Phylogenetic inference and philosophy, different approaches for the same purpose

************** This post was updated on 27.01.2016***************

Phylogenetic inference attempts to elucidate the evolutionary relationships among organisms.
Various approaches have been made for this purpose, they differ in their rationale for addressing the problem (De Queiroz & Poe, 2001). Among the best known approaches are parsimony, bayesian inference and  likelihoodism. Below I will discuss some of its characteristics, basic assumptions and finally express which one, in my opinion, comes more adequately to face a phylogenetic analysis.

Parsimony has its grounds in the principle of simplicity. Proponents of the principle of parsimony argue that this approach is justified by the ideas of Karl Popper. This implies that the phylogenetic hypothesis must be falsifiable and  rigorous tests, so be corroborated. From this perspective, those hypotheses with the least amount of  changes should be preferred, thus minimizing the number of ad hoc explanations (Grupe & Harbeck, 2015). But the preference for simpler explanations does not mean that nature behaves well, evolution does not have to be parsimonious. This seems difficult to understand, and in fact, sounds contradictory.

Statistical approaches such as maximum likelihood or Bayesian inference share using evolutionary models that take into account the probability of  changes  between  character states and base frequencies (Archibald, Mort, & Crawford, 2003). In a parsimonious approach  seems that these changes are equally likely.

The likelihood method can be defined as the probability of a hypothesis given the data   of the data given a hypothesis. This approach seeks to find that hypothesis explains the observed data (characters) in the manner that maximizes the probability that these are observed.

Bayesian inference is different from the likelihood that takes into account prior knowledge to the observations,  it is posibe assign probabilities to hypotheses (Topologies) before observations are made. The main problem with the Bayesian inference is its distinguishing feature. The priors can be a double-edged sword, on the one hand allow the process to incorporate prior knowledge of phylogenetic inference, but actually priors are difficult to accurately estimate  (Velasco,2008). For several authors is a common practice then assign equal priors, but this means that the main advantage of this method had just wasted . Additionally, what if the priors are estimated incorrectly, this could result in a bias in the results of the process.

The advantages of statistical methods seem obvious, they make assumptions on a given model. Parsimony however, assumes any evolutionary model, or does this mean that the changes are equally likely, it does not seem logical, especially if we speak of continuous characters. Given these difficulties with the priors, in my opinion, a likelihoodism approach is most appropriate for phylogenetic inference.

References

• Grupe, G., & Harbeck, M. (2015). Taphonomic and Diagenetic Processes. En W. Henke & I. Tattersall (Eds.), Handbook of Paleoanthropology (pp. 417–439).
•  De Queiroz, K., & Poe, S. (2001). Philosophy and phylogenetic inference: a comparison of likelihood and parsimony methods in the context of Karl Popper’s writings on corroboration. Systematic Biology, 50(3), 305–321.
• Archibald, J. K., Mort, M. E., & Crawford, D. J. (2003). Bayesian inference of phylogeny: a non-technical primer. Taxon, 187–191.
• Velasco, J. D. (2008). Philosophy and The Tree of Life (Doctoral dissertation, Ph. D. Thesis). University of Wisconsin-Madison).

  

Maximum Likelihood versus Parsimony and Bayesian inference

Many authors emphasize in parsimony method by resorting to realism, and the simplicity of the assumptions (Goloboff, 2003). While others say that parsimony subject to specific models is the same as Likelihood (Farris, 1983). Below I will discuss some arguments that lower use of parsimony as a method to clarify the evolutionary relationships among organisms. 

First, that offers simplicity parsimony in assumptions does not mean that these are clear and they are the best. Many wonder what really are the assumptions about the evolutionary process that takes parsimony method? Just assume that the offspring having modification with respect to their ancestors? Assumptions parsimony leave many doubts. 

Second, parsimony does not discriminate changes in the branches are more probability or improbable. It not assumed if a branch is more probability to change over another (Sober, 2004). It is, for parsimony no selection for one character over another (Sober, 2002). It is at this point that the Maximum Likelihood method has its advantages. Using evolutionary models allows us from propositions given by the data and calculate the probability given the hypothesis (Goloboff, 2003). In addition to the rate of Likelihood we can measure the strength of the statistical evidence and so choose the topology more Likelihood (Royall, 1999). 

 On the other hand, it is the Bayesian inference method, a probabilistic method like Likelihood uses evolutionary models. This method uses priors basis for calculating the posterior probability of the data given hypothesis. One risk of using priors is that these can become subjective and condition the calculation of posterior probabilities. I personally think that Bayesian inference is a modification of Likelihood, but with more potential for bias given the priors. 

Andrea Lizeth Silva Cala 

Reference

Goloboff, P. A. (2003). Parsimony, likelihood, and simplicity. Cladistics, 19(2), 91-103.

Farris, J. (1983). The logical basis of phylogenetic analysis (pp. 7-36). na.

Sober, E. (2004). The contest between parsimony and likelihood. Systematic biology, 53(4), 644-653.

Sober, E. (2002): “Reconstructing Ancestral Character States – A Likelihood Perspective on Cladistic Parsimony.” The Monist 85: 156-176.

Royall, R. (1999): The Strength of Statistical Evidente. Johns Hopkins University Department of Biostatisks 615 North Wolfe Street Baltimore MD 2120.5 USA

Bayesianism and likelihoodism

¿Bayesianism or Likelihoodism?

Let me start with the Royall's three questions:

1. ¿What does the present evidence say?

2. ¿What should you believe?

3. ¿What should you do?

Although Likelihoodists and Bayesians both share the likelihood principle and the law of likelihood which are important in the philosophy of scientific method, they disagree on several instances:

Its necessary highlight that the most remarkable difference between them is that Bayesians use prior probabilities in other words posterior probability distributions that require prior probability distributions and likelihood functions and likelihoodists not.

Another difference points to the meaning of evidence: Likelihoodists characterize data as evidence and they don't use them to guide our beliefs or actions and maintain that this characterization is valuable in itself (Royall 1997, Ch. 1). Then, you couldn't give answer to the second nor the third question of Royall because they say nothing about what you should believe after you receiving the evidence without take into account what you believe before receiving the evidence. On the other hand forBayesians the prior is updated in the light of new data that is the evidence (Sober, 2008) from this perspective you could give answer to all questions.

Regarding to the second question about your degree of belief Bayesians answer this question from the concept of confirmation where the observation (O) provides confirmation of hypothesis 1 (H1) when this has a higher likelihood than its own negation (Gandenberger, 2013). Unlike Likelihoodists whom doesn't use this concept of confirmation, they don't take into account if the evidence raises, lowers or not change the probability of the hypothesis. They compare hypotheses to each other which have their own likelihoods and use the law of likelihood to interpret the data where: the observation (O) favors hypothesis 1 (H1) over hypothesis 2 (H2) if Pr (O | H1) > Pr (O | H2) and the likelihood ratio is used to show the degree to which O favors H1 over H2 that is given by Pr(O | H1) / Pr(O | H2), and they ask if H1 has a higher likelihood than H2. So, for likelihoodists is enough use the likelihood ratio as a measure of degree favoring one hypothesis over other one (Sober, 2008). In contrast to Bayesian for whom is not enough and then implemented the use of posterior probabilities, see below.

In Bayesian inference you assign a probability to the hypothesis (H) before doing an observation in other words is the distribution of the parameters before doing analysis of the data (prior probability) and after of doing it there is a reallocation of the probability assigned to H and the probability in the light of evidence is known as posterior probability and is denoted Pr(H|O) that means probability of the Hypothesis given the Observation. In contrast Maximum likelihood where the likelihood of the hypothesis is the probability that H confers on O Pr(O|H) (Sober, 2008).

Other thing in common is that ML and BI use the same models of evolution, but the way to measure the support of relationships in the topology are different, ML uses bootstrap support (BS) which is a measure of confidence, and uses data resampling to estimate the support (Cummings et al., 2003). Unlike BI that uses the posterior probability (PP) which is calculated from prior probability, likelihood functions and data. Both measures have been controversial because of several reasons and some claim there is a equivalence between both measures (Efron, H. and Holmes, 1996), but some studies like Erixon et al. (2003) reject this assumption and others claim PP is a better measure of support (Alfaro, Zoller, and Lutzoni, 2003).

Given the similarities and differences between them I think that Bayesian inference is the best method of all.

Bibliography

Alfaro, M. E., Zoller, S., & Lutzoni, F. (2003). Bayes or bootstrap? A simulation study comparing the performance of Bayesian Markov chain Monte Carlo sampling and bootstrapping in assessing phylogenetic confidence. Molecular Biology and Evolution, 20(2), 255–266.

Cummings, M. P., Handley, S. A., Myers, D. S., Reed, D. L., Rokas, A., & Winka, K. (2003). Comparing bootstrap and posterior probability values in the four-taxon case. Systematic Biology, 52(4), 477–487.

Efron, B., Halloran, E., & Holmes, S. (1996). Bootstrap confidence levels for phylogenetic trees. Proceedings of the National Academy of Sciences, 93(23), 13429.

Erixon, P., Svennblad, B., Britton, T., & Oxelman, B. (2003). Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylogenetics. Systematic Biology, 52(5), 665–673.

Gandenberger Greg . 2013. Why I am not a likelihoodist.

Royall, R. Statistical Evidence: A Likelihood Paradigm, Boca Raton, Fla.:Chapman and Hall.(1997).

SOBER, Elliott. Evidence and evolution: The logic behind the science. Cambridge University Press, 2008.

 

Philosophy in the biological world

The discussion about construction of how knowledge is built are not new, from Plato and his proposed world of ideas to Kant in his criticism to pure reasons(1) is underlined that the construction of knowledge which we call science is not dogmatic and static, instead it is a non volatile element and  a conditioned subject to time-space paradigm own of humanity, reducing everything to a purely linguistic problem (2). Therefore, syncretism is not a symptom of intellectual immaturity or inferiority of it, but a prudent demonstration against scholastic thought own religious processes, some scholars confused with scientific work.

Added to all this it is important to clarify that, contrary to sciences like mathematics, physics, and chemistry. The theoretical corpus in biological sciences completely lacks axiomatic systems that support the developed theories. While evolution is a fact. The causality of the phenomenon is highly debated due to the number of ad-hoc theories and hypotheses (3, 4). It is in this environment that the phylogenetic theories that attempt to answer the evolutionary relationships of organisms are developed. Therefore this essay  put on the table Bayesian analysis , the likelihood and parsimony as "irreconcilable" philosophical. Trying to approach the reality of evolutionary phenomena (not yet finished to be clear) to consider some as "the best ".

Let's start with the parsimony in which methodologically the tree with fewer transformations is selected, this is derivative of the philosophical principle that the simplest theory must be correct for being the least complex (5). A strongly nominalism position that can result in multiple ad- hoc theories that could never be applied to different events rather than the themselves cases. Following this logic we could generate own theories for each type of phylogenetic relationships of every living form. Which will lead to a greater number of hypotheses the number of species (counting the species already extinct). Which paradoxically ends up being contrary to the principle of parsimony.

In contrast to the  parsimony, the probabilistic models certainly have an advantage developing stochasticity in their methods, thus avoiding a possible fall in phylogenetic Laplace demon advantage. Maximum likelihood analyzes the conditional probability of the observations given the hypothesis, or in more colloquial terms how well the data fit in a given hypothesis. In which each tree is considered a hypothesis generated by choosing the highest likelihood. However likelihood ignores previously gathered evidence about the event at that epistemological terms can only be assigned certain degree of value as truth. By contrast,  Bayesian analysis is an excellent tool for the analysis of phylogenetic hypothesis by quantifying past evidence (prior) and included in the phylogenetic analysis. It is therefore the most appropriate tool to address the problem to elucidate the evolutionary relationships of living forms.

References

1. Kant, Immanuel, and Norman Kemp Smith. 1929. Immanuel Kant's Critique of pure reason. Boston: Bedford.
2. Wittgenstein, Ludwig. 1922. Tractatus logico-philosophicus. London: Routledge & Kegan Paul.
3. Margulis, Lynn; Dorion Sagan (2003). Captando Genomas. Una teoría sobre el origen de las especies. Ernst Mayr (prólogo). David Sempau (trad.) (1ª edición). Barcelona: Editorial Kairós
4. Darwin, Charles Robert. The Origin of Species. Vol. XI. The Harvard Classics. New York: P.F. Collier & Son, 1909–14.
5. Robert Audi, ed., Ockham's razor, The Cambridge Dictionary of Philosophy (2nd Edition), Cambridge University Press.