The role of **mathematical modelling** in evolutionary biology is pretty questioned, although its integral role in studies on evolution. Differently from other scientific disciplines, such as Physics or Chemistry, Biology was born as a descriptive science, and the affirmation of mathematics as an effective and indispensable part of investigation is still to be fully accomplished. In evolutionary research, an important role of mathematics is to provide a “**proof-of-concept**” test of verbal explanations, paralleling the way in which empirical data are used to test hypotheses.

Whereas **the connection between empirical analyses and theoretical modelling** is straightforward in some cases, such as the construction of likelihood functions for parameter inference and model choice, empiricists may not appreciate the importance of **highly abstract models**, which might not provide immediately testable predictions. Probably, skepticism stems from some misconceptions and misunderstandings about mathematical modelling, and a clarification about its role may ease the communication between experimentalists and theoretical biologists.

Some evolutionary biologists from the USA point this out in a very clear paper, published some days ago on **PLOS Biology**, and first-authored by **Maria Servedio** from the **University of North Carolina**. The parallels between empirical experimental techniques and proof-of-concept modeling in the scientific process are explained in the following flowchart.

As shown, the proof-of-concept models are **best suited to test the logical correctness of verbal hypotheses**, such as the effectivity certain assumptions have to lead to certain prediction. Hypotheses which assumptions are most commonly met in Nature, are instead argued to be possibly addressed by **empirical approaches only**.

Discussion on most common misunderstandings is centred around **three main points**.

The authors **first** argue that the main misunderstandings, in matter of mathematical modelling, happen as theoreticians are asked how they might **test their proof-of- concept models empirically**. The models are discussed to be themselves tests of validity of verbal assumptions, and their outcome can thus determine **whether a verbal model is valid or defective**.

**Second**, this does not mean that **proof-of-concept models** do not need to **interact with empirical work**. Actually, in most of cases, quite the contrary is true. Many vital links between theory and natural systems can be found in assumption stage, prediction stage and even in discussion stage, when empirical results are threaded into a broader conceptual framework.

**Third**, authors point out that a **discordance between theoretical predictions and empirical data** may be a great point of interest, giving to both theoreticians and experimentalists the opportunity to appreciate underrated phenomena, or to reconsider the assumptions and empirical procedures.

Despite this paper discusses in detail the role of theoretical modelling in evolutionary biology, we should take our time to reflect, in general terms, on the relationship between experimental work and mathematical modelling. I am very next to write about the criticism that is investing some of the most common algorithms for NGS data analysis, because I have the feeling that the search of proper mathematical modelling algorithms will be one of bioinformaticians’ main occupation in coming years. This article serves thus as a fair example, even if not directly applicable to all the fields of life sciences, of how the relationship between empirical and mathematical work should be properly interpreted.

Evolution is 4th grade math and nothing more (set theory). For example each progeny is an intersection of its parents genes. This is fact necessarily creates a nested hierarchy whereby each generation is permitted only a very slim margin for error and all other characteristics come from the predecessor. It’s not a coincidence that all apes have fingernails and no reptiles do. Rather, it is a necessary consequence that arises from a nested hierarchy simply being set and subsets.

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