Why is the role of mathematics in biology still controversial?

[Cincinnatus]

Unlike in the physical sciences, the role of mathematics in biology is still somewhat controversial. Many leading biologists still know very little about mathematics. This seems to me to be more the influence of history than anything compelled by the field itself.

Many areas of biology today are quite quantitative (and becoming more so) including most (or all) molecular biology. This is due to the influence of bioinformatics, systems biology etc.

Some areas of biology have traditionally been much more quantitative, like neurophysiology since Hodgkin and Huxley. Other areas of biology have maintained both traditions, i.e. evolutionary theory has a highly mathematical branch as well as a large amount of more observational work, such as occurs in paleontology.

I'm interested in what you think about:
a). The historical reason for this lack of quantitative methodology in most of biology.
and
b). Do you think this will change in the future? If so, how long do you think it will be before one won't be able to rightly call themselves a biologist without knowing more math than calculus?

 

[jim mcnamara]

The only graduate math class I ever had was Statistics. But as an undergrad we were required 12 hours of analysis, plus linear algebra, statistics and "modern algebra" - 50 years ago. After trying to read the math forums here I think the course was really "antiquated algebra". :grumpy: I've used statistics a lot.

I now use math extensively, lower level stuff, because I do work for the utility industry, which has only a little to do with Biology.

My take on the primary question is that Biology came into its own well before biochem was even thought about. Physiology, taxonomy, ecology all used some limited math, but applying statistical methods was not really part of the deal until the 1950's. Modeling populations and ecosystems came along in the 1960's.

The reason is fro all this simple. Biology was an alpha-endeavor Science - largely descriptive for many years. It answered questions like: what plants and animals exist, and where do they live, how are they classfied. This is still going on. We have not descibed all of the invertebrate or higher plant species even now. Mammals and birds: we are close to complete - IMO.

Applying math in the sense you describe is more of an omega-endeavor Science. This means putting it all together from the molecular level all the way through to whole ecosystems and climatology. There's only one thing in biology that does that: the Theory of Natural Selection or Evolution if you like. Other disciplines have lots of Laws of this and that. Not Biology.

This means of all of the available problems and directions in Biology, a lot of them are not radically different from the questions we were asking 100 years ago - descriptive.

 

[BoomBoom]

Bioinformatics and systems biology involve huge datasets and probably would be impossible without computers. So, I believe, it's easy to see why in the pre-computer era, there was little mathematics involved in biology.

I also don't believe it is necessary to have higher math skills in this day and age to be a biologist. It all depends on your specialisation. One biologist may choose the path of analysis and become a computational biologist while another may choose a more hands-on bench type of experimental experience. These would both be considered biologists, but require completely different skill-sets and knowledge base.

Going down the road into the future, all a biologist needs to do is punch his data into a computer program that models a biological system. While this would require no higher math skills, the person who develops the program would probably need those skills.

There is nothing really "controversial" about it... IMO

 

[iansmith]

here's my 2 cents

Coming from microbiology, we can dealt with several system where it's an all or none system so math don't real matter in those case. However, biology is moving toward analysis where none or all might not be an option. therefore math models and maths in general becomes more of a prerequisite.

In my opinion, bioinformatics is not really biology is more computer science but using biological theories. I use bioinformatics tools without knowing much of the math being the concept; I however understand the biology behind the concept.

So as boomboom said, it all depend on the field, speciallity and questions that are asked by the biologist.

 

[Bystander]

(snip)My take on the primary question is that Biology came into its own well before biochem was even thought about. Physiology, taxonomy, ecology all used some limited math, but applying statistical methods was not really part of the deal until the 1950's. Modeling populations and ecosystems came along in the 1960's.(snip)

Biometrika, http://biomet.oxfordjournals.org/archive/ , is an excellent and entertaining journal of applied statistical methods, and began publication in 1901; don't recall any models, but lots of pop. studies and stats. Is it NOT a mainstream journal for the life sciences crowd? The library at work had it filed with the math journals, but I'd never really thought it had anything to do with the content, more a matter of where to put non-physics and non-chem literature.

 

[Invictious]

For MY 2 cents,

It is simply due to the nature of biology, that it is descriptive. If it were mathematical, then it would mean applying an equation to many things, and we know for a fact, that it hardly ever applies, as our expected value will differ remotely from the actual value.
There are just so many living things in the world, putting a formula on them will be pointless.

Though, for other things, such as data analysis (standard deviation, concentration of solute etc), there IS some math. I would say there is more 'stoichiometry' than 'mathematics', if I were to put a label on it.

 

[Moonbear]

My view on it is that we can't develop mathematical models until we understand more of the variables first. Math can only be used after there's a sufficient understanding of the field to apply it.

I actually sat through a seminar where someone who was developing mathematical models of neuronal systems got about halfway through the seminar, describing this really complex mathematical formula that only worked for a very simple neuronal model (a synapse between two neurons), and then said, "This is where most people give up trying to model biological systems and go back to engineering." (He was an engineer by training.)

 

[jim mcnamara]

Bystander -
I've never cited any publication from Biometrika for anything. But I also have not published anything in Biology since the 1980's. That does not in any way make it a bad journal, by the way.

As I said stats have been used and sometimes dismissed by a lot of researchers up until the 1960's. Read Moonbear's post. I sat thru lots of seminars where people used eigenvectors and other math tools and statistics to model population genetics, cladistics - you name it. Most of those things were an exercise, fun for the researchers or maybe for mathematicians because of proofs, but none of: informative, predictive, useful. IMO.

 

[Jekertee]

For MY 2 cents,

It is simply due to the nature of biology, that it is descriptive. If it were mathematical, then it would mean applying an equation to many things, and we know for a fact, that it hardly ever applies, as our expected value will differ remotely from the actual value.
There are just so many living things in the world, putting a formula on them will be pointless.

I appreciate anyone who has such insights into biology,
I also agree that it is biology's own problem, and I am completely sure it WILL NEVER help to solve others' problems.
Biology is biology, we might apply math to solve biological problems but never in reverse do we apply biology to model an equation.

 

[BoomBoom]

There are just so many living things in the world, putting a formula on them will be pointless.

Well, yeah, it would be pointless to put a formula on a living thing (unless it had to do with some sort of population study or something). Where math comes into biology though is at the cellular level. A formula wouldn't be modeling an organism, but more likely a cellular pathway (signaling, metabolic, regulatory, etc.). This IS the current frontier in biology these days and math IS involved.

But I still stand by my previous statement that it is not essential for the biologist to come up with these formulas. That is the realm of computational biologists.

 

[Cincinnatus]

I'm actually surprised by the responses here, most people I know think quantitative methodology is the future of Biology.

With regard to the past, don't the neuroscientists here agree that neurophysiology is a pretty classical area of biology which has always been pretty heavily quantitative? Even 50 years ago Hodgkin and Huxley were solving partial differential equations by hand, Katz was using Poisson processes to describe synaptic events etc.

 

[Rade]

This idea that there is more math in other sciences than in biology is true, but for trivial reasons. Biologists study what physicists call "classical" objects and their interactions. The mathematics used in classical physics no different or more advanced than mathematics used by biologists. However, chemists and physicists also study relativistic questions--near speed of light interactions of electrons and nucleons etc.--and such questions derive answers only from advanced mathematics. All of the sciences classify things. Chemists classify elements into a periodic table, physicists classify particles into a standard model, biologists classify species into higher phyla--none of these efforts require any use of advanced mathematics.

Ask a quantum physicist to present you the quantum math equations of all the interactions of the quarks and gluons in the Lead atom. You will see how quickly they turn into biologists in their understanding of mathematics of interactions of complex systems with many interacting parts.

 

[hokiehokie]

Some papers I have read about 80 to 100 years old demand that biologists begin to act like the other sciences and begin to provide a quantitative description of their work.

Some surprising issues have surfaced due to this process. Consider the revelations Has Elias had when he discovered that all of the textbooks had been wrong in describing the structure of the mammalian liver! He realized the transformations that occur when tissue is sectioned and observed under the microscope. This led him to discover a number of other descriptive errors in the literature.

A seemingly simple procedure should be to count the number of something in an organ. It might be cells, organelles, alveoli, corpuscles, capillaries, synapses, nuclei, etc. This turns out to be a rather tricky issue. It is relatively easy to locate papers in journals in which the counting is done wrong.

Counting mistakes have led to misunderstandings in all sorts of research areas. Even though mathematically correct and feasible methods have been developed in the last 20 years, many incorrect studies are done on a regular basis.

Does alcoholism led to loss of neurons? That has been answered yes when counting incorrectly. The answer by properly done studies is no.

Quantification is important. Understanding enough of the math to do proper quantification is important.

The problems encountered in biological quantification require complex mathematics. Maybe the biologist does not see this, but the development of the techniques certainly does. The variance estimation techniques for counting are complex. In fact, at the time of their discovery this was only the second variance estimation known. The only other variance estimation is for simple random sampling.

 

[Moonbear]

I'm actually surprised by the responses here, most people I know think quantitative methodology is the future of Biology.

With regard to the past, don't the neuroscientists here agree that neurophysiology is a pretty classical area of biology which has always been pretty heavily quantitative? Even 50 years ago Hodgkin and Huxley were solving partial differential equations by hand, Katz was using Poisson processes to describe synaptic events etc.

Quantitative methodology means something different from applying mathematical models.

Quantitative methodology simply means you get numbers that are consistent with some standard so you can compare them using statistics. Quantitative methods are things like quantitative real time PCR, where you can say, yes, this cell or tissue sample has more of a certain type of RNA than this other cell or tissue sample. It gives you a number that you plot against a standard. Hormone assays are also quantitative methods. It requires no more mathematics than fitting a line to a curve. We have software that does that for us now, but back before the prevalence of computers, a lot of the original hormone assays were simply plotted by hand on semi-log graph paper...no need to know any more math than how to draw a graph. Toss in some statistics to describe the amount of variation and confidence intervals of your data and you're done. A lot of biology is quantitative in this sense, strives to be quantitative, and has been for some time, though some aspects are necessarily still qualitative/descriptive (i.e., tracing of neuronal pathways).

Mathematical modeling means creating predictive models using mathematical tools. I have not yet seen a mathematical model that is sufficiently predictive of real life events in biology to be confident it is complete or works at all. Biology is about learning and understanding how living organisms work. If we knew all that sufficiently to hand it off to someone to develop predictive models to use where we could enter all the variables of, for example, the full set of genes a person has, all of the environmental factors to which they have been exposed from conception to the present, all the psychosocial factors they have been exposed to from birth to the present, and could stick those all into a model to get an output telling us what diseases they will get in 2 years, 5 years, 10 years, then we'd be ready for mathematical modeling to play a role. So far, there's too little to plug into any equation with certainty for that approach to have much utility. For example, we might know that a particular gene predisposes a person to diabetes. It doesn't mean if they have that gene they'll definitely get diabetes, but they might. What would you put into mathematical terms about that? If X, maybe Y? Obviously, there are some other factors that contribute to whether that person WILL get diabetes, but we don't know what they are. The tool being used there is statistics...in patients with diabetes, factor A (i.e., obesity) is greater than patients without diabetes. Okay, we now have gene X and factor A. But, we'll still find that there are people who are obese and have gene X who still don't get diabetes, and people with neither who do. This all tells us we're not ready to model this, because there is no yes or no answer yet.

 

[hokiehokie]

I would disagree that "consistent with some standard" is required. The statistical comparisons assume a model, not the quantification method.

I think toxicologists would disagree on the predictive issues. As far as utility is concerned there are models used in epidemiology.

Fuzzy issues apply to geology as well. The exact minerals condensing out of a pluton are predictable, but there is some uncertainty. Why? Because of the complexity of the situation. Maybe a better example is the weather. The models are based on well understood equations yet it rained today despite a forecast of sun.

Instead of me prattling on about each science having its descriptive side, its mathematical complexity, and mathematical simplicity, I think it might be good to mention an observation by Feynman in his book. He tells a story about visiting a friend in his biology lab. He looks through a microscope and asks why the chloroplasts are circulating. His friend says he has no idea. Feynman's revelation is that in his discipline of physics it took a long time to come up with an experiment to find something that was not known, and that in biology very little is known and that it took a long time to decide what unknown was to be investigated.

Feynman's story sounds like your comments: biology is not understood. At times it seems hopelessly complex. The predictive mathematics seems overwhelming complex. So little is understood.

To solidify my claim that biology is incredibly complex I want to point out that it has only been 1 decade since the first good estimates were made of the number of cells in the human brain. Just 10 years! Even counting, one of the basic things we do, is hard to do in biological tissue. People have been counting cells in brains for 115 years yet only recently was it done correctly.

If these problems are so simple, if the math is simple, why did it take so long to do it right?

 

[Cincinnatus]

Quantitative methodology means something different from applying mathematical models.

Point taken, the term quantitative methodology is too broad for what I meant when I started the thread. I was really asking about the role of more advanced mathematics. This may be in modeling, or elsewhere.

Mathematical modeling means creating predictive models using mathematical tools. I have not yet seen a mathematical model that is sufficiently predictive of real life events in biology to be confident it is complete or works at all. Biology is about learning and understanding how living organisms work.

I disagree, the purpose of mathematical modeling is not to predict what an organism/cell/molecule will do in a given situation. As you point out, the number of variables involved in such a task is prohibitively large. Moreover, we already know that much, since we have the thing we are modeling itself. In principle we could predict the behavior of a cell by modeling every atom individually, but this on its own, would not tell us anything interesting about the cell that we couldn't already get from observing the cell itself.

We build mathematical models in order to help us isolate the important factors that are causative of the behavior we are observing. For example, we might want to know why we observe 40 Hz oscillations in local field potential recordings from many parts of cortex. We certainly would not try to build a model incorporating everything we know about neurophysiology. Instead we would build a simplified model incorporating only the variables that we hypothesize to be most likely necessary and sufficient to observe the oscillations in question. This model certainly would not predict everything the brain does. But what it would do is either show 40 Hz oscillations, or not. In the former case we could conclude that our assumptions are sufficient, in the latter case we've learned that additional variables are important for giving rise to this behavior.

Mathematical modelers in biology aren't like weathermen, just trying to predict what the weather will do tomorrow. They are scientists who employ the scientific method, testing hypotheses just the same as experimental biologists. The difference is that modelers make hypotheses about "what is possible" rather than "what is". For that reason, the most interesting results to come out of the theoretical biology tend to be negative. For example, we might ask: Is it possible that changes in synaptic weight are sufficient to explain memory? If the answer turns out to be "yes" then we are just confirming something everyone already believes. Though, if the answer is negative then we've learned something of considerable interest, which implies the existence of additional processes that must exist and can then be searched for experimentally.

(A sidenote: the example of synaptic weight changes underlying memory turning out to be impossible is from a real paper: Abbott and Fusi 2007 "Limits on the memory storage capacity of bounded synapses" Nature Neuroscience).

 

[Cincinnatus]

Here's a link to a mathematician's view of this subject.

http://www.wisdom.weizmann.ac.il/~holcman/whatismodeling-versIII.PDF

It seems to be aimed more at convincing people with a quantitative background to be interested in biology rather than the other way around.

i.e. he claims Biology is having the "Viagra effect" on mathematics!