# Mathematics for Theoretical Ecology?

## Main Question or Discussion Point

Hi, I just found this great forum and I am hoping to get some advice.

I am starting an ecology degree with the hope of, one day, getting into grad school. I don't know yet what type of research I would like to do but I want to keep the door to theoretical work open. As my math background is not yet well developed I don't have a clear understanding of the kind of math involved in theoretical ecology.

Assuming I continue to get solid marks in math courses, I am considering building a mathematics minors to accompany the ecology degree. A math minor at the school I am transferring to is 18 upper division credits of my choice. This is the list if anyone has specific recommendations https://courses.students.ubc.ca/cs/main?pname=subjarea&tname=subjareas&req=1&dept=MATH" [Broken] , general recommendations are great too!

I have seen a few other posts on mathematical biology on this forum but they seemed to concentrate on smaller scale biological issues. I am unsure as to whether the math involved is the same so I apologize if I am rehashing an old thread.

I know I need calculus I-III, linear algebra, and differential equations as fundamentals. The mathematical biology courses also appear to be no-brainers, but I am lost beyond that.

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Simfish
Gold Member
Here's a very good list of useful courses:
http://www.washington.edu/students/crscat/appmath.html

And here's a guy who does research in theoretical ecology:
http://octavia.zoology.washington.edu/

Anyways, theoretical ecology can be surprisingly math-intensive. Math up to dynamical systems is very helpful (start with nonlinear dynamics and chaos and then move to dynamical systems and stochastic processes), as is game theory-like math (because you have to deal with payoff matrices). In fact, the theoretical ecologists at my school generally study math all the way up to graduate-level applied math.

Statistics (up to senior and intro graduate level) is also quite helpful, especially if you want to collect some data to inform the theory (lots of the theoretical ecologists at my school don't even collect data at all - they just theorize).

http://depts.washington.edu/qerm/

Anyways, I just created an Amazon.com Listmania list here:

https://www.amazon.com/lm/RT4R6U5XU53K3/ref=cm_lm_pthnk_view?ie=UTF8&lm_bb=

It's still incomplete, since I still have to add more books.

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This information gathering project is challenging because I am at the "I don't know what I don't know" stage of ignorance and there doesn't seem to be a lot of information on theoretical ecology floating around. I've tried emailing a few people working in the field but, unsurprisingly, I'm not getting responses. Your reply gives me a great place to start. The amazon list is great! Thanks!

In fact, the theoretical ecologists at my school generally study math all the way up to graduate-level applied math.
Do you think taking a math minor along with an ecology degree is a strong enough quantitative background to do work in the field?

Simfish
Gold Member
Do you think taking a math minor along with an ecology degree is a strong enough quantitative background to do work in the field?
Hm, to be honest, I think that a BS in applied math or statistics would be most helpful (you'll need more math than what's required in a BS in applied math - you'll also need some grad level courses too, although you don't need them all while you're an UG). Most theoretical ecologists seem to major in math/applied math/physics/statistics and then later decide to go to grad school in theoretical ecology (they just do undergrad research with a theoretical ecologist, and self-study the biology they need). The biology major in most schools is honestly catered towards a fairly low denominator, especially for a quantitative ecologist.

That being said, abstract algebra/topology/real analysis isn't really needed so you don't really need to pursue pure math.

For a simple idea of the math you really need for this:

http://www.scholarpedia.org/article/Predator-prey_model

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Most theoretical ecologists seem to major in math/applied math/physics/statistics and then later decide to go to grad school in theoretical ecology (they just do undergrad research with a theoretical ecologist, and self-study the biology they need).
Oh really? That seems very strange to me, but what do I know? I would have imagined that self studying that quantity of information would be quite challenging. I wonder if it comes with significant deficits in biological understanding?

The biology major in most schools is honestly catered towards a fairly low denominator, especially for a quantitative ecologist.
I am not sure exactly what you mean by this, can you clarify? I am not being critical I just don't have a clear understanding of your meaning.

I guess the difficulty then is that I *know* I want to work in ecology but theory is just a door I want to keep open. Neither my biological nor my mathematical education is sophisticated enough be sure that a leap into a mathematics BSc is a good idea.

Simfish
Gold Member
Oh really? That seems very strange to me, but what do I know? I would have imagined that self studying that quantity of information would be quite challenging. I wonder if it comes with significant deficits in biological understanding?
It's not challenging at all if you find it fun. :) Anyways, it's *much* easier to start with math and then self-study biology than to start with biology and then self-study math. And no, it doesn't come with significant deficits in understanding - researchers learn most of what they do through interaction with others, not through class.

And actually, I'd argue that the math really enhances biological understanding in a way that biology cannot do by itself. Diffusion, for example, is much clearer when you understand the mathematics of Fick's Law. If you don't know math, then you could explain diffusion in words, but it's really not the same as understanding it mathematically.

I am not sure exactly what you mean by this, can you clarify? I am not being critical I just don't have a clear understanding of your meaning.
Okay, to put it simply, most biology students aren't especially bright, and this affects how the professors teach the classes. Classes are often more about memorization than conceptual understanding. Mathematical ecology is extremely math-heavy, and it would be very difficult to enter the field with just a biology degree. Honestly, even Edward O. Wilson's "Sociobiology" book was too difficult to be used for the the SENIOR-LEVEL sociobiology class at my school, for example.

I guess the difficulty then is that I *know* I want to work in ecology but theory is just a door I want to keep open. Neither my biological nor my mathematical education is sophisticated enough be sure that a leap into a mathematics BSc is a good idea.
Oh okay I see. In any case, quantitative ecology doesn't have to be as math-intensive as I described. You don't need dynamical systems theory to study the populations of crows in the real world, for example. Theoretical ecology is very math-intensive though. It is easier to get research with a professor in theoretical ecology simply since so few students are interested in the subject.

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This thread embodies my struggle with the path my education is taking. I beleive that the math is very important hence my applied math minor, but knowledge actual biological and ecological objects, organisms, and systems is important, hence biology/ecology major. My interests lie in actually designing pathways for energy and nutrients in practical uses, such as agriculture or production of other materials through biological means in an ecological framework. So I guess my question is for something like this do you think that a math undergraduate education up to and including Calc I-III and Differential equations and linear algebra would be appropriate? Even E.O. Wilson had to go back for some serious math remediation when he got involved with MacArthur.

Also I am looking at possible grad schools to see what they would require as far as math, such as MIT and Caltech. Do you happen to anyplace that has some focus in what I have described?

Simfish
Gold Member
My interests lie in actually designing pathways for energy and nutrients in practical uses, such as agriculture or production of other materials through biological means in an ecological framework. So I guess my question is for something like this do you think that a math undergraduate education up to and including Calc I-III and Differential equations and linear algebra would be appropriate?
Sounds like systems biology.

And I don't think that's sufficient enough now. You also need stochastic processes and possibly dynamical systems. And statistics http://depts.washington.edu/qerm/ should provide a good guide

Even E.O. Wilson had to go back for some serious math remediation when he got involved with MacArthur.
Lol seriously? What did he have to do? He knows A LOT of math for an ecologist. When I showed his book to a theoretical biologist, the theoretical biologist was like "Wilson knows p log p??"

First of all University of Washington seems like a cool place to be for this stuff. Second, I don't think stochastic and dynamics are offered as an undergraduate in any but the most advanced of schools and definitely not at Slippery Rock University. But I should probably get involved with some more statistics for sure. The curriculum for Washington had about four semesters worth of stats as pre reqs. Anyways thanks for all the info like Draidgoch said the information on this stuff is minimal or hidden very well.

And I read in The Song of the Dodo by David Quammen that Wilson used to be just the naturalist type but when he realized that to study the cool stuff he had to learn math and had to do some serious remediation. Specifically I don't know what he had to learn but he made it out to be quite a lot. Thats a very good book if you want to know some of the history of mathematical ecology and biogeography.

And I read in The Song of the Dodo by David Quammen that Wilson used to be just the naturalist type but when he realized that to study the cool stuff he had to learn math and had to do some serious remediation. Specifically I don't know what he had to learn but he made it out to be quite a lot. Thats a very good book if you want to know some of the history of mathematical ecology and biogeography.
That is definitely a situation that I want to avoid. Like you said, it seems the really cool stuff in ecology requires a lot of math. Don't get me wrong, I'm an avid naturalist but I want a deeper understanding of the processes involved.

Thanks for the review! I'll go pick that book up asap.