✨ bodymass-ratio

02_bodymass_ratio.qmd

@@ -14,8 +14,47 @@ This concept of using body mass ratios to determine potential feeding links betw
 
 ## Methods
 
+Core idea relates to the ratio between consumer and resource body sizes - which supposedly stems from niche theory (still trying to reconcile that myself). The probability of a link existing between a consumer and resource (in its most basic form) is defined as follows:
+
+$$
+P_{ij} = \frac{p}{1+p}
+$$
+
+where
+
+$$
+p = exp[\alpha + \beta log(\frac{M_{i}}{M_{j}}) + \gamma log^{2}(\frac{M_{i}}{M_{j}})]
+$${#eq-bodymass}
+
+The original latent-trait model developed by @rohr2010 also included an additional latent trait term $v_{i} \delta f_{j}$ however for simplicity we will use @eq-bodymass as per @yeakel2014. Based on @rohr2010 it is possible to estimate the parameters $\alpha$, $\delta$, and $\gamma$ using a GLM but we will use the parameters from @yeakel2014, which was 'trained' on the Serengeti food web data and are as follows: $\alpha = 1.41$, $\delta = 3.75$, and $\gamma = 1.87$.
+
 ## Example
 
+```{julia}
+
+using CSV
+using DataFrames
+
+include("lib/bodymass/bodymass.jl")
+
+# set seed
+import Random
+Random.seed!(66)
+
+# import the mock dataset
+df = DataFrame(CSV.File("data/toarcian_subset.csv"))
+
+# were going to create some interim bodymass values
+using Distributions
+bodymass = rand(Truncated(Normal(0, 1), 0, 1), nrow(df))
+
+bodymass_network = bmratio(df.species, bodymass)
+
+# this is a probabilistic network by default we can make it binary using the random draws function
+randomdraws(bodymass_network)
+
+```
+
 ## References {.unnumbered}
 
 ::: {#refs}

Project.toml

@@ -1,5 +1,6 @@
 [deps]
 CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
 DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 IJulia = "7073ff75-c697-5162-941a-fcdaad2a7d2a"
 SpeciesInteractionNetworks = "49e116ef-912f-4766-9e56-896a49944adc"

_freeze/02_bodymass_ratio/execute-results/html.json

@@ -0,0 +1,12 @@
+{
+  "hash": "225aa7d0971f1d13a486b74649325c8e",
+  "result": {
+    "engine": "jupyter",
+    "markdown": "---\ntitle: \"Bodymass-ratio\"\ndate: last-modified\nformat:\n    html:\n        embed-resources: true\ntitle-block-banner: true\nbibliography: references.bib\n---\n\n## Overview\n\nThis concept of using body mass ratios to determine potential feeding links between species was primarily developed by @rohr2010 and has become quite popular in paleo settings [@yeakel2014; @pires2015]\n\n## Methods\n\nCore idea relates to the ratio between consumer and resource body sizes - which supposedly stems from niche theory (still trying to reconcile that myself). The probability of a link existing between a consumer and resource (in its most basic form) is defined as follows:\n\n$$\nP_{ij} = \\frac{p}{1+p}\n$$\n\nwhere\n\n$$\np = exp[\\alpha + \\beta log(\\frac{M_{i}}{M_{j}}) + \\gamma log^{2}(\\frac{M_{i}}{M_{j}})]\n$${#eq-bodymass}\n\nThe original latent-trait model developed by @rohr2010 also included an additional latent trait term $v_{i} \\delta f_{j}$ however for simplicity we will use @eq-bodymass as per @yeakel2014. Based on @rohr2010 it is possible to estimate the parameters $\\alpha$, $\\delta$, and $\\gamma$ using a GLM but we will use the parameters from @yeakel2014, which was 'trained' on the Serengeti food web data and are as follows: $\\alpha = 1.41$, $\\delta = 3.75$, and $\\gamma = 1.87$.\n\n## Example\n\n::: {#782a14ec .cell execution_count=1}\n``` {.julia .cell-code}\nusing CSV\nusing DataFrames\n\ninclude(\"lib/bodymass/bodymass.jl\")\n\n# set seed\nimport Random\nRandom.seed!(66)\n\n# import the mock dataset\ndf = DataFrame(CSV.File(\"data/toarcian_subset.csv\"))\n\n# were going to create some interim bodymass values\nusing Distributions\nbodymass = rand(Truncated(Normal(0, 1), 0, 1), nrow(df))\n\nbodymass_network = bmratio(df.species, bodymass)\n\n# this is a probabilistic network by default we can make it binary using the random draws function\nrandomdraws(bodymass_network)\n```\n\n::: {.cell-output .cell-output-display execution_count=2}\n```\nA binary unipartite network\n → 8 interactions\n → 12 species\n```\n:::\n:::\n\n\n## References {.unnumbered}\n\n::: {#refs}\n:::\n\n",
+    "supporting": [
+      "02_bodymass_ratio_files/figure-html"
+    ],
+    "filters": [],
+    "includes": {}
+  }
+}

_freeze/04_PFIM/execute-results/html.json

@@ -1,10 +1,10 @@
 {
-  "hash": "e617860d0e7f4ddf3e20a7f12a6f5e5b",
+  "hash": "f8c10c5682f5950389a3da38281b8291",
   "result": {
     "engine": "jupyter",
-    "markdown": "---\ntitle: \"PFIM\"\ndate: last-modified\nformat:\n    html:\n        embed-resources: true\ntitle-block-banner: true\nbibliography: references.bib\n---\n\n## Overview\n\n> @fricke2022 methods discuss how in the *\"using functional traits (especially binary or categorical traits), one can overestimate the ecological similarity of species, and thus the similarity of interaction patterns\"*. \n\nThe Paleo Food web Inference Model (PFIM, @shaw2024) uses a series of rules for a set of trait categories (such as habitat and body size) to determine if an interaction can feasibly occur between a species pair.\n\n## Methods\n\n## Example\n\n\n::: {#79f5c86c .cell execution_count=2}\n``` {.julia .cell-code}\n# set seed\nimport Random\nRandom.seed!(66)\n\n# import the mock dataset\ndf = DataFrame(CSV.File(\"data/toarcian_subset.csv\"))\n\n# this is a probabilistic network\npfim_network = PFIM(df)\n\n# this is a probabilistic network by default we can make it binary using the random draws function\nrandomdraws(pfim_network)\n\n```\n\n::: {.cell-output .cell-output-display execution_count=3}\n```\nA binary unipartite network\n → 9 interactions\n → 12 species\n```\n:::\n:::\n\n\n## References {.unnumbered}\n\n::: {#refs}\n:::\n\n",
+    "markdown": "---\ntitle: \"PFIM\"\ndate: last-modified\nformat:\n    html:\n        embed-resources: true\ntitle-block-banner: true\nbibliography: references.bib\n---\n\n## Overview\n\n> @fricke2022 methods discuss how in the *\"using functional traits (especially binary or categorical traits), one can overestimate the ecological similarity of species, and thus the similarity of interaction patterns\"*. \n\nThe Paleo Food web Inference Model (PFIM, @shaw2024) uses a series of rules for a set of trait categories (such as habitat and body size) to determine if an interaction can feasibly occur between a species pair.\n\n## Methods\n\n## Example\n\n::: {#e1b56af1 .cell execution_count=1}\n``` {.julia .cell-code}\nusing CSV\nusing DataFrames\n\ninclude(\"lib/pfim/pfim.jl\")\n\n# set seed\nimport Random\nRandom.seed!(66)\n\n# import the mock dataset\ndf = DataFrame(CSV.File(\"data/toarcian_subset.csv\"))\n\n# this is a probabilistic network\npfim_network = PFIM(df)\n\n# this is a probabilistic network by default we can make it binary using the random draws function\nrandomdraws(pfim_network)\n\n```\n\n::: {.cell-output .cell-output-display execution_count=2}\n```\nA binary unipartite network\n → 9 interactions\n → 12 species\n```\n:::\n:::\n\n\n## References {.unnumbered}\n\n::: {#refs}\n:::\n\n",
     "supporting": [
-      "04_PFIM_files"
+      "04_PFIM_files/figure-html"
     ],
     "filters": [],
     "includes": {}

lib/bodymass/bodymass.jl

@@ -0,0 +1,34 @@
+using DataFrames
+using SpeciesInteractionNetworks
+
+function bmratio(
+    species::Any,
+    bodymass::Vector{Float64};
+    α::Float64 = 1.41,
+    β::Float64 = 3.73,
+    γ::Float64 = 1.87)
+
+    S = length(species)
+
+    prob_matrix = zeros(AbstractFloat, (S, S))
+    for i in 1:S
+        for j in 1:S
+            MR = bodymass[i]/bodymass[j]
+            if MR == 0
+                p = exp(α)
+                else
+                    p = exp(α + β*log(MR) + γ*log(MR)^2)
+                end
+                if p/(1-p) >= 0.0
+                    prob_matrix[i,j] = p/(1-p)
+                end
+            end
+        end
+
+    # make probabanilistic
+    prob_matrix = prob_matrix./maximum(prob_matrix)
+
+    edges = Probabilistic(prob_matrix)
+    nodes = Unipartite(Symbol.(species))
+    return SpeciesInteractionNetwork(nodes, edges)    
+end