The Statistics and Biology of Species-Area Relationship (Connor and McCoy 1979)

The Statistics and Biology of the Species-Area Relationship (Connor and McCoy 1979) cited 2,376 times

Commentary by Brian A. Maurer (1954-2018)

• co-founded the discipline of macroecology in the famous 1989 Science article (Macroecology: The Division of Food and Space Among Species on Continents)
• director for statistical training and consulting at Michigan State University
• 69 peer-reviewed publications and 2 books (Geographical Population Analysis: Tools for the Analysis of Biodiversity 1994; Untangling Ecological Complexity: The Macroscopic Perspective 1999)
• professor and mentor of undergraduates, grad students, and postdocs 
• talented singer, songwriter, guitarist

Education: 

• BS in Zoology (Brigham Young University,1977)

• M.S. Wildlife Management (1980, West Virginia University, Thesis Topic:  Avian foraging and habitat structure.) 

• M.S. Statistics (1982, University of Arizona, Thesis Topic:  Repeated measures in bioassay.) 

• Ph.D Major Wildlife Ecology, Minor EEB (1984, University of Arizona, Dissertation Topic:  Environmental heterogeneity and avian community structure.)

Career:  1984-1986 postdoc University of Arizona with Jim Brown; 1986-1999 professor in Zoology, Bringham Young University; 1988 Visiting Scientist, Lanzhou University, China;  1994-1995 research associate in community ecology, Museum of Natural History at University of Kansas; 1997 distinguished researcher in residence, Mountain Research Center at Montana State University; 1999-2018 professor department of fisheries and wildlife at Michigan State University; 2012-2018 director for statistical training and consulting at Michigan State University

Main Authors:

Edward F Connor (left): plant- insect interactions, population ecology, quantitative ecology, biogeography, macroecology

Professor in Biology Department at San Francisco State University

Earl D McCoy (right): biogeography, biostatistics, conservation, restoration 

Ph.D., Florida State University, 1977

Professor at University of South Florida

Paper Notes

History: Continuation off of work from Frank Preston (1948) who first described number of species in a community to be a log-normal distribution which later arrived at relation of power relation between species number and area.

       ---> Then was used for MacArthur and Wilson's "equilibrium theory of island biogeography" (species number is a dynamic result fo immigration or extinction or a combination of both)

Conceptual figure of equilibrium theory of equilibrium theory of
 island biogeography

       ---> Also was accepted at the time that number of species increased with area  and that number of species in a taxa increase with decreasing latitude. 

Theory Implications: conservations Single Large Many Small

Novelty: This paper is novel because Connor and McCoy sought out to quantitatively test these theories through a combination of 100 data sets

Summary

• No unifying theory to explain SAR. All depends.
• Studies vary on which model fits the data best though power function suggested. 
• Slopes and intercepts vary between datasets- skeptical of biological interpretation.
• Equilibrium theory should be used as a testable hypothesis. It doesn't fully explain causality and shouldn't be accepted as fact.
• Latitudinal-diversity relationship can be seen in correlation coefficients and not explained by intercept (alpha diversity) or slope (beta diversity).
• Interpretations of SAR should be based on 1) best model fit for the dataset, 2) correlation between number of species and area, 3) how parameter values compare to those published in the literature.

Is there a unique theory to explain Species Area Relationship (SAR) Theory?

3 Main Hypothesis of SAR:

1. Habitat- diversity (Williams 1964): as area sampled increases so does chance of getting more habitat thus species ++. With area+
2. Area-per se (Preston 1960, 1962; MacArthrur &Wilson 1963,1967): species# is from immigration and extinction rates not habitat. Immigration is independent of island size but more dependent on proximity to source population, and Extinction is inversely proportional to population size which is also related to area.
3. Sampling: null hypothesis...sampling phenomenon not biological- tend to sample large areas more.

       -----------> All have been supported in the literature around this time.  All must be taken into consideration, thus mechanism not exactly resolved.

Is there a best fit model?

Conventional SAR models tested with datasets

• species/area (S/A)... aka untransformed
• S= k +zA

• species/log_area (S/LA)... aka exponential
• S = log k + z log A

• log_species/area (LS/A)... aka untransformed
• log S = k + zA

• log_species/log_area (LS/LA)...aka power function**
• S = kA^z

 --> Not exactly.. Power is better than exponential but the same as untransformed. However, there doesn't seem to be a pattern that discerns what model is best. Power model is suggested to continue to be used.

Can parameters of  power function  be interpreted-biologically and statistically?

Other studies have argued for biological significance for intercept and slope of the power function

• Preston's power function  implies significance with the "caonical" slope of 0.262
•  Evaluation of 100 studies show this range of slope should ultimately be 0.20-0.40 which may be coincidence, but also is a trend seen regularly in biology. Should be used as a “criterion of subtraction” aka null slope values, where deviation from this range might mean something biologically.
• Slope and intercepts in a power function are interdependent so only intercepts can be compared.
• Slope 1= isometric relationship, <1= diminishing return or area for species , >1 = greater # species in larger areas
• Slope and intercepts of previous power functions not always true so not generalizable- view as fitted constants with no biological relevance

Interpretation of SAR (methods)?

• Correlation should be used if interested in degree of relatedness between species and area but regression should be used if comparing 2 or more bivariate distributions
• Parameter estimation: least-squares regression and reduced-major-axis method (geometric mean) 
• least squares regression chosen because yield similar slopes and intercepts
• Model I regression- only dependent variable assumed to have error but there’s often error in area which then underestimates slope
• "Berksen case" (error permitted but controlled by experimenter via chosen sizes) 
• **Model II: error  uncontrolled which is preferred for SAR
• Model II  should be used when trying to get parameter estimates, while Model I or II can be used for comparing parameter values

Islands vs continents/ isolated vs non isolated: 

Figure 3 in paper A on left and B on right

Figure 4 in paper: Slopes can be same even if intercept
starts off smaller for far isolates as opposed to near

Fig 3A: transient hypothesis (MacArthur and Wilson's view)- slopes will be smaller in non-isolated areas (within continental area or within an islands) due to many transients that will be encountered which decreases likelihood or achieving more species when expanding area.

Fig 3B: Schoener's view- slope is dependent on source pool of species - "distant archipelagoes have depauperate biotas"

However, slopes can still be the same if y intercepts are different for isolates (fig4)

-----> Both views are supported in the literature.

Alpha and Beta Diversity into slope and intercept parameters

Intro to Alpha/Beta/Gamma diversity: conceptual figure describing Whittaker's 1960 ideas on diversity found from: https://www.webpages.uidaho.edu/veg_measure/Modules/Lessons/Module%209(Composition&Diversity)/9_2_Biodiversity.htm

MacArthur and Wilson attempted to intertwine Whittaker's theory for interpretation in analysis by suggestion that alpha could be intercept (within island/habitat diversity) and beta could be slope (between islands/habitat diversity) .

----> But importance of alpha vs beta diversity in SAR trend is impossible to pull apart bc slope and intercept of the power function are interdependent… 

Latitude

MacArthur tries to use this theory to explain the inverse relationship between latitude and species number (but the same issues of slope and intercept interdependency exists)

• if intercept is related: pattern is driven mostly by increase within-habitat diversity
• if slope is related: increased between-habitat diversity
• if both intercept and slope: latitudinal-diversity gradients are driven by both within and between habitat diversity

---> Slope and intercept were tested but few to no datasets showed particular pattern in datasets.
However, correlation coefficients are negatively correlated with latitude (r=-0.3183, P<0.001; see figure 5 below); meaning log area explains more variation in log species at low latitude than at high latitudes. 

Figure 5- correlation decreases with latitude

Discussion Points:

1. Can you think of any confounding factors that could change this general pattern of species increasing with area?
2. Considering what has been stated by theory on continuous vs separate habitats, do you agree with the general transient hypothesis? Could you think of ways that having many transients might not lead to an overinflated species numbers in small areas?
3.  Do you think you might find the same patterns on smaller scales and global scales?