1.1. Biodiversity and crisis on West Indies
Oceanic islands, due to their discrete geographic isolation, differ distinctly from terrestrial ecosystem, offer great opportunities for species conservation, and are regarded as the natural laboratory for the study of biogeography and evolutionary ecology (Adsersen, 1995; Crawford and Stuessy, 1997; Ricklefs and Bermingham, 2008). Island habitat heterogeneity and the gene flow barrier between the island and its neighboring islands or land are the most important driving forces leading to new species differentiation and formation (Cherry et al. 2002). The colonized species from continents or nearby islands are then subjected to unique evolutionary processes, for example, geographic isolation, character displacement, and adaptive radiation. The accumulated mutations gradually and ultimately make colonized species into new indigenous species that are genetically different from the original one. One of the most distinctive features of the biota on oceanic islands is the large number of endemics occurring in small areas (Francisco-Ortega et al. 2000).
West Indies was identified as a biodiversity hotspot by Myers et al. (2000). A significant percentage of the Earth’s known terrestrial biota is distributed on islands of the West Indies, many of these species are endemic to the region, to individual islands, and even to isolated areas within some islands (Hedges, 2001). But a large majority of the vast complex of islands in West Indies is changing rapidly, resulting in dramatic alterations of habitats, and nearly all of them are mediated by human activities (Powell and Henderson, 2012). Small population size, gene drift, isolated gene flow, and the complexity of island environment have already made the endemic herpetofaunal species easy to be endangered or extinct, human disturbances undoubtedly worsen the situation. Therefore, critical conservation concerns in West Indian region are increasingly important and required.
1.2. Species-area relationship (SAR)
The species-area relationship is one of the most fundamental patterns in macroecology and an important tool in assessing species diversity, extinction rates and species hotspots (Tjorve, 2009).
According to the equilibrium theory (MacArthur and Wilson, 1967), the relationship between immigration and the extinction of species to island depends on the island size and its distance to mainland. MacArthur-Wilson’s theory provided impetus for numerous studies on species-area relationships (SARs) that have provided biological interpretations for several taxa and have suggested factors and mechanisms that can determine species richness (Simaiakis et al. 2012).
And the theory has an enormous influence on perspectives of species conservation and nature reserves design.
The main objective of this chapter is to discuss SARs for herpetofaunas in West Indies regions, with the aim of discover which factors may determine their distribution over the whole range of island sizes. We choose to fit some candidate models including the power model and some sigmoid models to see whether a J-shaped part exists at the lower end of the curve. Small-island effect (SIE) holds that, on islands smaller than a certain critical minimum area, one cannot observe an increase in species number with increasing area (Simaiakis et al. 2012). We choose to fit candidate models including the power model and some sigmoid models to see whether a J-shaped part exists at the lower end of the curve. If the best fitted model has a sigmoid shape, a J-shaped part will exist at the lower end, and then we accept SIE. If the best fitted model has a convex shape, a J-shaped part will not exist at the lower end, and then we deny SIE. There are also other reasons why it is so important to know the shape of species-area curve. Based on the curve shape, we could estimate total species diversity from limited numbers of samples, or estimate species extinction as a result of habitat loss and fragmentation (Tjorve, 2003).
Candidate species-area models are proposed from two sources. The first source is species-area literature which has traditionally fit data with power or exponential models, the second source involves a broader search of the literature for models that increased monotonically to an asymptote (Flather, 1996).
Although the shape of the curve has been extensively debated over the years, power and exponential curves are the most commonly applied and best known ones, lately, an increasing number of authors have argued some SARs are perhaps best represented by functions that are sigmoid in arithmetic space and there are also a number of recent studies where sigmoid models have been fitted to empirical data (Tjorve, 2003). Some sigmoid models behave similar with others, for instance, the Extreme value function behaves quite similar to the Logistic and Gompertz models; The Cumulative beta-P distribution behaves similarly to the Weibull distribution (Tjorve, 2003).
In this study, we are trying to solve 3 questions:
Question 1: What is the species-area relationship (SAR) for herpetofaunas in West Indies? Is the SAR same for native and invasive species? And is it the same among each animal group classification under amphibian and reptile?
Question 2: Due to human’s help, invasive species are supposed to have a higher dispersal ability as compared to the native. So, in the linear form of the power model (LogS/LogA) is there a higher z-value for the invasive species than the native species?
Question 3: What geographic factors may determine species richness over the whole range of island sizes? Are these factors also applicable to other group of islands that located in similar latitude areas to determine their species richness?
3. Material and Methods
Data on species occurrences originate from Powell and Henderson (2012). Multiple basemaps in ArcMap 10 and ArcGlobe 10 will be used to digitize islands map. We use different scales to digitize islands with various areas. Fractal Analysis will be used to estimate the perimeters at a uniform scale (Farina, 2007). For comparisons of the fit of different models, the Akaike’s information criterion (AIC) was applied (Burnham and Anderson, 2002). Model selection analyses will run using “mmSAR” package (Guilhaumon et al. 2010) for the R statistical and programming environment (R Development Core Team, 2011).
Aim 1: Model selection
we use the 8 most general models composed in “mmSAR” package (Guilhaumon et al. 2010) to fit the data, which include 5 convex models (Power, Exponential, Negative exponential, Monod, Rational function) and 3 sigmoid models (Logistic, Lomolino, Cumulative Weibull).
Aim 2: LogS/LogA linear regression
We analyze the linear function of the LogS/LogA and compare parameter values with vertebrates from global oceanic islands (Triantis et al. 2012).
Aim 3: Find out the geographic factors affect species richness/Steps
Initially selected variables are
X1 Distance to mainland
X2 Latitude of island centroid
X3 Longitude of island centroid
X4 Island No. within 0.1km
X5 Island No. within 0.1-1km
X6 Island No. within 1-5km
X7 Island No. within 5-10km
X8 Islands Area within 0.1km
X9 Islands Area within 0.1-1km
X10 Islands Area within 1-5km
X11 Islands Area within 5-10km
X12 Area of the island
X13 Perimeter of the island
X15 Percentage of vegetation
X16 Percentage of human area
X17 Rivers within the island
X18 Invasive spp. within the island
X19 Percentage of invasive spp.
X1 and X3 are used to examine species dispersal from mainland; X2 is used to examine the nearness to equator; X4, X5, X6, X7 are used to examine stepping stones in each loop circle; X8, X9, X10, X11 are used to examine total area of stepping stones in each loop circle; X12 is used to examine area effect; X13 and X14 are used to examine shape (irregularity) of island; X15, X17 are used to examine habitat quality; X16, X18, X19 are used to examine human disturbance and invasive species.
Principal Component Analysis and Hierarchical Partitioning Analysis will be made based on the residuals distribution of LogS/LogA linear regression to examine which geographic factors are the significant contributions of species richness in West Indies.