THE SPECIES-AREA RELATIONSHIP (SAR) OF ARRHENIUS
This page deals with the question how much minimum space of anecosystem is needed to capture a significant representation and secure the highest possible survival of the species represented. This in turn is essential to determin the minimum size of protected areas for conserving viable minimum populations of species.
For more than eighty years, ecologists have recognised that the size of an area of wild habitat correlates strongly with the number of plant and animal species to be found in that area. In 1921, a Swedish plant ecologist named Olof Arrhenius published a paper straightforwardly titled "Species and Area", which is considered a classical work in ecology and has been embraced by most ecologists in the world. Based on investigation of species diversity within certain delimited plots, Arrhenius (1921) concluded that the number of species increases continuously less as the area increases. This phenomenon is known as the species/area relationship (SAR). This is reflected in the quantitative formula S = cAz, in which S represents the number of species and A the size of the area. The constant c is an empirically determined multiplier that varies among taxa and areas (USA Commission on Life Sciences 1995), and which may be ignored when comparing the percentages of S and A, as done in this analysis. The exponent z varies according to the topographic diversity, the isolation of the area and the mobility of the taxon. It is usually higher* for islands (around 0.3) than for the mainland (commonly assumed less that 0.2). Dobson (1996) suggests 0.15. Figure 5 plots the percentages of species lost against the percentage of ecosystem lost for (a) an island situation in which z = 0.3 and (b) for a large land mass in which z = 0.15. The curve is often referred to as the "species-area curve". (* the lower z, the less space is needed to capture a greater number of species.)
Often the species-area relationship is used in disregard of spatial differentiation in ecosystems. However, within reasonably homogeneous ecosystems, species populations are still spread differently across a ecosystems, depending on factors such as population density and micro variations in the terrain. Welter-Schultes and Williams (1999) warn that "habitat" cannot be ignored in species-area relationship studies, and it is assumed that the SAR applies to homogeneous or very gradually changing environments. The moment one passes from one ecosystem to a next, a new assembly of species with differentiation in population densities gets to be included, which leads to a sudden in crease in differentiation of the species assembly, which then is ruled by the mechanism of the SAR for the new ecosystem. After the initial increase of species in the new ecosystem, the curve levels off again, until another boundary is passed into yet another ecosystem. The application of the formula to model the number of species lost or conserved requires a reasonably detailed distinction of different ecosystems.
How good is the species-area curve equation? Several mathematicians have attempted to theoretically explain its validity. As recently as in 2000 an attempt by Hartman (2000) to mathematically explain the validity of the curve, was rebuked by Maddux (in press 2002) and no satisfactory explanation seems to be available yet; however, none of the theoreticians seems to challenge the validity of the model itself (R.D. Maddux pers. com.). The mere convenience of its simplicity is no reason to embrace its universal validity, particularly not in the context of the present bald attempt to set minimum sizes for ecosystems. For its validity, one must rely on evidence from literature. On a small scale, the model has been commonly practiced to estimate the minimum plot sizes required for relevés or plot-sizes in different plant communities (e.g. Mueller-Dombois and Ellenberg 1974, Küchler and Zonneveld 1988). Many biologists have used the equation to predict or test species-area relationships on islands, usually applying it to one selected faunal taxon (e.g. Diamond 1975, Welter-Schultes and Williams 1999). Given the numerous indications for validity and application over a period of more than 80 years, we consider the model a responsible tool for theory development to set selection criteria for protected areas systems, although opinions about the z-values for continents varies. As always must be the case with models, great prudence and continued alert for alternative propositions must be upheld.
While we have not found scientific data on the matter in literature, Arrhenius, principle does not seem to be limited to ecosystems, but has a far greater scope, as it one could apply it in human society. For instance, when one observes a large parking lot, in the first row, one would observe mostly different models of cars. When one adds, another row to the observation, more models get added, but probably less than from the first row. Once one doubles the sample again to a total of 4 rows, again a lower percentage of models gets added, etc. Also in time observations, this is the case. Whomever keeps records of birds in a new area of observation, will record the greatest number of species to the list during the first hour, and as time progresses, it takes longer and longer to add more species. The same principle is true for the observation of models of vehicles observed in traffic. These observation seem to corroborate the Arrhenius principle even further. Experimenting with the Arrhenius principle both in nature and society would be a valuable exercise for for biology students.
also seems to apply to observations spread over time, in which
Variation in the exponent of the species-area curve
A fundamental criticism that one may raise against the principle is that rarely all species of an area are known, given that many species of arthropods, fungi and oligocellular organisms are never considered in inventories that have lead to the plotting of the species area curve. This is correct, but a researcher that investigates the increase of species always uses the same assemblage of species of his/her knowledge consistently in the study area. Therefore, we may assume that the mechanism applies for different assemblages of species, even though the species area curve can never have been applied to a complete dataset of species that also included all lower organisms of a wild ecosystem, as such dataset does not exist for any wild ecosystem in the world.
Table 1: Percentage of Species conserved for different z values.
An important question is if the species-area equation works the same for all organisms. To answer this question, Prins (2002) has compared known z values of island dwelling walking mammals and reptiles with those of island dwelling birds and bats. He found that walking mammals and reptiles have much lower dispersal power among island dwelling fauna than flying animals. Therefore, their z value is much higher.
Apparently, the value of z varies per taxon and is reversely related to the dispersion power of taxa (Prins 2002), with flying, wind and water dispersed organisms, probably having the lowest z values. The dispersal power of species on continents is much better than on islands, which is reflected in lower z values. Given the z values of flying animals for island situations in Table 1, being in the range of 0.24 logic would suggest that for continental situations the z values might indeed be lower than 0.2, with estimates between 0.12 and 0.19 (Connor and McCoy 1979, Reid 1992) for different subsamples of continuous habitat. Ney-Nifle and Mangel (2000) observe that z varies with the location and shape of the area conserved, depending on the distribution power of the species assemblies concerned. We have plotted the species-area curve for different variables: Click for species-area curve variables
A factor that we have not found mentioned should be the following. The analysis of the species-area curve is based on an area based increase of the sample plot and therefore the area size increases quadratically. In the initial plot of the analysis, the investigator probably finds each individual species of his/her study set. However, as the plot area increases, the chance of overlooking additional species increases considerably, and therefore the z values often even may be a bit on the pessimistic (in casu high) side as they should actually be a bit lower and thus the species area curve a bit steeper.
In this document, the differentiation of species assemblages is based on rather detail-defined ecosystem classes, which favours the capture of more species than would be the case when using much coarser defined ecosystems. The approach of seeking representation of each ecosystem in a country several times, leads to geographical variation, within the same ecosystem. This would result in the selection of further variation in species assemblages of a the ecosystem in question. Therefore, by passing from one region in the country to a different one, but with equivalent ecological conditions, more species would be included, than would be the case if one would expand from the same plot area.
This has been corroborated by S. Mori (pers. com.), who has extensively sampled French Guinea and maintains a large database for the country. The database of woody species, shows that continued sampling in the same region of the country does not lead to considerable increase in species. However, datasets from another region of the country with the same ecological conditions, does show a number of different species. This is probably one of the factors that contribute to the shape of the species-area curve. Also, geographical spread across a country automatically leads to the incorporation of bio-geographical differentiation without having to know the bio-geographical units.
Taking in consideration these different factors, it is assumed that the use of the species-area-curve can be considered as one of the most significant tools in determining the minimum areas for biodiversity conservation and for establishing the minimum sizes of protected areas and ecosystems.
Keywords: area, species, Arrhenius, relationship, curveThis page is part of our web-book on Biodiversity Conservation. For organized reading go to our on-line Table of Content, or download our book in pdf format.
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