Speciation continues to be one of the most intriguingphenomena in evolutionary biology; even though ourunderstanding of many of the mechanisms involved duringspeciation has improved considerably in the last twodecades (Howard and Berlocher 1998, Gavrilets 2004,Coyne and Orr 2004). Recently, Emerson and Kolm(2005) suggested a new agent that could potentially drivespeciation: species diversity itself. Emerson and Kolm(2005) argued that data on numbers of endemic speciesindicate that speciation rate increases with increasing plantand arthropod diversity on the Canary and HawaiianIslands. According to Emerson and Kolm, the proportionof endemic species in taxonomic groups can be used as asurrogate for speciation rate because that proportion isaffected mainly by in situ island speciation rather than byextinction and speciation on other islands (cf. Cadena et al.2005). It follows then that a higher proportion of endemicspecies means a higher in situ island speciation rate. Theproportion of endemic species was found to increase withincreasing diversity on the Canary and Hawaiian Islands,leading to the conclusion that species diversity itself couldbe driving speciation (Emerson and Kolm 2005).Emerson and Kolm’s (2005) study received skepticalresponses (Cadena et al. 2005, Kiflawi et al. 2007, Pereiraet al. 2007, Whittaker et al. 2007, Gruner et al. 2008) thatcame up with several reasons why Emerson and Kolm’s(2005) analysis fails to identify the agent responsible for theobserved relationship between the proportion of endemicsand species diversity. In one of these responses, Witt andMaliakal-Witt (2007) showed with a null model that therelationship can arise by chance alone through stochasticcolonizations and extinctions; however, their null model didnot incorporate speciation, extinction, and inter-islandcolonization. Our main interest is whether Witt andMaliakal-Witt’s (2007) conclusion still holds when theseprocesses are included.The null model presented here is constructed as apresence/absence matrix. The columns are islands and therows are species, where ‘‘1’’ means the species is presenton that island and ‘‘0’’ means absent. Species diversity onthese islands is determined by speciation, extinction, andmigration between the islands; each of which depends onchance. Each species has the same probability of undergoingthese events, and these probabilities are kept constantthroughout the simulation.Presence/absence matrices have been used widely forbuilding null models in community ecology and islandbiogeography (Connor and Simberloff 1979, 1983). Thesemodels have been very influential, but at the same time,have been criticized for potential statistical biases built intothe matrices (Diamond and Gilpin 1982, Wright and Biehl1982, Wilson 1995, Gotelli and Entsminger 2001, 2003).In these models, the ‘‘assemblies’’ of species on islands hasbeen the main interest, so the critical issue was the way ‘‘1’’sand ‘‘0’’s were distributed in a given matrix with fixedcolumn and/or row sums (Gotelli 2000). In our model,however, the distribution of ‘‘1’’s and ‘‘0’’s in the matrix isnot of interest. Moreover, in our model, the size of thematrix changes during the simulation; the matrix growswhen a new row is added after a speciation event (whichensures that the new daughter species is present only on thatisland and nowhere else) and shrinks if a species goes extincton all the islands. Migration between the islands does notaffect the matrix size, but converts the ‘‘0’’s to ‘‘1’’s if themigration event is successful. Thus, the model is unbiased asit does not test whether or not there are certain speciesassemblages on islands.At each time step, each species can potentially speciate,go extinct, or migrate to another island; whether they willdo so depends on chance determined by a random numberdrawn at each time step. For example, if the randomnumber drawn for a particular species is less than thespeciation probability assigned for that simulation, then thespecies undergoes a speciation event. After a speciationevent, the existing species on the island can potentially goextinct depending on the random number drawn at eachtime step for each species. As before, all the species have thesame extinction probability that remains constant through-out the simulation. Lastly, all species that survive on anisland can potentially migrate to other islands, thusreducing the proportion of endemics.
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