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CDarwin

Mathematics in Paleontology

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I'm wondering what sort of mathematics one should be looking at pursuing in undergraduate courses with a view applying them to work in paleontology. What kind of math is math is most commonly used? I believe principal component analysis and multivariate statistical techniques like that are pretty important, not that I know at at all what that means. Is there a lot of mathematical ecology, population modeling and what-not, these days? I'm ever leery of calculus.

Edited by CDarwin

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Statistics is an absolute must, and the higher level, the better.

 

While it doesn't really come under "math", I'd strongly suggest a good background in programming, as it'll *definitely* prove useful for data management, and IIRC, some of the phylogenetic software packages have programming built in as scripts and such.

 

Beyond that, it really depends on what you want to do within paleontology. One of the folks in my dept (and hopefully on my thesis committee, when I get around to asking) does dinosaur locomotion from a biomechanical perspective, so he's always using engineering-based concepts which require stuff like calculus. Other paleo folks I know don't need much math beyond the above and what they learn from papers (after all, there's no college course in phylogenetic independent contrasts). Still other folks do some form of ecological modeling.

 

IMHO, the best thing you can do is take a fair bit of math, stats and programming. If you're in a geo-based program, go out of your way to take bio, as much as possible, possibly even to double-major. Don't just take evolution and animal behavior classes - comparative physiology, vertebrate anatomy, all of those can be essential. And do undergrad research - it'll set you apart and demonstrate your ability to do research, which is really what grad programs are looking for.

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Don't underestimate the simple fact that mathematics is an excellent environment to learn problem solving skills -- that are obviously applicable to any other field. Math is a good environment for this because math has well defined tools, and math problems until you get to some very high level problems, always have an answer and have answers that are clearly correct or incorrect. Most real-world problems aren't that clear cut; real world problems may not have a solution, or may have multiple solutions and you have to weigh which is best. Nevertheless, the problem solving skills that you hone in a mathematics class can still be used to solve real-world problems.

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One of the interesting applications of math to paleontology is a field called stereology. The field is used to determine things like length, volume, surface area, etc. Often fossils are revealed on sections, i.e. polished surfaces sliced through the rock. The question is what can be determined about the fossils from what is seen in the section?

 

The application of stereological methods involves little more than algebra. The background requires a bit more. Regardless, you have to have an understanding of statistics.

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First of all, I think that if you suck at maths, you shouldn't study science. Especially if you're interested in evolution, you just wouldn't be able to follow many (most?) articles in journals such as "Evolution". There is a strong trend towards greater use of quantitative tools, Yule's speciation model (a continuous-time Markov chain) even made it into an article about patterns of frog diversification in last month's issue of "Evolution".

 

So I strongly agree with Mokele's point that the best thing you can do is take a fair bit of math, stats and programming..

 

The kind of math really depend on what you're interested in (I know, what a cheap answer). Is there a particular subject you're passionate about ?

 

In any case, it's best to have at least some basic understanding of all the major branches of mathematics. That being said, there aren't many good courses to teach undergrad students in biology and geology how to use maths and computers...

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Is there a lot of mathematical ecology, population modeling and what-not, these days? I'm ever leery of calculus.

 

As an example of something I covered a while ago on my current course, and this was basic population modelling was using the Lotka Volterra equations, which are very straightforward, but you need to understand vector fields, how to solve partial differential equations, systems of differential equations, and be familiar with matrices (the Jacobian in this instance.)

 

I'm not sure if any of that sounds a little scary (it's not that bad), but it just illustrates how many different methods are required even with something that basic. So a sound grasp of a number of techniques would definitely be beneficial, and give you a much deeper understanding of a given model.

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The kind of math really depend on what you're interested in (I know, what a cheap answer). Is there a particular subject you're passionate about ?

 

 

I'm mostly interested in primate and human evolution. I'm an anthropology major, actually. I think the Eocene is really interesting, but I've oscillated back and forth a lot around paleoanthropology.

 

 

Thanks everyone for your advice, incidentally.

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Most biologist I know (apart from those that are really physicists or mathematicians working on "biological problems" ) are very poor in mathematics skills.

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Yes and no. Most biologist never have to use some of the insanely complex stuff physicists do, and so lack those skills (and often can get by on just algebra). But IME, biologists tend to have much more complex statistical skills, as a result of having to deal with statistical problems like evolutionary relatedness, individual variation, behavioral motivation, etc.

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I would expect the average experimental biologist to be far more familiar with statistics and analysis of experimental data than I am.

 

Both my brother and his girlfriend are biologists. Neither has any real mathematical knowledge or sophistication. Other biologists I have met are the same. The only notable exceptions are those who work in mathematical biology.

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So statistics aren't math?

 

Many people, including many statisticians do not consider statistics to be mathematics. So, maybe the answer to your questions is a matter of opinion.

 

Either way, it does not change my initial assertion.

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