Xref: utzoo sci.math:12035 sci.bio:3450 Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!wuarchive!uunet!mcsun!ukc!tcdcs!swift.cs.tcd.ie!vax1.tcd.ie!cemurphy From: cemurphy@vax1.tcd.ie Newsgroups: sci.math,sci.bio Subject: Re: Mathematical ecology Message-ID: <6750.26ca85bc@vax1.tcd.ie> Date: 16 Aug 90 11:38:36 GMT References: <1482@ntmtv.UUCP> Organization: Computer Laboratory, Trinity College Dublin Lines: 137 In article <1482@ntmtv.UUCP>, behm@ntmtv.UUCP (Gregory A. Behm) writes: > I'd like to get some general information about the field of mathematical > ecology. Would someone please share with me what they know about this > field? Some of the questions I have are: > > What is it? (i.e. a definition, please) > How does it differ from "traditional" ecology? > (I assume it's a relatively young science) > What are the areas of research to which it pertains? > What are the tools and methods used? > Etc. > > Any other information you can give will be appreciated. > > E-mail is preferred, but you may post if you cannot reach me. > > Thanks, > > Greg Behm > > ntmtv!behm@ames.arc.nasa.gov > {amdahl | ames | hplabs}!ntmtv!behm Hello Greg. My background is computer engineering so I don't know if what I will write is of much use to you. Anyway... What is mathematical ecology? It seems to me that it all depends on what ecology is. Mathematics is just a model-building kit; it's just a set of building blocks with which you can construct a simplifed re-PRESENTATION ( I hate the use of the word representation as it doesn't direct your attention to the actual meaning of word) of some (percieved!) reality; In your case this reality is ecology; so in mathematical ecology you would be building models of things in ecological space. Again, it all depends on what ecology means to you. What 'stuff' or things are present in ecology. In an earlier reply to your posting I think remember someone talk about insect migration. Well then, you would be focusing on what are the 'elements'/ entities/ influencial factors present in your perception of the insect migration system. You are asking yourself 'what are the important, interacting factors that are of interest to me as a model-builder?' For example (?) the countries of origin and destination/ the weather/the insect population itself/....... (I'm sure someone expert in insect migration could provide many, many more influential factors. For instance, they could achieve finer focus/ more details within the concept of 'insect population'). what are the attributes/characteristics that you perceive are 'part-and-parcel' of the above relevent factors or of the system as a whole. For example the size of the insect population. Here you could be sticking on a measurement tool onto your entities' attributes. You may take your weather element to be made up of temperature [ deg-c ], wind speed [mph], .... what are the various activities/processes that change the value of these attributes. For example, when the temperature goes up this causes an increase in the insect population (??). But it also causes the developement of 'pressure-belt' (????????) which increases wind speed, which hampers insect reproduction and so gives rise to a falling in the population of the insect population. ... and so on.... Having picked out what you consider are the important things of your ecological system you can go ahead and build your model. (it is however an iterative process). You could build your model using any model-building system. Examples are LANGUAGE, MUSICAL NOTATION, LEGO_TECHNIC, MECANNO(?),MATHEMATICS.... What I've written above is a very,very crude language model. So why would it be a good thing to build the model using maths? Well, once you have assigned variables to the things in ecological space, and expressed the interactions (network of processes) using equations, well then you can just "GO_THROUGH_THE_MOTIONS" of finding out the implications of you model. If you add '+4' to one side of the equals sign then you must add '+4' to the other side. Of course your specification of the interactions may be in the form of differential equations, and so on. BUT in the end its just a question of adding '+4' to both sides! Nowadays we can get a computer to do the work. The skill of model-building is to achieve GOOD FOCUS. The math-toolkit is just a device to extend your initial perception of the insect migration system to the full set of it's implications. It's like a plumbing system: it carries whatever you put into one end of the pipe to the other end. The real skill lies in putting the right 'stuff' into the pipe initially. SO, Mathematical ecology (for me, with my limited perception) is the building of models of aspects of ecological space using the mathematical model-building toolkit. As to what ecology is, or what aspects you may what to examine, well that is up to you. How does mathematical ecology differ from traditional ecology? ummmmm.....prehaps it is in its use of the math model-building kit as opposed to the building of language models. And with the building of these math-models prehaps it differs in the use of the computer tool for 'carrying the stuff from one end of the pipe to the other'. You could also have pretty pictures produced to aid you understanding of the model you have built! and to prehaps help in suggesting areas where you could achieve better FIT between your model (your perceived SIMPLIFIED RE-PRESENTION) and the aspect of ecological space you are interested in. What are the areas of research to which mathematical ecology pertains? Again, it depends on what ecology is. What are the things that 'inhabit' ecological space: insects, birds, foxes and chickens (ah! memories of past lectures on differential equations.....), their activities etc. Prehaps there is someone else reading this who has an idea of what ecology concerns itself with, and what are the questions that this science asks of world. What are the tools and methods used? Well, maybe I covered this as best as I can. I would suggest that a good book on computer modelling and simulation could be useful....A book on maths modelling. I bought myself a box of Lego-Technic and WOW was it expensive stuff! So there you go, Greg. I gave it a try. Cormac.