NetLogo User Community Models

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## WHAT IS IT?

According to Gauss competitive exclusion principle (Gauss, 1932) two species cannot exist in a same environment. However, thousands of species found coexists in tropical forests.
This model is a simulation model for the Chisholm and Pacala (2010) analytical model. Chisholm and Pacala (2010) relaxed one of the fundamental neutral assumptions that all species in the community interact in the same zero-sum game and derive a high-diversity approximation for the metacommunity SAD under the new model.

This model used to explains the two macro-ecological patterns species abundance distribution (SAD) and species area relationship (SAR). The model consists of two parts.

### Meta-community
Meta-community (size _J__M) is very large compared to local community (size _J__L). Meta-community is saturated. That is there is no vacant sites (space). This is one of the main assumptions of neutral theroy. Meta-community has demographic fluctuations (stochastic drift). Trees dies and rebirth every time step. It has also mechanisam called speciation. Speciation allows new species to appear. When a tree dies the vacant space is occupied by offsprings of a randomly selected individual or from a new species (speciation is a rare event. Probability of happening that event is very very small). Number of species in the meta community depends on the fundemental bio-diversity number (_θ_) and the meta-community size (_J__M). Species are generated at the beginning using the Hubbell's (2001) species generating flow chart (pg. 291). Each species has _J__i number of individuals.

Chisholm and Pacala (2010) divided the metacommunity into _K_ niches and allowed each niche to operate according to its own neutral dynamics, independently of the other _K_ − 1 niches. He assigned each patch in the metacommunity to a niche and assumed that a vacant location is always captured by an individual with a matching niche. He retained the other neutral assumptions: immigration rate (_m_), the speciation rate (_ν_), and the density of individuals per unit area (_ρ_) are constant across niches.

### Local community
Local community has demographic fluctuations (death and birth of trees). Local community is saturated. That is there is no vacant sites (space). This is one of the main assumptions of neutral theroy. Original version of the Hubbell's neutral model assumes single death in each time steps. When a tree dies randomly the vacant space is occupied by a offspring of a randomly selected individual. This randomly selected individual is either from a local community or meta-community. If its from meta-community then offspring immigrates from meta-community to local community to occupy the vacant site. If there is no immigration local community undergoes mono-dominance (all the sites occupied by one species). Therefore to maintain the species diversity immigration is necessary. Local community has _S_ number of species. Species are generated at the beginning using the Hubbell's (2001) species generating flow chart (pg. 291). Number of species in the local community depends on the fundemental bio-diversity number (_θ_₂) and the local community size (_J__L). Each species has _J__i number of individuals.

Chisholm and Pacala (2010) assumed that the scale of observation is large enough that the relative sizes of niches in the local community are the same as in the metacommunity (_J__i = _β__i._J_). He assigned each patch in the local community to a niche and assumed that a vacant location is always captured by an individual with a matching niche. He retained the other neutral assumptions: immigration rate (_m_), the speciation rate (_ν_), and the density of individuals per unit area (_ρ_) are constant across niches.

## HOW IT WORKS

Each agent has a property called 'species'. Each patch has a property called 'niche'. Species have different colors. Niches have different colors also. When an agent dies, an offspring with a matching niche is randomly selected occupied that empty space. Only one agent exists in a patch.

**(1) Meta-community:** When an agent dies, the vacant space is occupied by offsprings with a matching niche is randomly selected or from a new type of agent (probailities are 1-_v_ and _v_ respectively).

**(2) Local community:** When an agent dies, randomly the vacant space is occupied by a offspring with a matching niche is randomly selected. This randomly selected agent is either from a local community or meta-community (probabilites are 1-_m_ and _m_ respectively). If its from meta-community then offspring agent immigrates from meta-community to local community to occupy the vacant site.

## HOW TO USE IT

### Sliders
1. **w1:** Used to change meta-community size. _J__M = (w1+1)²
2. **w2:** Used to change the local community size. _J__L = (w2+1)²
3. **θ:** Fundamental biodiversity numbers used for meta-community.
4. **_θ_₂:** Fundamental biodiversity numbers used for local-community.
5. **Immigration:** Used to control the immigration rate (0-1).
6. **D:** Used to defines the number of death per each time step in the local community. Hubbell's (2001) original model _D_ = 1. Here it can takes any value from 1 to JL.
7. **speciation-initiation-rate:** Defines the speciation rate in the Hubbell's (2001) model. Hubbell used Wright-Fisher equation to define the point mutation speciation. In this model it has additional three additional switches (off-on) that used to set the speciation rates according to either Hubbell (2001) or Moran or Etinne-Alonso-Hubbell.
8. **tau-protracted:** Hubbell (2001) used only point mutation (instant specitation). However, this model has an slider called tau-protracted to shift from Hubbell's (2001) point mutation to Rosindell et al. protracted speciation. When tau-protracted is 0 it is Hubbell's instant point speciation, else it is protracted speciaiton (Rosindell et al. 2010).
9. **Equilibrium-run:** Use to decide the number of runs before stop the process.
10. **K:** Number of niches in meta-community and local community.

### Switches
1. **graphic?:** switch is used to switch on-off graphics. Off graphics? speeds the process.
2. **Moran?:** θ = _J_²_M. _v_
3. **Etienne-Alonso-Hubbell?:** θ = _J__M.(_J__M-1). _v_
4. **Hubbell-200-Wright-Fisher?:** θ = 2._J__M. _v_
5. **immigration-number?:** If switch is 'on' then θ₂ = _m_._J__L / (1 - _m_)

## THINGS TO NOTICE

### Monitor:
1. **Meta-community size:** Shows the meta-community.
2. **Protracted Speciation events happened in the meta-community:** Shows number of protrated species in the community.
3. **Point-mutations:** Shows number of point mutations.
4. **Total number of deaths in the local community:** Shows total number of deaths in the local community. Equals to number of ticks in netlogo.
5. **Meta-community species richness at time _t_ = 0:** Shows initial species richness in the meta-community.
6. **Meta-community species richness at time _t_ = t:** Shows the current species richness in the meta-community.
7. **Number of species appeared in the meta-community _t_ = 0 to _t_ = t:** Total number of new species appeared in the meta-community.
8. **Effective-meta-community size:** See Etienne and Alonso (2007).
9. **JL:** Current local community size.
10. **JM:** Current meta-community size.
11. **Number of temporal extinct species in the meta-community:** Number of species temporally extinct from local community. Temporal extinction happens only if immigration rate is non-zero. Otherwise it is shows number permenant extinct species.

### Plots:
1. **Total speciation events happen in the meta-community:** Cumulative function of speciations over time.
2. **Meta-community species richness:** Number of meta-community species presents over time.
3. **Local community species richness:** Number of local community species presents over time.
4. **Incipient species in the meta-community:** "During the transition period of a lineage undergoing protracted speciation, the individuals of this lineage are interpreted as an incipient species (Rosindell et al., 2010)"
5. **Generic-tree meta-community:** Similar to meta-community pylogenetic tree that also includes extinct lineages.
6. **Generic-tree local community:** Similar to local-community pylogenetic tree that also includes extinct lineages.
7. **Species Abundance Distribution meta-community:** Meta-community species abundance fluctuations.
8. **Species Abundance Distribution local community:** Local-community species abundance fluctuations.
9. **Number of extinct species from local-community:** Cumulative distribution of temporaly extinct species from local-community.
10. **Relative Species Abundance Meta Community:** Species abundance (_J_) / Meta-community size (_J__M).
11. **Species Abundance Distribution of Meta-Community:** Number of individuals from each species in the meta-community sorted.
12. **Number of extinct species from meta-community:** Cumulative distribution of permenantly extinct species from meta-community.
13. **Relative Species Abundance Local Community:** Species abundance (_J_) / Local-community size (_J__L).
14. **Species Abundance Distribution of Local-Community:** Number of individuals from each species in the local community sorted.
15. **Relative species abundance distribution of niche in local community:** Relative abundance of species in each habitats in local community.
16. **Relative species abundance of niches in meta-community:** Relative abundance of species in each habitats in meta-community.
## THINGS TO TRY

* Move sliders w1 and w2 to change the meta and local community size.
* Move sliders theta and theta2 to change the fundamental Biodiversity number for meta and local community.
* Move slider immigration-rate to change the immigration rate (0-1).
* speciation-initiation-rate is determine by one of the swithces (Moran, Hubbell-2001-Wright-Fisher, Etienne-Alonso-Hubbell) usually. Off three swiches to change the speciation-initiation-rate user defines values.

## EXTENDING THE MODEL

## NETLOGO FEATURES

## RELATED MODELS

Gause, G.F. (1932). "Experimental studies on the struggle for existence: 1. Mixed population of two species of yeast". _Journal of Experimental Biology_, **9**: 389–402.

Moran, P.A.P. (1958). Random processes in genetics. _Proceedings of the Cambridge Philosophical Society_, **54**: 28 60-71.

Ewens, W.J. (1972). The sampling theory of selectively neutral alleles. _Theoretical Population Biology_, **3**: 87-112.

Kimura, M. (1983). _The Neutral Theory of Molecular Evolution_. Cambridge, UK: Cambridge University Press.

Hubbell, S. P. (1979). Tree Dispersion, Abundance, and Diversity in a Tropical Dry Forest: That tropical trees are clumped, not spaced, alters conceptions of the organization and dynamics. _Science_, **203**(4387), 1299–1309.

Hubbell, S. P. (1997). A unified theory of biogeography and relative species abundance and its application to tropical rain forests and coral reefs. _Coral Reefs_ **16**:S9–S21.

Hubbell, S. P. (2001). _The Unified Neutral Theory of Biodiversity and Biogeography_. Princeton, NJ: Princeton University Press.

Etienne, R. S., & Alonso, D. (2007). Neutral Community Theory: How Stochasticity and Dispersal-Limitation Can Explain Species Coexistence. _Journal of Statistical Physics_, **128**(1–2), 485–510.

Rosindell, J., Cornell, S. J., Hubbell, S. P., & Etienne, R. S. (2010). Protracted speciation revitalizes the neutral theory of biodiversity. _Ecology Letters_, **13**(6), 716-727.

Chisholm, R. A., & Pacala, S. W. (2010). Niche and neutral models predict asymptotically equivalent species abundance distributions in high-diversity ecological communities. _Proceedings of the National Academy of Sciences_, **107**(36), 15821–15825.

## CREDITS AND REFERENCES

For the model itself:

* Punchi-Manage, R. (2023c). NetLogo Chisholm and Pacala (2010) Niche Based Neutral Model. http://netlogo/models/NetLogo-Chisholm-and-Pacala-(2010)-Niche-Based-Neutral-Model.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.