The simplest description of the difference between these two approaches that I have found are on this site who summarise the difference as:

Mechanistic model: a hypothesized relationship between the variables in the data set where the nature of the relationship is specified in terms of the biological processes that are thought to have given rise to the data. The parameters in the mechanistic model all have biological definitions and so they can be measured independently of the data set referenced above.

Phenomenological/Statistical model: a hypothesized relationship between the variables in the data set, where the relationship seeks only to best describe the data.

Could someone exemplify this difference with a short example. I have used and understand the principals of a statistical model (multiple regression etc) but haven't come across any simplistic examples of a mechanistic model and I don't understand what the difference would be in practice.

Edit: I am leaving the question open for a week to see if anyone wants to create a very small 'MWE' of the two types to illustrate what the difference would look like in practice, if not I will accept Memmings answer

  • $\begingroup$ If you are interested in mechanistic models a great resource comes from books on statistical thermodynamics and in general anything coming out of physically motivated biological research. A good reference is "Physical Biology of the Cell" which is supposed to be a physics driven equivalent to the Alberts et al "Molecular Biology of the Cell" book. $\endgroup$ – nbafrank Feb 13 '16 at 5:07
  • $\begingroup$ The question is interesting (+1) and on-topic here. However, I think that you might want to consider asking such question on Philosophy.SE. $\endgroup$ – Remi.b Feb 13 '16 at 22:13

Mechanistic model answers the how question. These models are usually biophysically detailed, and designed to be causal. Say you discovered a linear relation between blood pressure drug and heart rate. This would be a statistical model. It doesn't tell you how the two are related biophysically. One could build a detailed model that describes intermediate processes from the drug entering the system, to binding to receptors, and modulating levels of hormones, and acting as a signal to the heart rate modulation system. This model would have more parameters, and if it predicts the phenomena and generalizes well, then it might be a good approximation of the system. Moreover, it generates hypotheses and is more interpretable.

That being said, I do not think the two concepts are mutually exclusive. Some mechanistic/biophysical models can also be statistical at the same time. It's a matter of having enough data and constraints to be able to fit the model or not.

  • $\begingroup$ Thank you for your answer. So for the mechanistic model lets say that the processes you mentioned are the only ones (enter the system, bind to receptor, modulate levels of hormones, signal to the heart rate modulation system). So for the first stage the mechanistic model would take into account amount of drug and work out absorption relating to the concentration gradient? While a statistical approach would look at marginal increases in drug absorption given a set increase in drug administered? $\endgroup$ – PaulBarr May 15 '15 at 8:28
  • $\begingroup$ @PaulBarr I think you are missing the point. If you had the appropriate data, you can always use statistics to answer the how question. Mechanistic models sometimes don't have that luxury, and are pieced together from partial knowledge from here and there. Statistical modeling exploits the observed variables, in my example, those would be only the drug administration and the heart rate. $\endgroup$ – Memming May 15 '15 at 14:29
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    $\begingroup$ I understand that you can use statistics to answer how something works. Specifically I don't understand the difference in how the model would actually look in practice, when it has been coded in R etc. As a side question are you saying mechanistic models work best when there is partial knowledge, it appears intuitive to me that the opposite would be true. Thanks for your help $\endgroup$ – PaulBarr May 15 '15 at 16:48
  • $\begingroup$ @PaulBarr Usually, you can simulate the mechanistic model, but often difficult to fit its parameters from data. To build the mechanistic model, it is often necessary to make assumptions about the dynamics and parameters which are not strongly supported by data. $\endgroup$ – Memming May 15 '15 at 17:14
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    $\begingroup$ No worries, I'm not looking for an actual realistic model I just would like to see the difference illustrated if possible. I will leave the question open for a week and if no-one is keen Ill accept your answer. Thanks again $\endgroup$ – PaulBarr May 15 '15 at 17:45

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