The historical biogeographical inference required single locations for terminal linages. This reduced the geographical ranges of contemporary species to a point in two-dimensional space. This was the limitation of most methods in historical biogeography.
More computationally efficient and robust methods have developed because of the significant advancement in continuous methods in historical biogeography and phylogeography. Model-based Methods that calculate parameters using Bayesian estimation of posterior distributions by Markov Chain Monte Carlo (MCMC) or maximum likelihood have been favored over non-model-based approaches in recent years. Itâ€™s a fact that species ranges can be large, irregularly shaped, or spatially diffused. This makes these methods limited by the need to specify a single geographic location for each taxon.
Homogeneous Diffusion or Brownian Motion
Brownian motion is a simple, flexible, and analytically tractable model for species migration over evolutionary periods. Under BM a lineage evolves which behaves as an individual particle moving randomly on a plane. Under univariate BM, after some time t,
the trait change from the ancestral value follows a normal distribution with mean a and variance tÏƒ2, where Ïƒ2 is a constant evolutionary rate. If a is the starting value, then the value x evolving under BM after time t with constant rate Ïƒ2 has a normal probability density:
Island Biogeography Theory
In 1967, a study was conducted on isolated oceanic islands and characterized species distribution by Robert MacArthur and Edward O. Wilson. The studies and the theories were applied to more complex isolated or semi-isolated landscapes, without excluding forests fragmented by agriculture and inland lakes rather than only island ecosystems. The theories of MacArthur and Wilson were based on assumptions about the number of species on each island which is estimated by overall extinction rates and colonization and their proximity to the mainland. The process of colonization is likely to occur near the mainland. Early biogeographers found that due to the availability of a greater amount of resources, as well as a larger area, larger islands are highly likely to have more species than smaller islands. Even though, with more individuals, the risk of extinction for each species decreases, the increase in the number of species within a habitat increases, so does the total extinction rate.
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