Forest Dynamic Model III - Rosindell et al. 2010

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WHAT IS IT?

Dispersal-limited local community case:The Rosindell et al. (2010) algorithm-3.

He had a census of a dispersal limited local community of size J. To obtain the species abundances for these J individuals, they again used coalescence. they traced the ancestry of K lineages as before, where initially K = J. With each time step there is a probability K/J (initially 1) that he picked one of the lineages, which might then immigrate with probability m or coalesce with probability (1 − m) . K − 1 / J − 1 . The calculations are analogous to the metacommunity case except that instead of a speciation-initiation rate μ they now have an immigration rate m. Lineages that immigrate are then passed to the metacommunity algorithm which accounts for them being drawn from a metacommunity species pool.

HOW IT WORKS

Algorithm 3. Local community dispersal limited sample from a metacommunity with protracted speciation.

This algorithm presents below is published by Rosindell, et al., (2010) in Ecology Letter supporting information section (see ELE1463sm_appendix.pdf).

  1. Input θ and J, τ and m.

  2. Define a vector S of length J with Si = 1 for i = 1, 2, . . . J and define K = J, the number of lineages in the vector.

  3. Define an empty vector V which will contain a list of groups of individuals descending from each immigration from the metacommunity species pool.

  4. Pick a random number 0 ≤ r ≤ 1 (to choose if coalescence or immigration will happen).

  5. Pick a random entry Si from the vector S (to choose which lineage this will happen to).

  6. If r1 <= (m . (J - 1) / [m . (J - 1) + (1 - m) . (K - 1)]) speciation happens: remove Si from the vector S and append it to vector V (then go to 8.).

  7. If r1 > (m . (J - 1) / [m . (J - 1) + (1 - m) . (K - 1)]) coalescence happens: pick a random entry Sj from vector S (where j = i) and set Si = Si + Sj. Then remove Sj from the vector S ( then go to 8.)

  8. Set K = K − 1; now the vector S should have one less element.

  9. If (K > 0), we are not finished so go to 4.

  10. If (K ≤ 0), define t = 0 the total number of units of coalescence time that have passed.

  11. Pick a random number 0 ≤ r ≤ 1 (to choose how many generations until the next coalescence event).

  12. Set t = t − ( ln(r) / [K(K−1)] ).

  13. If τ > t, pick two random entries Vi and Vj from the vector V (where j not equal to i), set K = K - 1 and Vi = Vi + Vj. Then remove Vj from the vector V (then go to 3).

  14. If τ ≤ t, define an empty vector W which will contains a list of species abundances when the algorithm terminates.

  15. Pick a random number 0 ≤ r ≤ 1 (to choose if coalescence or speciation will happen).

  16. Pick a random entry Vi from the vector V (to choose which lineage this will happen to).

  17. If r ≤ θ / [θ+K− 1] , speciation happens: remove Vi from the vector V and append it to vector W (then go to 12).

  18. If r > θ / [θ + K − 1] , coalescence happens: pick a random entry Vj from vector V (where j not equal to i) and set Vi = Vi + Vj then remove Vj from the vector V.

  19. Set K = K − 1; now the vector V should have one less element.

  20. If (K > 0), we are not finished so go to 8.

  21. If (K ≤ 0), the algorithm is complete and W contains the abundances of all species.

HOW TO USE IT

Set the meta-community size, K = (w1 + 1)2.

Decide the fundamental biodiversity number, θ

Decide the τ.

THINGS TO NOTICE

Number of speciations happened in the meta-community is represents by arrow heads.

THINGS TO TRY

Increase the θ and see the number of speciations presents in the given θ and meta-community size.

Increase the meta-community size, K = (w1 + 1)2 and see the number of speciations presents in the meta-community for given θ and τ.

Increase the τ and see the number of speciations presents in the given θ and meta-community size.

EXTENDING THE MODEL

NETLOGO FEATURES

RELATED MODELS

Rosindell, J., Cornell, S. J., Hubbell, S. P., & Etienne, R. S. (2010). Protracted speciation revitalizes the neutral theory of biodiversity: Protracted speciation and neutral theory. Ecology Letters, 13(6), 716–727.

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extensions [table csv]
globals [V K W-vec index rspec speciation specia spec Wvec speciesi meta-speciesi JM meta-sp meta-time meta-a0  meta-j2 meta-a meta-set2 extinct-species number-of-meta-trees a initial-meta-richness dlocx dlocy random-number2 number time num j x-cor y-cor N richness a0 n-speciation local-set local-di-set local-off-set set-species-who-di set-species-who-off sp hist-frq rel-hist-frq s local-set0 remove-set richness-counts species-who-di di-locx di-locy species-who-off set1-species-who-off meta-set effective-meta-cmmunity-size number-of-local-trees item-x meta-set-new meta-sp-count sp-count j1 i1 k1 j2 i2 k2 meta-richness-counts meta-richness local-richness-counts local-richness hist-frq-meta rel-hist-frq-meta hist-frq-local rel-hist-frq-local t]
breed [meta-trees meta-tree]
breed [trees tree]
meta-trees-own [species meta-species n-speciation-no]
trees-own [species h]
circles-own []
breed [circles a-circle]
patches-own[elevation]

to setup3
  clear-all
  set local-richness-counts map count table:values table:group-agents trees [species]
  set local-richness length local-richness-counts
  set sp 0
  set meta-sp 0
  set speciation 0
  set specia []
  set spec []
  set Wvec []
  set J (w1 + 1) * (w1 + 1)
  resize-world 0 w1 0 w1
  set JM 0
  set K J
  set t 0
  species-gen1
  set hist-frq-local sort-by > map count table:values table:group-agents trees [ species ]
  set rel-hist-frq-local map [ i -> i / count trees ] hist-frq-local
  set richness-counts map count table:values table:group-agents turtles [ species ]
  set richness length richness-counts
  set hist-frq-meta sort-by > map [ i -> i] Wvec
  update-plots
  reset-ticks
end 

to species-gen1
  set k1 -1
  while [k1 < w1 ] [
    set k1 k1 + 1
    set i1 -1
    while [i1 < w1 ] [
      set i1 i1 + 1
      create-trees 1 [
        setxy k1 i1
        set shape "circle"
        set size 1
        set num random-float 1
        set j1 j1 + 1
        set species (sp + 1)
        set sp sp + 1
        set color random-float -50
        set spec fput sp spec
      ]
    ]
  ]
  set local-richness sp
end 

to go3
  while [K > 0] [
    let r1 random-float 1
    if (length spec = 0 )[stop]
    set rspec one-of spec
    if-else (r1 <= (m * (J - 1) / (m * (J - 1) + (1 - m) * (K - 1))))[
      set speciation speciation + 1
      set specia fput rspec specia
      set spec remove rspec spec
      let Wvec1 count trees with [species = rspec]
      set Wvec fput Wvec1 Wvec
      set sp sp + 1
      let color0 60 + random-float -50
      ask trees with [species = rspec] [
        set species sp
        set color color0
        ;set shape "arrow"
      ]
    ]
    [
      if (length spec = 0 )[stop]
      set spec remove rspec spec
      let color01 [color] of one-of trees with [species = rspec]
      ask trees with [species = rspec] [
        if (length spec = 0 )[stop]
        set rspec one-of spec
        set species rspec
        set color color01
      ]
    ]
    set K K - 1
    set richness-counts map count table:values table:group-agents turtles [ species ]
    set richness length richness-counts
    set hist-frq-local sort-by > map count table:values table:group-agents turtles [ species ]
    set rel-hist-frq-local map [ i -> i / count turtles ] hist-frq-local
    set hist-frq-meta sort-by > map [ i -> i ] Wvec
    update-plots
    tick
  ]
  If (K = 0) [go]
end 

to go
  set K J
  while [K > 0] [
    let r1 random-float 1
    if (length spec = 0 )[stop]
    set rspec one-of spec
    if-else (K > 1) [set t t - (ln (r1) / (K * (K - 1 )))]
    [set t 100000]
    if-else (tau >  t) [
      set spec remove rspec spec
      ask trees with [species = rspec] [
        set rspec one-of spec
        set species rspec
        set color [color] of one-of trees with [species = rspec]
      ]
      set K K - 1
      set t 0
      set richness-counts map count table:values table:group-agents turtles [ species ]
      set richness length richness-counts
      set hist-frq-local sort-by > map count table:values table:group-agents turtles [ species ]
      set rel-hist-frq-local map [ i -> i / count turtles ] hist-frq-local
      set hist-frq-meta sort-by > map [ i -> i ] Wvec
      update-plots
      tick
    ]
    [
      if (length spec = 0 )[stop]
      if-else (r1 <= theta / (theta + K - 1)) [
        set speciation speciation + 1
        set specia fput rspec specia
        set spec remove rspec spec
        let Wvec1 count trees with [species = rspec]
        set Wvec fput Wvec1 Wvec
        set sp sp + 1
        let color0 60 + random-float -50
        ask trees with [species = rspec] [
          set species sp
          set color color0
          ;set shape "arrow"
        ]
        set K K - 1
        set richness-counts map count table:values table:group-agents turtles [ species ]
        set richness length richness-counts
        set hist-frq-local sort-by > map count table:values table:group-agents turtles [ species ]
        set rel-hist-frq-local map [ i -> i / count turtles ] hist-frq-local
        set hist-frq-meta sort-by > map [ i -> i ] Wvec
        update-plots
        tick
      ]
      [
        if (length spec = 0 )[stop]
        set spec remove rspec spec
        let color01 [color] of one-of trees with [species = rspec]
        ask trees with [species = rspec] [
          set rspec one-of spec
          set species rspec
          set color color01
        ]
        set K K - 1
        set richness-counts map count table:values table:group-agents turtles [ species ]
        set richness length richness-counts
        set hist-frq-local sort-by > map count table:values table:group-agents turtles [ species ]
        set rel-hist-frq-local map [ i -> i / count turtles ] hist-frq-local
        set hist-frq-meta sort-by > map [ i -> i ] Wvec
        update-plots
        tick
      ]
    ]
  ]
end 


; Copyright 2023i Ruwan Punchi-Manage.
; See Info tab for full copyright and license.

There is only one version of this model, created almost 2 years ago by Ruwan Punchi-Manage.

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