{"title":"Generalized Logarithmic Species-Area Relationship Resolves the Arrhenius-Gleason Debate","authors":"Mark Carey, John Boland, Gunnar Keppel","doi":"10.1007/s10666-023-09873-6","DOIUrl":null,"url":null,"abstract":"Abstract The species-area relationship (SAR) is widely applied in ecology. Mathematically, it is usually expressed as either a semi-log or power-law relationship, with the former being introduced by Gleason and the latter by Arrhenius. We here resolve the dispute about which form of the SAR to prefer by introducing a novel model that smoothly transforms between the Gleason semi-log (GSL) and Arrhenius power law (APL) forms. The model introduced has the form of ln q ( S ) = a + z ln A , with ln q being a generalized logarithmic function, which is a linear map ( y = x ) for q = 0 and a logarithmic map ( y = ln x ) for q = 1 and q can take any intermediate value between 0 and 1. We applied this model to 100 datasets (mostly islands), linking species richness to island area. The APL was the preferred model in 68% of head-to-head comparisons with the GSL. Both models were supported in 40% of cases. In just under half (44%) of the cases, an intermediate model best explained the data. The results demonstrate the utility of a simple intermediate SAR model. Visualizing the profile of the range of model fits for all q ∈ [0 , 1] (a q chart) allows us to gain extra insight into SARs not yielded by head-to-head comparisons of GSL and APL. The mathematics related to the generalized logarithmic function introduced here should have applications to other areas of ecological modelling.","PeriodicalId":50515,"journal":{"name":"Environmental Modeling & Assessment","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2023-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Environmental Modeling & Assessment","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s10666-023-09873-6","RegionNum":4,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ENVIRONMENTAL SCIENCES","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract The species-area relationship (SAR) is widely applied in ecology. Mathematically, it is usually expressed as either a semi-log or power-law relationship, with the former being introduced by Gleason and the latter by Arrhenius. We here resolve the dispute about which form of the SAR to prefer by introducing a novel model that smoothly transforms between the Gleason semi-log (GSL) and Arrhenius power law (APL) forms. The model introduced has the form of ln q ( S ) = a + z ln A , with ln q being a generalized logarithmic function, which is a linear map ( y = x ) for q = 0 and a logarithmic map ( y = ln x ) for q = 1 and q can take any intermediate value between 0 and 1. We applied this model to 100 datasets (mostly islands), linking species richness to island area. The APL was the preferred model in 68% of head-to-head comparisons with the GSL. Both models were supported in 40% of cases. In just under half (44%) of the cases, an intermediate model best explained the data. The results demonstrate the utility of a simple intermediate SAR model. Visualizing the profile of the range of model fits for all q ∈ [0 , 1] (a q chart) allows us to gain extra insight into SARs not yielded by head-to-head comparisons of GSL and APL. The mathematics related to the generalized logarithmic function introduced here should have applications to other areas of ecological modelling.
期刊介绍:
Environmental Modeling & Assessment strives to achieve this by publishing high quality, peer-reviewed papers that may be regarded as either instances of best practice, or as studies that advance the evolution and applicability of the theories and techniques of modeling and assessment. Consequently, Environmental Modeling & Assessment will publish high quality papers on all aspects of environmental problems that contain a significant quantitative modeling or analytic component, interpreted broadly. In particular, we are interested both in detailed scientific models of specific environmental problems and in large scale models of the global environment.
We invite models of environmental problems and phenomena that utilise, in an original way, the techniques of ordinary and partial differential equations, simulation, statistics and applied probability, control theory, operations research, mathematical economics, and game theory.
Emphasis will be placed on the novelty of the model, the environmental relevance of the problem, and the generic applicability of the techniques used. Generally, papers should be written in a manner that is accessible to a wide interdisciplinary audience.