Paper 43. Conner, E.F. and E.D. McCoy. 1979.

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?

Baldi, Andras. 2008.

Baldi, Andras. 2008. Habitat heterogeneity overrides the species-area relationship. Journal of Biogeography35(4): 675-681.

Blog author: Maria Goller

Author bio:

> Received his PhD in 1996 in environmental sciences at L. Eötvös University

> Director of the Centre for Ecological Research at the Hungarian Academy of Sciences

> Broad focus is biodiversity (mainly bird communities)

> More specifically, he is interested in how human land use shapes ecosystem services (pollination and soil decomposition) and how these affect biodiversity

> Was a partner on the Liberation project which investigated farmland biodiversity and ecosystem services. 

Summary/Main Points

Background:

> Many explanations for the species-area relationship fail to incorporate habitat heterogeneity

            > Random model: just because larger area => more individuals => more species

            > Equilibrium model: based on immigration and extinction, and isolation of habitat patches

> But habitat heterogeneity is potentially extremely important

Assumptions:

> Larger reserves conserve more species

> Area is more important than heterogeneity of habitat

Main question:

> Baldi wanted to directly compare the effects of area and heterogeneity – does the species-area relationship still hold if larger areas have lower heterogeneity?

Methods:

Data:

> Study site in Hungary – 16 reserves

> Field surveys for all animal species from 1977 to 1980

> Focused on arthropods for analysis

Methods:

> Used observations for various arthropod families

> Graphed species-area curves and looked at the relationship between habitat type density (heterogeneity) and species density (richness)

Results:

> Heterogeneity was positively correlated with number of species

> Small patches were more heterogeneous than larger patches

            > Richer habitat (soil, etc…) => greater productivity

> Some families/groups of taxa greatly influenced by very small-scale changes (such as in soil) that are not related to area

> Certain taxa with good dispersal have a strong positive species-area relationship

Conclusions:

> Protect areas with greater heterogeneity

> But also keep creating large preserves – these often have specialized species that are only found there, and not in small reserves, even if small reserves have a greater total number of species

> Productivity is also an important factor

Questions:

> How useful do you think it is to spend years doing surveys to compare reserves?  

> What other factors – aside from heterogeneity and productivity – could affect the species-area relationship?

> While conserving multiple small reserves may be more beneficial to conserving biodiversity, is it actually feasible in the long run?

Rybicki and Hanski (2013)

Rybicki and Hanski (2013)

Species–area relationships and extinctions caused by habitat loss and fragmentation

 Blog author: Sebastian Botero

·     Paper authors: 

Joel Rybicki

o   PhD from the University of Helsinki and Aalto University in 2016.

o   Currently, a Postdoctoral researcher at the Institute of Science and Technology of Austria.

o   Computer scientist working on theoretical questions related to distributed and self-organizing systems. In ecology, he is interested in spatial models, metacommunities, habitat loss and fragmentation.

Ilkka Hanski 

o       One of the most influential ecologists of recent years, developer of the metapopulation theory. 

o      born in 1953 in Lempäälä, Finland, died in 2016.

o      Studied biology at the University of Helsinki and gained his doctorate, on the community ecology of dung beetles, from the University of Oxford in 1979.

o       Did research around the globe, from Sweden to Madagascar.

o      Recommended book by Hanski: Messages from Islands: A Global Biodiversity Tour, where he presents his ideas on biodiversity at the time that he gives an account of his field work.

·     Paper summary

1.    Main question: 

Background:Since it was first quantified by Arrheius in the 1920s, the species-area relations (SAR) has been of interest to ecologists. Although the mechanisms behind this pattern are not completely understood, it appears that increase in heterogeneity (more habitats) and population sizes (thus reducing extinction risk) with area are the main drivers of it. One application of SAR curves has been the estimation of extinction rates from data on habitat loss. In fact, this has been one of the main tools to quantify human-induced extinction. There is controversy over the best way to apply this equation to assess species extinction, with opposite views on whether it overestimates extinction (given that more area is necessary to detect the first individual than for extirpating the last one) or underestimates it by not considering the extinction debt from unviable populations. As a response to this, researchers have proposed modifications of the curves to assess the effect of habitat loss, mainly the Endemics–area relationship (EAR) which accounts for the species only present in the lost habitat and the remaining species–area relationship (RAR), which gives the fraction of species surviving habitat loss as a power of the fraction of remaining area

Assumptions:to test the behavior of power-law SAR as well as the other relations in predicting species extinction under habitat loss and fragmentation, the authors created a simulated model of a realistic landscape that assumed:

-      Several species distributed in a bounded area.

-      Spatially variable habitat type.

-      No interspecific interactions

-      Different ecological traits among species

-      Different dispersal capacities among species.

-      performance of a local population in a lattice cell is determined by the match between the species phenotype and habitat type.

-      Environmental stochasticity. 

Main question:how species-area relation and its derivates behave under realistic habitat loss and fragmentation scenarios?

2.    Methods

This paper used a simulation approach where a “virtual landscape” was created. The landscape contains different habitats and a set of species with different habitat affinities (simulation environmental heterogeneity). Each site in the landscape will have a colonization and extinction parameter that will be influenced by habitat loss and fragmentation. After running the simulation, it is possible observe the effect of these to processes on the virtual species and determine the behavior of SAR, EAR and RARs under different habitat loss and fragmentation scenarios.

3.    Results:

o   Each of the relations provided different types of information and behave differently under different fragmentation and habitat loss scenarios. The EAR best describes the species going extinct after habitat loss occur but omits from the calculation unviable populations that would go extinct in the future, on the other hand, the SAR appears to best predict the species loss in the long term.

o   The effect of the configuration of the habitat on SAR will depend on the total amount of remaining habitat in the landscape, being only important when there is little remaining habitat.

o   Clustering of the remaining fragments results in lower extinction rates after habitat loss.

4.    Conclusion: 

o   This paper demonstrates through simulations that SAR are not overpredicting species loss, as that model is the one that best incorporates species extinction from unviable populations.

o   It also demonstrates that the effect of habitat loss above certain threshold will depend on the configuration of the remaining habitat.

o   A practical rule of thumb for conservation spatial prioritization is proposed in which the third of the region is selected as conservation landscapes comprising clusters of habitat and within those landscapes, a third is protected.

5.    Comments

I find this paper as a unique instance of how highly theoretical work can have very practical applications. The fact that the paper has implications for reserve design and provides advice on how to proceed to achieve the Aichi targets is one of the most interesting aspects of this work to me. 

6.    Questions:

o   How realistic do you think the model was? Under different assumptions would it provide the same results?

2. Arrhenius, O. 1920.

2. Arrhenius, O. 1920. Distribution of the species over the area. Meddelanden FranK. Vetenskapsakademiens Nobelinstitut 4:1-6.

Blog Author: Devra Hock

Blurb Authors: 

Ethan P. White, Department of Wildlife Ecology and Conservation, University of Florida 

Field of Study/Research: Data-Intensive Ecology, Ecological Forecasting, Computational Ecology, Quantitative Ecology, Macroecology. 

Ethan’s studies data-intensive problems in ecology including ecological forecasting and using high resolution remote sensing to understand individual level patterns in ecological systems at large scales. He is actively involved in computational training efforts as a Data Carpentry founder, The Carpentries Executive Committee member, and lead developer of the semester long Data Carpentry course.

Paper Authors:

Olaf Arrhenius. 

Summary/Main Points

1. Main Question:

            Background—Expansion on previous paper analyzing the relationship between geographic area and the number of species

-Understanding the distribution of species across areas of unequal size. 

            Assumptions—Calculating species across a transect is an accurate representation of total species in the area

-Mathematical equation still applies to areas of various and unequal sizes, different elevations, and different habitats (i.e. islands, lowlands, mountains).

            Main Question—Determining the distributional relationship of species in various geographical areas

2. Methods:

            Data—Species counts from collection data

            Methods—Synecological transect-examination method, i.e. the collection of vegetation along a transect is the same as the collection over the whole surface through which the transect is laid

-Measure the length of associations crossed by the line and expresses the length of every association in percentage of the whole line

-1 line per 150 meters provides accurate results.

3. Results

            For the equation x=k/y^n, n=0.55 from observations. From calculation1, values correspond to n=0.55, from calculation2, n=0.5 The calculated values agree nearly equally with observed values. 

-The relation between the linelength and the mean deviation is what is expected according to probability. Mean deviation is inversely proportional to the square root of the number of observations 

4. Summary

            -Increase of species within an area can be expressed by a mathematical approximation; holds true for areas with large distances between them, and areas of unequal size. 

            -The mean deviation between transect lines can be calculated according to the law of probability

5. Questions

            -I would have liked to see an expanded results section that better talked about the numbers shown in the tables. What species were found, where certain species found with more abundance, etc. Better explanation would have made the mathematical equations and numbers easier to understand. 

            -I would have also liked to see a discussion on the species’ distribution. There was almost no discussion of the numbers calculated and it hard to comprehend the full importance of the research. 

Paper 2- Arrhenius (1920)

Blog author: Sebastian Botero

Distribution of the species over the area

·     Blurb author: Ethan P. White.

o   PhD Biology (with distinction), University of New Mexico

o   BA Biology (magna cum laude), Colorado College

o   When his commentary on Arrhenius (1920) was published, he was a professor at the Dept. of Biology and Ecology Center, Utah State University (from 2007 – 2017).

o   Currently, associate Professor, Dept. Wildlife Ecology & Conservation, University of Florida.

o   His research focus on “Data-intensive problems in ecology including ecological forecasting and using high resolution remote sensing to understand individual level patterns in ecological systems at large scales” – Sounds like macroecology.

o   He has an interesting lab webpage with the projects and publications as well as data management software. http://www.weecology.org

·     Paper author: Olaf Arrhenius

o   Born in Stockholm, Sweden, on 2 November 1895 and died in 1977.

o   The son of the Nobel laureated chemist Svante Arrhenius.

o   Got a D.Sc in agricultural chemistry in 1920 (at the time he was publishing this paper) and then moved to work at an agricultural experimental station in Stockholm.

o   Received several awards during his career.

·     Paper summary

1.    Main question: 

Background:the author doesn´t give much background, he just mentions that knowledge on the species-area relations is important for plant geography and then continues to discuss the empirical findings on the species-area relations.

Assumptions:There are no explicit assumptions, but I guess that the main one would be that differences in species numbers from the compared sites is not very much influenced by sampling effort.

Main question:What is the mathematical relationship between the area of a site and the number of species present on it? And how well this relation fits the data and is consistent across scales and regions?

The last part of the paper also covers the question on the precision of a transect method for quantifying vegetation types covering an area (only the species-area section of this paper will be covered below).

2.    Methods

Data:Arrhenius used plant species number and area for several sites at each of five regions representing different sampling scales (from dm to Ha).

Method:The author used the following equation to describe the relation between area size and the number of species present on it:

y/y1=(x/x1)ⁿ

where y represents the area and x the species richness of one site and y1 and x1 represents the area and richness of a second site. n is a constant and is the parameter of interest for the author.

The data was used to derive an empirical value of n, which was compared among regions and sizes to determine how general the pattern was.

3.    Results

o   Four of the studied regions presented the same scaling parameter (3), with a good match between the number of species predicted by the equation and the observed number. It was significant that the prediction appeared to work well for disparate geographical areas and sampled area sizes. 

o   The data from the Aland regions showed an exponent of 5.6 in discordance with the other sites. Arrhenius attribute this to the small range of sizes sampled there.

4.   Conclusion:The relation between the area of a site and its species richness can be described by the above equation, generally using an exponent of 3. This pattern holds true for different spatial scales of analysis and different areas.

5.    Comments:

o   To compare these results, take into account that with the way the equation is formulated by Arrhenius, the values for n are equivalent to z values from 0.2 to 0.3. 

o   I find interesting how a paper that just describes a pattern, with a concrete result, but with further discussion of its implications or underlying mechanisms had such an important impact.