doc: betadiv measures

docs/SpeciesInteractionNetworks.bib

@@ -215,4 +215,46 @@ @Article{Bascompte2003nested
   publisher = {Proceedings of the National Academy of Sciences},
 }
 
+@Article{Whittaker1960Vegetation,
+  author    = {R. H. Whittaker},
+  journal   = {Ecological Monographs},
+  title     = {Vegetation of the Siskiyou Mountains, Oregon and California},
+  year      = {1960},
+  issn      = {0012-9615},
+  month     = {jul},
+  number    = {3},
+  pages     = {279-338},
+  volume    = {30},
+  doi       = {10.2307/1943563},
+  publisher = {Wiley},
+}
+
+@Book{Magurran1988Ecological,
+  author    = {Magurran, Anne E},
+  publisher = {Princeton university press},
+  title     = {Ecological diversity and its measurement},
+  year      = {1988},
+}
+
+@Book{Southwood2009Ecological,
+  author    = {Southwood, Thomas Richard Edmund and Henderson, Peter A},
+  publisher = {John Wiley \& Sons},
+  title     = {Ecological methods},
+  year      = {2009},
+}
+
+@Article{Wilson1984Measuring,
+  author    = {M. V. Wilson and A. Shmida},
+  journal   = {The Journal of Ecology},
+  title     = {Measuring Beta Diversity with Presence-Absence Data},
+  year      = {1984},
+  issn      = {0022-0477},
+  month     = {nov},
+  number    = {3},
+  pages     = {1055},
+  volume    = {72},
+  doi       = {10.2307/2259551},
+  publisher = {{JSTOR}},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}

docs/mkdocs.yml

@@ -46,6 +46,7 @@ nav:
     - Nestedness: community_level/nestedness.md
   - Meta:
     - Beta-diversity: meta_level/betadiversity.md
+    - Beta-diversity measures: meta_level/dissimilarities.md
     - Set operations: meta_level/sets.md
   - Random:
     - Permutations: random_networks/permutations.md

docs/src/meta_level/dissimilarities.md

@@ -0,0 +1,19 @@
+# List of dissimilarity functions
+
+!!! abstract
+
+    The methods in this page are from [Koleff2003Measuring](@citet); when called on the output of [`betadiversity`](@ref), they will return a (dis)similarity score.
+
+In the original paper [Koleff2003Measuring](@cite), the measures are expressed
+as a function of ``a`` (the number of shared elements), ``b`` (the number of
+elements unique to the right/neighbouring set), and ``c`` (the number of
+elements unique to the left/focal set). In this documentation, we use a slightly
+different convention, where ``c = L`` (left), ``a = S`` (shared), and ``b = R``
+(right).
+
+## List of measures
+
+```@docs
+KGL01
+KGL08
+```

src/meta_level/measures.jl

@@ -1,3 +1,18 @@
+"""
+    KGL01(S::T) where {T<:NamedTuple}
+
+
+
+``\beta_w = \\frac{L+S+R}{(2S + L + R)/2}``
+
+###### References
+
+[Magurran1988Ecological](@citet)
+
+[Southwood2009Ecological](@citet)
+
+[Whittaker1960Vegetation](@citet)
+"""
 function KGL01(S::T) where {T<:NamedTuple}
   return (S.shared+S.right+S.left)/((S.shared + (S.shared+S.right+S.left))/2.0)
 end
@@ -29,6 +44,18 @@ function KGL07(S::T) where {T<:NamedTuple}
   return exp(KGL06(S))-1.0
 end
 
+"""
+    KGL08(S::T) where {T<:NamedTuple}
+
+``\beta_t = \\frac{L+R}{(2S + L + R)}``
+
+This method is used in [Poisot2022Dissimilarity](@citet), and has a lot of
+desirable properties. We suggest its use as a default.
+
+###### References
+
+[Wilson1984Measuring](@citet)
+"""
 function KGL08(S::T) where {T<:NamedTuple}
   return (S.right + S.left) / (2*S.shared + S.right + S.left)
 end