behm@ntmtv.UUCP (Gregory A. Behm) (08/08/90)
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!behmjsod@athena.mit.edu (Jordi Sod) (08/10/90)
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 I presume it refers to the use of mathematical modeling applied to things like population growth, etc. To take a rather simplistic example, stability problems concerning population, or fourier analysis of insect migration (that sounds like fun!). I might be wrong. I'm rather ignorant about the field, however that is my impression. Jordi Sod (jsod@athena.mit.edu) (Sorry,all. I tried regular e-mail to no avail)
jy2y1@vax5.cit.cornell.edu (08/14/90)
In article <1990Aug9.180603.5489@athena.mit.edu>, jsod@athena.mit.edu (Jordi Sod) writes: > 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 > I don't have a definition, but have read reports on seminars concerning mathematical ecology. They related to epidemiological interactions and modelled them in mathematical terms.i.e. systems of ODEs I believe the tools used are the same any applied mathematician would use. Just thought I'd put my 2 cent comment :-0). Bye.
JAHAYES@MIAMIU.BITNET (08/15/90)
Mathematical ecology is simply the application of mathematical techniques to the analysis of ecological problems. This might consist of using linked differential equations to describe, say, n-species interactions -- obviously, this could be addressed easily using matrix techniques. I'm currently using cellular automaton theory to examine species distributions on a (roughly) two-dimen- sional surface (e.g. coral reefs). I suppose that falls into the field of mathematical ecology. Some prominent workers in the field include Robert May, Simon Levin, and Robert Levins. There are several textbooks, although Pielou's "Mathematical Ecology" is more a guide to enumeration techniques (i.e. diversity indices, measures of contagion, etc.). I could supply a list of some sample texts if you could be more specific in your request (I especially recommend May's 1973 "Stability and Diversity in [or is it 'of'?] Model Ecosystems"; I believe it to be a flawed analysis, but it gives you some idea of what can be done. Also check out recent issues of the journals Theoretical Population Biology, the Journal of Theoretical Biology, Ecological Modelling, and the American Naturalist for some more or less mathematical approaches. Hope this helps. (Sorry if I've repeated some of this thread; I've been out of town and our news server has gotten flakey in the interim). ------ Josh Hayes, Zoology, Miami University, Oxford OH 45056 jahayes@miamiu.acs.muohio.edu or jahayes@miamiu.bitnet I don't need a disclaimer, because I never lie, and I'm always right. So there. Nyah.
cemurphy@vax1.tcd.ie (08/16/90)
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.
elmo@uhura.cc.rochester.edu (Eric Cabot) (08/17/90)
In article <1482@ntmtv.UUCP> it was 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: I am intrigued by your question. Mathematical ecology was "big" in ecology in the seventies. Those were transitional days in the field of ecology. At that time people interested in applying mathematical approaches to ecological problems were gradually replacing older ecologists who studied phenomena in a rather more qualitative fashion. Nowadays, almost all biologists calling themselves ecologists are very mathematically oriented and the older style of study is usually referred to as natural history. The early roots of what was considered "mathematical ecology" were vegetation analyis (ie floristics)- particulary the "Zurich-Montpellier" school and marine benthic community ecology. When eco-system analysis became big in the late sixties that too became included in mathematical ecology. Certainly as the field of population dynamics devloped, it too, was considered to fall under the aegis of mathematical ecology, as was the area of computer simulations. But then, there are other ecological areas that are very mathematical these days too. Particulary behavioral and evolutionary ecology. These fields have more of a theoretical than a data analysis approach. I have been out of ecological research for a about seven years now, so I don't know if the people who consider themselves evolutionary ecologists think of themselves as "mathematical ecologists" or not. I am not saying this because the evolutionary/behavior types like to think of themselves as being in the most unique and important sub- discipline of biology. Rather I am trying to stress that the term mathematical ecology has really lost its functional utility because all ecology is mathematical. However, if you are interested in two books on the subject that were considered of biblical importance back when mathematical ecology was the hotest new rage I direct you to your nearest university library which will almost certainly contain (or can get) E.C. Pielou's Mathematical Ecology and Poole's Quantitative Ecology (could have the title wrong here). The reason why I am so intrigued by your posting is that the question is a little off beat. I can't help but wonder if you stumbled across the term in the recent literature or ... ? Furthermore, I wondered why you didn't check the library to begin with. (That's a bic-lighter sized flame for you :-) =+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= Eric Cabot | elmo@{uhura | db1}.cc.rochester.edu "insert your face here" | elmo@urodbv.bitnet -- =+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+= Eric Cabot | elmo@{uhura | db1}.cc.rochester.edu "insert your face here" | elmo@urodbv.bitnet =+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=+=