Add in sub-module Diversity.Jost to provide support for Jost's divers…

…ity measures.

jostD() is simply qD() from the main package or hillnumbers() from Diversity.Hill
jostbeta (or jostβ) is Jost's naive beta diversity, the gamma diversity of the ecosystem divided by the alpha diversity.

src/Diversity.jl

@@ -21,6 +21,13 @@ export generalisedsimpson, simpson
 
 end # sub-module Compatibility
 
+module Jost
+
+include("Jost.jl")
+export jostD, jostbeta, jostβ
+
+end # sub-module Jost
+
 module Hill
 
 include("Hill.jl")

src/Jost.jl

@@ -0,0 +1,31 @@
+using Diversity
+
+## jostD - calculate naive diversity of order q of a population with
+## given relative proportions
+##
+## Arguments:
+## - proportions - relative proportions of different individuals /
+##                 species in population
+## - qs - single number or vector of orders of diversity measurement
+jostD = qD
+
+
+## jostbeta - calculate Jost's beta diversity of multiple sub-communities
+## Calculates Jost's beta diversity of a series of columns representing
+## independent community counts, for a series of orders, repesented as
+## a vector of qs. This is just the naive gamma diversity divided by
+## the naive alpha diversity
+##
+## Arguments:
+## - proportions - population proportions
+## - qs - vector of values of parameter q
+##
+## Returns:
+## - array of diversities, first dimension representing sub-communities, and
+##   last representing values of q
+function jostbeta{S <: FloatingPoint,
+                  T <: Number}(proportions::Matrix{S}, qs::Union(T, Vector{T}))
+    Ḡ(proportions, qs) ./ Ā(proportions, qs)
+end
+
+jostβ = jostbeta

test/runtests.jl

@@ -124,6 +124,15 @@ using Diversity.Compatibility
 
 @test_approx_eq simpson(communities) ᾱ(communities, 2) .^ -1
 @test_approx_eq generalisedsimpson(communities, Ḡ, Z1) 1
+
+# Checking Jost's diversities
+using Diversity.Jost
+
+@test jostD == qD
+@test jostβ == jostbeta
+@test_approx_eq jostbeta(communities, 1) B̄(communities, 1)
+@test_approx_eq jostbeta(allthesame, qs) ones(qs)
+
 # Checking Hill numbers
 using Diversity.Hill