long run. Science is the natural selection and adaptation of models. W.I.B. Beveridge Theories Models can lead to theories: Interrelated and internally consistent collections of models about processes (or causes ) that account for the patterns that we observe. Theories often have two components: Statement about a pattern that exists in the natural world. Hypothetical process (or set of processes) that explain (account for) the pattern. Example: theory of population genetics. Observation: populations change in genetic composition and structure over time. Explanatory processes: mutation and linkage, gene flow, genetic drift, natural selection, etc. 9

10 Scientific models Science is the ultimate democratic and capitalistic enterprise, in which ideas are the currency. Anyone is allowed to play. Players are limited only by knowledge and creativity. Long-term success of a scientist is judged by ability to: (1) Devise experiments having a greater ability to distinguish between competing models. (2) Make unexpected observations that can t be accounted for by current models. (3) Devise new models having greater explanatory and predictive e power. All new knowledge and ideas immediately become public domain: To be tested by others. To be modified and improved by others. Scientific models Good models require creativity and imagination. Initial models and theories (especially big ones) often are associated with the names of their creators: Newtonian physics (theory of gravity). Bohr s theory of the atom. Einstein s theory of relativity. Mendelian genetics. Watson & Crick model of DNA structure. Darwinian evolution. Often not immediately accepted by other scientists until either: et e Deficiencies are corrected. New observations are made that are predicted by the model. Models later become modified, elaborated and dissociated from the originator. 10

11 The phylogenetic model Two components: anagenesis and cladogenesis. To what extent is this model satisfactory or unsatisfactory? What assumptions are being made in using this model? Fitting models to data The purpose of data is to test alternative models. Models suggest data. Data restrict t models (e.g., continuous vs. discrete). Null model: Statement of minimal or random structure in the data. Forms the basis for hypothesis-testing in classical statistics. In general: null hypotheses can be rejected, but not accepted. Q: What is the null model in a phylogenetic study? 11

12 Fitting statistical models to data A particular model is fitted to data by finding the instantiation that best matches the data. For example: Finding the straight line (slope + intercept) that best fits a scatter of data points. Finding the tree (topology + branch lengths) that best matches the distribution of character states among taxa. The best model is the one that is most consistent with the data in some sense. The fitting of a model is always based on some set of assumptions. Residual variation: variation in the data that is not accounted for by the model. Maximizing consistency = minimizing residual variation. Finding the best model is an optimization problem. Based on: An optimization criterion (=objective function, =cost function) that can be scored for each instantiation of the model. A procedure for finding the instantiation (from the set of all possible instantiations) having the minimum or maximum value of the optimization criterion. Different optimization criteria produce different fits. Choice of an optimization criterion is often based on statistical rather than biological considerations. For complex models, results are often locally optimal approximations rather than globally optimal solutions. Different models can be compared only by how well they fit the data with respect to a particular optimization criterion. The fitting of a model is conceptually separate from utilizing the model for interpretation and understanding. 12

13 Regression: example of fitting a model Regression is a statistical procedure for fitting a line to a set of observations. 2+ variables Line may be straight (linear) or curved (nonlinear) Objective: to find the line of best fit Q: what is meant by best? Assumptions Optimization criterion Result: partition of the variation in the data into two components: (1) Variation accounted for by the model (line). (2) Residual variation not account for by the model. X X1 Possible least-squares regression models Y 10 r = Y r = 0.30 Y X r = X Y X 10 r = 0.00 X on Y MA Y on X X 13

14 Different assumptions and optimization criteria give different fits (instantiations). Produce different parameter estimates (slope + intercept). p) All are optimal, but in different senses. Can t be compared for degree of fit because there is no common criterion. A claim that one model is better than another must be based on extrinsic criteria (arguments about assumptions and optimization criteria). The linear-regression model is the assumption of ignorance. There are an infinite number of kinds of nonlinear models. Trees are models fitted to data Finding the best tree is a regression problem. Both produce decomposition: Model + residual variation. Given assumptions and an optimization i criterion. i Regression: line + residual variation. Phylogenetic inference: tree + residual variation (homoplasy). In both cases, the result in an average solution for the data. The regression line lies in the center of the scatter of data. The root of the tree has an average characterstate value. 14

15 X2 X2 X1 X1 The best tree is the one that is most consistent with the data in some sense. Different inference methods (models) are based on different optimization criteria. Parsimony (=minimize sum of absolute branch lengths). Least-squares (=minimize sum of squared branch lengths). Maximum likelihood (=find the tree that best predicts the data, given a particular model of evolution). Infinite number of possible optimization criteria. Arguments about which model is best can t be solved by comparing degree of fit. No biological criteria for choosing among alternatives. Assumptions are usually based on statistical or computational expediency. E.g., assumptions that characters are independent (uncorrelated) and equivalent. 15

16 All criterion-based methods are based on some model of evolutionary process, usually a random-walk model. Parsimony : Lévy walk Least-squares: Brownian walk Maximum-likelihood (Felsenstein implementation for continuous characters): Brownian walk Somewhat more stringent assumptions than leastsquares. An infinite number of other maximum-likelihood models are possible, one for each type of random process. Some methods of inferring trees are based on algorithms rather than optimization criteria. E.g., distance methods such as UPGMA and neighborjoining trees. Not guaranteed to be optimal in any sense. Repeat: Finding the best model is an optimization problem. Based on: An optimization criterion (=objective function, =cost function) that can be scored for each instantiation of the model. A procedure for finding the instantiation (from the set of all possible instantiations) having the minimum or maximum value of the optimization criterion. Different optimization criteria produce different fits. Choice of an optimization criterion is often based on statistical rather than biological considerations. For complex models, results are often locally optimal approximations rather than globally optimal solutions. Different models can be compared only by how well they fit the data with respect to a particular optimization criterion. The fitting of a model is conceptually separate from utilizing the model for interpretation and understanding. 16

17 Trees are summaries of data Models are summaries of data; therefore trees are summaries of data. From the data, there ain t nothing but character trees (e.g., gene trees). Cladogram / dendrogram: summary of data. Phylogenetic tree: Assume that characters are representative of taxa. Assume that nodes represent hypothetical ancestors. Replace terminal character states by taxon names. Evolutionary tree: add the dimension of time. Branch lengths assumed to represent rates of evolution (anagenesis). Nodes represent speciation events (cladogenesis) Character states Taxa 1 3 A B C D E F G H Cladogram I Phylogenetic tree 17

18 Problems with the practice of phylogenetics: Too many mental shortcuts. E.g., treating a cladogram as if it were a phylogenetic or evolutionary tree. Over-reliance on software. Using favorite methods based on software availability or the bandwagon effect. Use of computer programs as black boxes. Use of diagnostic tools without an understanding of what they mean. Bootstrap support values Permutation-test probabilities Bayesian posterior probabilities Information statistics In science, appeal to authority is never, pp y an adequate justification to do anything. 18