43. Conner, E.F. and E.D. McCoy. 1979. The statistics and biology of the speciesarea relationship. American Naturalist 113:791-833
Blog author: Ben Clinch
Blurb author: Brian A. Maurer
-BS, Zoology, Brigham Young University
-MS, Wildlife Management, West Virginia University
-MS, Statistics, University of Arizona
-PhD, Wildlife Ecology, University of Arizona
-Research interests: Macroecology, Biogeography, Quantitative Ecology
-Associate Professor at Michigan State University: Department of Fisheries & Wildlife, Department of Geography
Paper author: Edward F. Conner
-Professor at San Francisco State U. since 1997
-Specializes in population and quantitative ecology, as well as insect-plant interactions
-You can find his lab webpage at http://online.sfsu.edu/efc/lab/lab.htm
Paper Summary
1. Main Question: Is the power function model the best fit model for SAR data sets? Does the equilibrium model give unique theoretical basis for SAR? Can the power function or any other SAR model parameters be interpreted biologically?
a. Background: SARs have been used to find the optimal sample size, to calculate the minimum area for a "community," and to estimate the number of species in larger areas. The power function model by Preston gave rise to the equilibrium hypothesis. This connection between the two construes efforts to pin the presence of equilibrium in an area using the power function.
b. Assumptions: Calculation techniques. Power function model assumes dynamic equilibrium of species exchanges between islands. This assumption of dynamic equilibrium lead to the equilibrium hypothesis. Immigration rates are dependent on the distance from the source pool to the sample area.
2. Methods:
a. Meta-data used from 100 SAR data sets gathered from various literature. Compiled and compared sets to analyze resultant patterns. SPSS ran on a CDC 6400 was used for statistical calculations.
b. Various theories and mathematical calculations used from literature: area-per-se hypothesis, passive sampling, equilibrium hypothesis, power function, habitat-diversity hypothesis.
3. Results:
a. Theoretical basis of SAR was found inconclusive. Habitat-diversity and area-per-se may be correct, but aren’t quantitatively or qualitatively different.
b. Untransformed (35 of 100) and power function (36 of 100) models were found to be the best fit most frequently. This result may be due to a narrow range of sample areas.
c. 45 (of 100) of the SAR curves had log/log slopes between .2 and .4.
d. Many previous predictions of parameters from literature could not be confirmed by available data.
4. Conclusions:
a. Power function may have justification for its use as a SAR model, but the data lacks biological interpretation.
b. More and larger data sets needed for complete analysis of parameter predictions. Predictions could not be confirmed.
c. Habitat-diversity, area-per-se, and sampling hypotheses were not confirmed, but could all play roles in the positive SA correlation.
d. No single best-fit model, untransformed and power function found to have a good-fit frequently.
5. Questions/Comments:
a. How did Watson determine that SAR curves are inherently logarithmic?
b. I was surprised by the community’s acceptance of the power function method based on its theory. The author basically said it was taken as the gold standard and wasn’t scrutinized until this paper.
c. The author went into a huge math tirade to answer the parameters question, which made this section difficult to follow.
d. Slightly disappointed that everything in here was deemed inconclusive, but the blurb author insisted that the paper has ushered in more modern approaches to this topic. Is this true?
I appreciate the point of this paper, in that no equation is universal. What factors are impacting what variables is difficult, almost impossible to answer unless you are considering individual situations. What is the barrier that isolates the island? What type of environment and resources are available? And you have to consider what types of species are you looking at.
ReplyDeleteI also appreciated the point that different models may fit best for different habitats. It makes sense to me that there is not going to be one universal equation. There is simply too much variation for that to be true. Unfortunately, it appears that the parameters of the equation can't be readily compared between areas. I guess my main question would be, how truly useful are these equations?
ReplyDeleteI think this approach is a good format when evaluating previously established models. The authors do a good job at breaking down the concepts behind the models and why they are not as universal as some like to make them out to be. I also appreciated that the authors compared a large dataset of real communities and analyzed how many of their datasets matched which models. I do think that this type of research, one that critiques established models, should be done before the models reach the level of prominence in the field that large-scale decisions, such as conservation efforts, are made using them.
ReplyDeleteThis paper uses the same equation as the one mentioned in the last paper, but does a much better job at explaining how the equation works. It is understandable that no equations can accurately predict species-area relationship. The author had to assume that the population he was looking at was homogeneous, which is never the case in real life. There are just too many variables affecting these results.
ReplyDeleteI like that the author set to analyze the idea of "one equation to rule them all". There is so much variability in Biology, that we can not risk to just apply one equation because it worked before in a some different systems. However, I understand that sometimes it is easier to apply what has previously worked in order to see if our data also goes by that rule. So I find this paper as a warning call: make sure that model is actually a good fit for your data, and not just apply it and interpret something out of it.
ReplyDeleteConner sure had a lot to say about his colleagues’s work when he relied so heavily on their data. Although he had a point about scrutinizing hypotheses, any discussion about a topic leads towards understanding. I don’t think we would have been friends.
ReplyDeleteThe underlying reasoning for each explanation and logics were well explained. Also, the paper has a great literature review on different models and discussed the goods and bad which make this research more acceptable. However, I am not sure if they have the all the answers. Nowadays, it is already have been answered. The data they have used is quite diverse to make a good assumption on species-area relationships. I like the word mechanistic explanations. This paper is great because it was well supported by statistical and sampling power (metadata). The appendix has all the raw data organized and ready to be re-used to answer more questions using modern statistical tests and tools. It is little to long paper with complex mathematical explanations but it was an important research.
ReplyDeleteI never realized how much scientists contradict each other until the author pointed it out. This paper is very similar to the paper that we read earlier this week when it comes to its equations. I enjoyed the fact that it gave a background as to why the math is the way that is due to the many perspectives of other scientists. I also remember us going over in class why we use log when making our graphs, but I loved the fact that he went into depth about it, showed us what some of the graphs look like without using the log form and showed us why it was prettier to use log.
ReplyDeleteI enjoyed a lot reading this paper. I think it has a great review and provide a very good background to understand the implications of their analyses. Additionally, it is interesting from a historical perspective as it gives a sense of what were the main questions being studied at the time in ecology.
ReplyDeleteI also think that they have sound methods (despite the lack of high speed computers and advanced statistical software – e.g. visual inspection of fit), with a large sample size and performing the same analysis using different methods. I especially liked the null model approach where they show that the range of z is probably an artifact of how the linear regression is calculated for a species vs. area dataset rather than a biologically meaningful parameter. This caught my attention and I think this type of null models should be a standard practice when discussing the biological implications of statistical patterns.