Re: [ECOLOG-L] Fuzzy Logic in Ecology
That is what niche theory is all about, and as I posted before, these ranges do not have sharp boundaries. That is why I proposed the idea of a fuzzy niche. Some temperatures , for example, are highly suitable for an organsim, so the membership in the niche is 1. Some are impossible, and the membership is zero. In between you have marginal conditions with memberships taking an intermediate value. Bill Silvert - Original Message - From: "Wayne Tyson" To: Sent: Saturday, August 08, 2009 6:13 AM Subject: Re: [ECOLOG-L] Fuzzy Logic in Ecology Imagine you have an organism and a habitat. You can sketch out that organism's "center" (more or less), its suite of needs or requirements and limitations like temperature, pH, nutrients, water, and a thousand other things that germplasm is heir to about which we know nothing, and you can do the same for its habitat. Then imagine that you can do the same for species, populations, and ecosystems. Given the impossibility of handling all of the known variables, not to mention the unknown ones, and the variables within the variables, what choices to ecologists have with respect to understanding how ecosystems function and malfunction and how are they limited? WT
Re: [ECOLOG-L] Fuzzy Logic in Ecology
My example may be overly simplistic intended only for purpose of conceptual understanding, however, based on your response I'm not sure if you understand fuzzy approaches and simply do not agree with them, or if you do not understand fuzzy approaches and are confusing the issue. In fact, fuzzy approaches are an alternative approach to other kinds of approaches used to deal with uncertainty. It is a very simple approach in application, but really requires a lot of thought is assigning the fuzzy sets. In fact, the fuzzy set would assign a membership value that is a loose estimate of the possiblitity of being correct and is very useful if you have incomplete data sets and/or high degrees of uncertainty. Fuzzy approaches should be viewed as a step in the process of risk assessment (for example) rather than the end all. IN the real world of ecology, the likelihood of a person knowing every variable involved in the system is low. If you can give a probability with a high degree of confidence, I would certainly use a finite number, but you could also use a fuzzy approach. Likewise, if you do have the data to insert into a baeysian approach (as each forthcoming probability is based on the probabilities previously assembled or estimated by observation of previous occurrences) then by all means use a bayesian approach, but you could also use a fuzzy approach. But if you have low confidence in your data and you are not confident in preliminary observations, a fuzzy approach is a very useful tool for understanding what may be going on. Fuzzy approaches do not use probability theory, they use possibility theory. THey are alternative approaches used for similar purposed to infer slightly to very different endpoints. When we use probability we are really trying to assess how likely a single point will happen, typically some mean or median. In possibility theory we are trying to identify what outcomes are definitely possible, what outcomes might be possible, and which outcomes are definitely not possible. The relationship between possiblity and probability could be seen in a similar way to how we view the relationship between Orders and species. For example, all Green Turtles are in Chelonia, but not all Chelonia are Green Turtles, however, All Tuataras are in Sphenodontia, and all extant Sphenodontia are Tuataras because there is only only one species of Tuatara (there may now be 2 species as I recall, but that isn't the point). So, if done correctly what is possible should encompass what is probable, but what is probable will not encompass all that is possible. Is it likely that someone will anonymously send you a million dollars in the mail? No. Is it possible that someone will anonymously send you a million dollars in the mail? yes. Sometimes it is more important to know what is possible and sometimes it is more important to know what is probable. IF you have a large set of outcomes that all have low probability, you may decide that discussing what is possible is more important, however, if you have a small range of variables with very high probability of occurrence, then you may choose to discuss in terms of probability. This is by no means a perfect explanation, but maybe some light bulbs will turn on for some folks? On Fri, Aug 7, 2009 at 8:31 PM, wrote: > malcolm McCallum wrote: >> >> Maybe this will help... >> >> Imagine you have two people sitting at a table drinking and you are >> the waiter/waitress. >> >> One customer says, "I have 13.21435343234 ml of alchohol in my drink." >> >> The other says, "My drink is low." >> >> Which is more meaningful??? When the first person makes their >> statement, do you really know what it means? You will need a lot more >> information to assess what it means such as: how big is their glass, >> how much ice is in it, was it a mixed drink? >> >> The second person has relayed a very useful statement that tells you >> exactly what is meant, however, you do not know how much it will take >> to fill the drink. >> >> The first example would be a standard estimate such as probability. >> It seeks to get to the exact number of concern. >> >> The second exaple is a fuzzy estimate, and provides a cognitive >> estimate that has obvious meaning but will need further investigation >> to work out the details. >> >> Standard estimates deal with what is probable. >> Fuzzy estimates deal with what is possible. >> >> does that make sense? >> > Not really! > > The first statement is (overly!) precise, and has no probability associated > with it. What it means depends on context, and understanding that is > outside of formal mathematics, of any sort. TBH, I think it's a red herring > that confuses rather than enlightens. > > The second statement is vague. Whether one deals with it as with > probability or fuzzy logic depends on whether you see the vagueness as ontic > or epistemic. > > If one thinks that there is a precise concentration of alcohol, and that > "low" is an
Re: [ECOLOG-L] Fuzzy Logic in Ecology
Imagine you have an organism and a habitat. You can sketch out that organism's "center" (more or less), its suite of needs or requirements and limitations like temperature, pH, nutrients, water, and a thousand other things that germplasm is heir to about which we know nothing, and you can do the same for its habitat. Then imagine that you can do the same for species, populations, and ecosystems. Given the impossibility of handling all of the known variables, not to mention the unknown ones, and the variables within the variables, what choices to ecologists have with respect to understanding how ecosystems function and malfunction and how are they limited? WT - Original Message - From: To: Sent: Friday, August 07, 2009 6:31 PM Subject: Re: [ECOLOG-L] Fuzzy Logic in Ecology malcolm McCallum wrote: Maybe this will help... Imagine you have two people sitting at a table drinking and you are the waiter/waitress. One customer says, "I have 13.21435343234 ml of alchohol in my drink." The other says, "My drink is low." Which is more meaningful??? When the first person makes their statement, do you really know what it means? You will need a lot more information to assess what it means such as: how big is their glass, how much ice is in it, was it a mixed drink? The second person has relayed a very useful statement that tells you exactly what is meant, however, you do not know how much it will take to fill the drink. The first example would be a standard estimate such as probability. It seeks to get to the exact number of concern. The second exaple is a fuzzy estimate, and provides a cognitive estimate that has obvious meaning but will need further investigation to work out the details. Standard estimates deal with what is probable. Fuzzy estimates deal with what is possible. does that make sense? Not really! The first statement is (overly!) precise, and has no probability associated with it. What it means depends on context, and understanding that is outside of formal mathematics, of any sort. TBH, I think it's a red herring that confuses rather than enlightens. The second statement is vague. Whether one deals with it as with probability or fuzzy logic depends on whether you see the vagueness as ontic or epistemic. If one thinks that there is a precise concentration of alcohol, and that "low" is an estimate of this, then the vagueness is epistemic, so one could set up a probability model for the concentration. Alternatively, one might view "low" as an objective category, where there are some concentrations that everybody would say are "low", and some where everybody would say that they are "high". But there are also concentrations in between where any person is not sure whether to say it is "low" or not. In this case, we might view "low" as being a vague property, and assign a non-integer truth value to the statement "the concentration is low", e.g. it might be "60% true". Note that this would be done even if the concentration was known exactly. The problem is not one of uncertainty about the actual concentration (which is what Bayesian probabilities measure), but about vagueness in the mapping of the exact value to the notion of "low". Bob -- Bob O'Hara Department of Mathematics and Statistics P.O. Box 68 (Gustaf Hällströmin katu 2b) FIN-00014 University of Helsinki Finland Telephone: +358-9-191 51479 Mobile: +358 50 599 0540 Fax: +358-9-191 51400 WWW: http://www.RNI.Helsinki.FI/~boh/ Blog: http://network.nature.com/blogs/user/boboh Journal of Negative Results - EEB: www.jnr-eeb.org No virus found in this incoming message. Checked by AVG - www.avg.com Version: 8.5.392 / Virus Database: 270.13.46/2288 - Release Date: 08/07/09 13:13:00
Re: [ECOLOG-L] Fuzzy Logic in Ecology
malcolm McCallum wrote: Maybe this will help... Imagine you have two people sitting at a table drinking and you are the waiter/waitress. One customer says, "I have 13.21435343234 ml of alchohol in my drink." The other says, "My drink is low." Which is more meaningful??? When the first person makes their statement, do you really know what it means? You will need a lot more information to assess what it means such as: how big is their glass, how much ice is in it, was it a mixed drink? The second person has relayed a very useful statement that tells you exactly what is meant, however, you do not know how much it will take to fill the drink. The first example would be a standard estimate such as probability. It seeks to get to the exact number of concern. The second exaple is a fuzzy estimate, and provides a cognitive estimate that has obvious meaning but will need further investigation to work out the details. Standard estimates deal with what is probable. Fuzzy estimates deal with what is possible. does that make sense? Not really! The first statement is (overly!) precise, and has no probability associated with it. What it means depends on context, and understanding that is outside of formal mathematics, of any sort. TBH, I think it's a red herring that confuses rather than enlightens. The second statement is vague. Whether one deals with it as with probability or fuzzy logic depends on whether you see the vagueness as ontic or epistemic. If one thinks that there is a precise concentration of alcohol, and that "low" is an estimate of this, then the vagueness is epistemic, so one could set up a probability model for the concentration. Alternatively, one might view "low" as an objective category, where there are some concentrations that everybody would say are "low", and some where everybody would say that they are "high". But there are also concentrations in between where any person is not sure whether to say it is "low" or not. In this case, we might view "low" as being a vague property, and assign a non-integer truth value to the statement "the concentration is low", e.g. it might be "60% true". Note that this would be done even if the concentration was known exactly. The problem is not one of uncertainty about the actual concentration (which is what Bayesian probabilities measure), but about vagueness in the mapping of the exact value to the notion of "low". Bob -- Bob O'Hara Department of Mathematics and Statistics P.O. Box 68 (Gustaf Hällströmin katu 2b) FIN-00014 University of Helsinki Finland Telephone: +358-9-191 51479 Mobile: +358 50 599 0540 Fax: +358-9-191 51400 WWW: http://www.RNI.Helsinki.FI/~boh/ Blog: http://network.nature.com/blogs/user/boboh Journal of Negative Results - EEB: www.jnr-eeb.org
Re: [ECOLOG-L] Fuzzy Logic in Ecology
At the heart of fuzzy logic is Zadeh's Principle of Incompatibility, which states that precision and significance are incompatible. Malcolm provides a good example of this. The first customer is obviously an ecologist by the way, who else would bore the waitress with so many significant figures? Bill Silvert - Original Message - From: "malcolm McCallum" To: Sent: Friday, August 07, 2009 4:59 PM Subject: Re: [ECOLOG-L] Fuzzy Logic in Ecology Maybe this will help... Imagine you have two people sitting at a table drinking and you are the waiter/waitress. One customer says, "I have 13.21435343234 ml of alchohol in my drink." The other says, "My drink is low." Which is more meaningful??? When the first person makes their statement, do you really know what it means? You will need a lot more information to assess what it means such as: how big is their glass, how much ice is in it, was it a mixed drink? The second person has relayed a very useful statement that tells you exactly what is meant, however, you do not know how much it will take to fill the drink. The first example would be a standard estimate such as probability. It seeks to get to the exact number of concern. The second exaple is a fuzzy estimate, and provides a cognitive estimate that has obvious meaning but will need further investigation to work out the details. Standard estimates deal with what is probable. Fuzzy estimates deal with what is possible. does that make sense?
Re: [ECOLOG-L] Fuzzy Logic in Ecology
Maybe this will help... Imagine you have two people sitting at a table drinking and you are the waiter/waitress. One customer says, "I have 13.21435343234 ml of alchohol in my drink." The other says, "My drink is low." Which is more meaningful??? When the first person makes their statement, do you really know what it means? You will need a lot more information to assess what it means such as: how big is their glass, how much ice is in it, was it a mixed drink? The second person has relayed a very useful statement that tells you exactly what is meant, however, you do not know how much it will take to fill the drink. The first example would be a standard estimate such as probability. It seeks to get to the exact number of concern. The second exaple is a fuzzy estimate, and provides a cognitive estimate that has obvious meaning but will need further investigation to work out the details. Standard estimates deal with what is probable. Fuzzy estimates deal with what is possible. does that make sense? On Fri, Aug 7, 2009 at 3:28 AM, William Silvert wrote: > Although Zadeh may have had the idea "of the best fit POSSIBLE" in the back > of his mind, that is hardly how I would characterise the motivation for > using fuzzy logic.For me it brings science closer to the way that people, > including scientists, think, and thus can do a better job of approximating > the best possible reasoning. > > Common examples can be found in some of the fuzzy decision tools that aare > widely circulated as demos. For example, if you are buying a house and your > rules include: > > IF the house is close to work AND not too expensive THEN ... > > the usual approach would be to define "close to work" and "too expensive" as > perhaps <10 km and >200.000 €, but a real person would probably settle for a > really great buy 12 km from work or a 220.000 € house within walking > distance. This is easily represented by treating these concepts with fuzzy > memberships. > > Another reason for using fuzzy logic is that it is simple. Literally so. The > first applications of fuzzy logic were in system control, because back in > the days before cheap high-speed processors it was possible to build > economical controllers to replace slow and expensive systems based on > traditional methods with systems of differential equations to be solved. > Unfortunately there are those who feel that any mathematical approach has to > be fancy and sophisticated and involve lots of equations, which is one of > the reasons that fuzzy logic has been slow to be adopted in ecology, but it > is really very simple. > > Bill Silvert > > - Original Message - From: "Wayne Tyson" > To: > Sent: Thursday, August 06, 2009 9:22 PM > Subject: Re: [ECOLOG-L] Fuzzy Logic in Ecology > > > Re: Ecology Logic Fuzzy* > > I was never much good at statistics, to put it mildly (two or three courses > put a real drag on my GPA and my intuition). > > It seems (intuitively) to me that Bayes and Zadaeh both had good ideas that > were aimed at the direction of the best fit POSSIBLE, the former seeming to > be more elegantly conforming to hypotheses, the latter embracing uncertainty > more certainly--maybe. > > I am grateful for those laboring in the fields of numerical research; > without them observers of the interplay of organisms and their environments > might tumble down some warren of fantasy and never to return. Yet, looking > in the looking-glass never hurt anybody. > > On the other hand, it seems that the Sword of Certainty, especially in the > form of irrelevant decimal points and other attempts to reduce complex and > constantly-changing phenomena to quantities that fit neat boxes carved out > for them, hangs threateningly over jiggly and evasive phenomena, threatening > to freeze it all in place for all time. Still, provided analyses don't stray > too far from the actual data manipulated and are not treated as license for > (ironically?) unbridled conjecture amongst self-ordained emperors, those > numbers can open up insights as well as interfere with them. I have no firm > answer for this conundrum. > > What are the Great Questions in ecology? What are the answers? What answers > have actually changed rather than just been re-clothed or bumped off the > mountain in, say, the last century or so? What new questions have been > added? > > WT > > *Sorry, Bill, in a lame attempt to please everybody I didn't fuss with the > subject line (what a wuss, eh?), I was going to ask Eric off-list but the > reply-to-all button didn't have his email address in it, so I just deleted > one of the apparently duplicate list addresses--gad, this is getting > complicated! Back
Re: [ECOLOG-L] Fuzzy Logic in Ecology
warm? high? serious? Maybe Bob can post an example of what he considers a fuzzy rule. Bill Silvert - Original Message - From: To: Sent: Friday, August 07, 2009 3:53 AM Subject: Re: [ECOLOG-L] Fuzzy Logic in Ecology William Silvert wrote: I missed Wayne's posting since the subject line had nothing to do with fuzzy logic, and although I know that I will raise a chorus of outrage I am changing the subject line. Quite a few papers on fuzzy logic aplications have been published, many in Ecological Modelling (including a couple of my own). I also have some PowerPoint presentations on my website, http://ciencia.silvert.org, and there are many in related fields such as soil science. I think that one of my first efforts was in niche theory, obviously the "multi-dimensional manifold" that Hutchinson defined must have fuzzy boundaries. Unfortunately a lot of work in the field seems to consist of lots of mathematics with little biological content. I like to think in terms of fuzzy rules like IF the weather is warm AND nutrient levels are high THEN there is a serious risk of bottom anoxia In what way is that fuzzy logic? The truth value of the statement above, Pr(Z|X & Y) > Pr(Z|!(X & Y)) is surely 1. Where is the fuzzy logic element? I'm confused. Bob -- Bob O'Hara Department of Mathematics and Statistics P.O. Box 68 (Gustaf Hällströmin katu 2b) FIN-00014 University of Helsinki Finland Telephone: +358-9-191 51479 Mobile: +358 50 599 0540 Fax: +358-9-191 51400 WWW: http://www.RNI.Helsinki.FI/~boh/ Blog: http://network.nature.com/blogs/user/boboh Journal of Negative Results - EEB: www.jnr-eeb.org
Re: [ECOLOG-L] Fuzzy Logic in Ecology
Although Zadeh may have had the idea "of the best fit POSSIBLE" in the back of his mind, that is hardly how I would characterise the motivation for using fuzzy logic.For me it brings science closer to the way that people, including scientists, think, and thus can do a better job of approximating the best possible reasoning. Common examples can be found in some of the fuzzy decision tools that aare widely circulated as demos. For example, if you are buying a house and your rules include: IF the house is close to work AND not too expensive THEN ... the usual approach would be to define "close to work" and "too expensive" as perhaps <10 km and >200.000 €, but a real person would probably settle for a really great buy 12 km from work or a 220.000 € house within walking distance. This is easily represented by treating these concepts with fuzzy memberships. Another reason for using fuzzy logic is that it is simple. Literally so. The first applications of fuzzy logic were in system control, because back in the days before cheap high-speed processors it was possible to build economical controllers to replace slow and expensive systems based on traditional methods with systems of differential equations to be solved. Unfortunately there are those who feel that any mathematical approach has to be fancy and sophisticated and involve lots of equations, which is one of the reasons that fuzzy logic has been slow to be adopted in ecology, but it is really very simple. Bill Silvert - Original Message - From: "Wayne Tyson" To: Sent: Thursday, August 06, 2009 9:22 PM Subject: Re: [ECOLOG-L] Fuzzy Logic in Ecology Re: Ecology Logic Fuzzy* I was never much good at statistics, to put it mildly (two or three courses put a real drag on my GPA and my intuition). It seems (intuitively) to me that Bayes and Zadaeh both had good ideas that were aimed at the direction of the best fit POSSIBLE, the former seeming to be more elegantly conforming to hypotheses, the latter embracing uncertainty more certainly--maybe. I am grateful for those laboring in the fields of numerical research; without them observers of the interplay of organisms and their environments might tumble down some warren of fantasy and never to return. Yet, looking in the looking-glass never hurt anybody. On the other hand, it seems that the Sword of Certainty, especially in the form of irrelevant decimal points and other attempts to reduce complex and constantly-changing phenomena to quantities that fit neat boxes carved out for them, hangs threateningly over jiggly and evasive phenomena, threatening to freeze it all in place for all time. Still, provided analyses don't stray too far from the actual data manipulated and are not treated as license for (ironically?) unbridled conjecture amongst self-ordained emperors, those numbers can open up insights as well as interfere with them. I have no firm answer for this conundrum. What are the Great Questions in ecology? What are the answers? What answers have actually changed rather than just been re-clothed or bumped off the mountain in, say, the last century or so? What new questions have been added? WT *Sorry, Bill, in a lame attempt to please everybody I didn't fuss with the subject line (what a wuss, eh?), I was going to ask Eric off-list but the reply-to-all button didn't have his email address in it, so I just deleted one of the apparently duplicate list addresses--gad, this is getting complicated! Back to square one . . . - Original Message - From: "William Silvert" To: Sent: Thursday, August 06, 2009 8:13 AM Subject: [ECOLOG-L] Fuzzy Logic in Ecology I missed Wayne's posting since the subject line had nothing to do with fuzzy logic, and although I know that I will raise a chorus of outrage I am changing the subject line. Quite a few papers on fuzzy logic aplications have been published, many in Ecological Modelling (including a couple of my own). I also have some PowerPoint presentations on my website, http://ciencia.silvert.org, and there are many in related fields such as soil science. I think that one of my first efforts was in niche theory, obviously the "multi-dimensional manifold" that Hutchinson defined must have fuzzy boundaries. Unfortunately a lot of work in the field seems to consist of lots of mathematics with little biological content. I like to think in terms of fuzzy rules like IF the weather is warm AND nutrient levels are high THEN there is a serious risk of bottom anoxia (which is similar to a rule composed for aquaculture siting) but many authors seem more concerned with whether the membership function is triangular or trapezoidal. As with any new field or approach, fuzzy ecology is experiencing growing pains. There was an international conference on the topic in Kiel many years ago, perhaps 15, but progress ha
Re: [ECOLOG-L] Fuzzy Logic in Ecology
William Silvert wrote: I missed Wayne's posting since the subject line had nothing to do with fuzzy logic, and although I know that I will raise a chorus of outrage I am changing the subject line. Quite a few papers on fuzzy logic aplications have been published, many in Ecological Modelling (including a couple of my own). I also have some PowerPoint presentations on my website, http://ciencia.silvert.org, and there are many in related fields such as soil science. I think that one of my first efforts was in niche theory, obviously the "multi-dimensional manifold" that Hutchinson defined must have fuzzy boundaries. Unfortunately a lot of work in the field seems to consist of lots of mathematics with little biological content. I like to think in terms of fuzzy rules like IF the weather is warm AND nutrient levels are high THEN there is a serious risk of bottom anoxia In what way is that fuzzy logic? The truth value of the statement above, Pr(Z|X & Y) > Pr(Z|!(X & Y)) is surely 1. Where is the fuzzy logic element? I'm confused. Bob -- Bob O'Hara Department of Mathematics and Statistics P.O. Box 68 (Gustaf Hällströmin katu 2b) FIN-00014 University of Helsinki Finland Telephone: +358-9-191 51479 Mobile: +358 50 599 0540 Fax: +358-9-191 51400 WWW: http://www.RNI.Helsinki.FI/~boh/ Blog: http://network.nature.com/blogs/user/boboh Journal of Negative Results - EEB: www.jnr-eeb.org
Re: [ECOLOG-L] Fuzzy Logic in Ecology
Re: Ecology Logic Fuzzy* I was never much good at statistics, to put it mildly (two or three courses put a real drag on my GPA and my intuition). It seems (intuitively) to me that Bayes and Zadaeh both had good ideas that were aimed at the direction of the best fit POSSIBLE, the former seeming to be more elegantly conforming to hypotheses, the latter embracing uncertainty more certainly--maybe. I am grateful for those laboring in the fields of numerical research; without them observers of the interplay of organisms and their environments might tumble down some warren of fantasy and never to return. Yet, looking in the looking-glass never hurt anybody. On the other hand, it seems that the Sword of Certainty, especially in the form of irrelevant decimal points and other attempts to reduce complex and constantly-changing phenomena to quantities that fit neat boxes carved out for them, hangs threateningly over jiggly and evasive phenomena, threatening to freeze it all in place for all time. Still, provided analyses don't stray too far from the actual data manipulated and are not treated as license for (ironically?) unbridled conjecture amongst self-ordained emperors, those numbers can open up insights as well as interfere with them. I have no firm answer for this conundrum. What are the Great Questions in ecology? What are the answers? What answers have actually changed rather than just been re-clothed or bumped off the mountain in, say, the last century or so? What new questions have been added? WT *Sorry, Bill, in a lame attempt to please everybody I didn't fuss with the subject line (what a wuss, eh?), I was going to ask Eric off-list but the reply-to-all button didn't have his email address in it, so I just deleted one of the apparently duplicate list addresses--gad, this is getting complicated! Back to square one . . . - Original Message - From: "William Silvert" To: Sent: Thursday, August 06, 2009 8:13 AM Subject: [ECOLOG-L] Fuzzy Logic in Ecology I missed Wayne's posting since the subject line had nothing to do with fuzzy logic, and although I know that I will raise a chorus of outrage I am changing the subject line. Quite a few papers on fuzzy logic aplications have been published, many in Ecological Modelling (including a couple of my own). I also have some PowerPoint presentations on my website, http://ciencia.silvert.org, and there are many in related fields such as soil science. I think that one of my first efforts was in niche theory, obviously the "multi-dimensional manifold" that Hutchinson defined must have fuzzy boundaries. Unfortunately a lot of work in the field seems to consist of lots of mathematics with little biological content. I like to think in terms of fuzzy rules like IF the weather is warm AND nutrient levels are high THEN there is a serious risk of bottom anoxia (which is similar to a rule composed for aquaculture siting) but many authors seem more concerned with whether the membership function is triangular or trapezoidal. As with any new field or approach, fuzzy ecology is experiencing growing pains. There was an international conference on the topic in Kiel many years ago, perhaps 15, but progress has been slow. Bill Silvert - Original Message - From: "Jonathan Nelson" To: Sent: Thursday, August 06, 2009 3:00 PM Subject: Re: [ECOLOG-L] Bayesian analysis in population ecology workshop, early registration deadline 10 August 2009 > On Wed, Aug 5, 2009 at 7:25 PM, Wayne Tyson wrote: >> >> Do you know if anyone has investigated the possible application of fuzzy >> logic theory to ecology/population ecology and why or why not? > > Re the first part of the question: > > Results 1 - 10 of about 12,300 for fuzzy logic ecology. > http://scholar.google.com/scholar?q=fuzzy%20logic%20ecology&oe=utf-8 > > The results include the 2002 overview paper by Regan, Colyvan, Burgman > (Ecological Applications, 12(2), 2002, pp. 618–628) as the 3rd result, > available as PDF. I had not seen this before but I'll be reading it > this evening, as it looks fascinating: > > "Abstract. Uncertainty is pervasive in ecology where the difficulties > of dealing with > sources of uncertainty are exacerbated by variation in the system > itself. Attempts at clas- > sifying uncertainty in ecology have, for the most part, focused > exclusively on epistemic > uncertainty. In this paper we classify uncertainty into two main > categories: epistemic un- > certainty (uncertainty in determinate facts) and linguistic > uncertainty (uncertainty in lan- > guage). We provide a classification of sources of uncertainty under the > two main categories > and demonstrate how each impacts on applications in ecology and > conservation biology. > In particular, we demonstrate the importance of recognizing the effect > of linguistic uncer- > tainty, in addition to epistemic uncertainty, in ecological > applications. The significance to > ecology and c
