| Title: | Simulation of Ecological Models |
|---|---|
| Description: | Computer simulations of classical ecological models as a learning resource. |
| Authors: | Alexandre Adalardo de Oliveira and Paulo Inacio Prado <[email protected]> |
| Maintainer: | Alexandre Adalardo de Oliveira <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.1 |
| Built: | 2024-11-15 06:34:34 UTC |
| Source: | CRAN |
Internal functions for graphics and animations of the simulations results.
grColExt(E, I, P, area)grColExt(E, I, P, area)
E |
extinction rate |
I |
colonization rate |
P |
species available in mainland |
area |
islands sizes |
The list below relates each function graphical and its primary functions:
animaCena - regNicho
animaGame - extGame
animaHub - simHub1, simHub2, simHub3
animaIsl - archip
animaMeta2 - metaPop, metaCi, metaEr, metaCiEr
animaMetaComp - metaComp
animaRandWalk - randWalk
grColExt - animaColExt, bioGeoIsl
grFim - metaPop, metaCi, metaEr, metaCiEr
Show simulation in a graphic device.
Alexandre Adalardo de Oliveira [email protected]
## Not run: grColExt(E = 0.5 , I = 0.5 , P = 100, area=1:10) ## End(Not run)## Not run: grColExt(E = 0.5 , I = 0.5 , P = 100, area=1:10) ## End(Not run)
Simulate the balance between extinction and colonization rates given the equilibrium number of species in a island, based on the Island Biogeography Equilibrium model.
animaColExt(min = 0.01, max = 1, cycles = 100, Ext = "crs", Col = "dcr")animaColExt(min = 0.01, max = 1, cycles = 100, Ext = "crs", Col = "dcr")
min |
between 0-1. The minimum value of the extinction and colonization rates. |
max |
between 0-1. The maximum value of the extinction and colonization rates. |
cycles |
number of cycles in the simulation. |
Ext |
a string representing the extinction rate. This can be 'crs' for an increasing extinction rate, 'fix' for a fixed extinction rate in 0.5, or 'dcr' for a decreasing extinction rate. |
Col |
a string representing the colonization rate. This can be 'crs' for an increasing colonization rate, 'fix' for a fixed colonization rate in 0.5, or 'dcr' for a decreasing colonization rate. |
The number of species is the balance between extinction and colonization rates at the equilibrium.
'animaColExt' returns a graph of the extinction and colonization rates varying one or both rates in relation with the number of species of an island.
Alexandre Adalardo de Oliveira [email protected]
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp.
archip bioGeoIsl
http://ecovirtual.ib.usp.br
## Not run: animaColExt(Ext='fix', Col="fix") ## End(Not run)## Not run: animaColExt(Ext='fix', Col="fix") ## End(Not run)
Simulate species colonization from mainland to islands with different sizes.
archip(n.isl, ar.min, ar.max, S, seed.rain, abund, tmax = 100, anima = TRUE)archip(n.isl, ar.min, ar.max, S, seed.rain, abund, tmax = 100, anima = TRUE)
n.isl |
numeric, number of islands. |
ar.min |
numeric, area of the smallest island. |
ar.max |
numeric, area of the biggest island. |
S |
numeric, number of species (species richness from mainland). |
seed.rain |
numeric, seed rain. Number of seeds colonizing islands on each time. |
abund |
numeric, abundance of each species in the seed rain. |
tmax |
numeric, maximum time for the simulations. |
anima |
logical; if TRUE, show simulation frames. |
The mainland has richness (S) and the evenness can be controled argument abund. The 'abund' argument can be one of these 3 options:
a vector with the same length of the species richness, meaning the proportion of each species population;
a single value more than 1 representing equal abundance of each species (maximum evenness);
a single value between 0 and 1, meaning the model of geometric species rank-abundance distribution. The model is: abund*(1-abund)*((1:S)-1), where S is the number of species.
'archip' returns 3 graphics:
The species-area
relationship: number of species x island area at the end of the simulation.
It also returns the coefficients c and z from species-area relationship
.
Colonization rate curves: colonization (number of species per cycle) x number of species for each island.
Passive colonization: number of species x time for each island.
'archip' also returns an invisible array with the simulation results.
Alexandre Adalardo de Oliveira [email protected]
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp.
animaColExt, bioGeoIsl,
http://ecovirtual.ib.usp.br
## Not run: archip(n.isl=10,ar.min=10, ar.max=100, S=1000, seed.rain=100, abund=10, tmax=100, anima=TRUE) archip(n.isl=10,ar.min=10, ar.max=100, S=1000, seed.rain=100, abund=0.5, tmax=100, anima=TRUE) ## End(Not run)## Not run: archip(n.isl=10,ar.min=10, ar.max=100, S=1000, seed.rain=100, abund=10, tmax=100, anima=TRUE) archip(n.isl=10,ar.min=10, ar.max=100, S=1000, seed.rain=100, abund=0.5, tmax=100, anima=TRUE) ## End(Not run)
Simulates island biogeographical models, with rates of colonization and extinction for islands of different sizes and distances to the mainland.
bioGeoIsl(area, dist, P, weight.A = 0.5, a.e = 1, b.e = -0.01, c.i = 1, d.i = -0.01, e.i = 0, f.i = 0.01, g.e = 0, h.e = 0.01)bioGeoIsl(area, dist, P, weight.A = 0.5, a.e = 1, b.e = -0.01, c.i = 1, d.i = -0.01, e.i = 0, f.i = 0.01, g.e = 0, h.e = 0.01)
area |
a vector with the sizes of the island areas. It must have the same length as 'dist' |
dist |
a vector with the distances of the islands to the mainland. It must have the same length as 'areas' |
P |
the number of species in the mainland (species richness of the pool). |
weight.A |
ratio between the area and distance effects. Should be a number between 0 to 1. When the ration is 1 the extinction is only affected by size and colonization only by distance. The default ratio is 0.5, meaning that distance and size equally influence colonization and extinction. |
a.e |
basal extiction coefficient for area. |
b.e |
extinction/area coefficient. |
c.i |
basal colonization coefficient for distance. |
d.i |
numeric, colonization/distance coefficient. |
e.i |
basal colonization coefficient for area. |
f.i |
colonization/area coefficient. |
g.e |
basal extinction coefficient for distance. |
h.e |
extinction/distance coefficient. |
'bioGeoIsl' returns a graph with the rates of colonization and extinction in relation with the species richness for each island.
'bioGeoIsl' also returns a invisible data frame with the values for area, distance and species richness (S) for each island.
Alexandre Adalardo de Oliveira [email protected]
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp.
animaColExt archip,
http://ecovirtual.ib.usp.br
## Not run: bioGeoIsl(area=c(5,10,50,80), dist=c(10,100,100,10), P=100, weight.A=.5, a=1, b=-0.01, c=1, d=-0.01, e=0, f=.01, g=0, h=.01) ## End(Not run)## Not run: bioGeoIsl(area=c(5,10,50,80), dist=c(10,100,100,10), P=100, weight.A=.5, a=1, b=-0.01, c=1, d=-0.01, e=0, f=.01, g=0, h=.01) ## End(Not run)
Simulates the trade-off between colonization and competition abilities in a multispecies system.
comCompete(rw, cl, S, fi, fsp1, pe, fr = 0, int = 0, tmax)comCompete(rw, cl, S, fi, fsp1, pe, fr = 0, int = 0, tmax)
rw |
number of rows for the simulated landscape. |
cl |
number of columns for the simulated landscape. |
S |
number of species. |
fi |
initial fraction of patchs occupied |
fsp1 |
superior competitor abundance. |
pe |
mortality rate. |
fr |
disturbance frequency. |
int |
disturbance intensity. |
tmax |
maximum simulation time. |
In the system, the competitive abilities are inversely proportional to the colonization abilities.
The number of patches in the simulated landscape is defined by rw*cl.
'comCompete' returns a graph with the proportion of patches occupied in time by each species and the trade-off scale, the superior competitor in one side and the superior colonizator in the other.
Alexandre Adalardo de Oliveira [email protected]
Tilman. R. 1994. Competition and biodiversity in spatially structured habitats. Ecology,75:2-16.
Stevens, M.H.H. 2009. A primer in ecology with R. New York, Springer.
metaComp, http://ecovirtual.ib.usp.br
## Not run: comCompete(tmax=1000, rw=100, cl=100, S=10, fi=1, fsp1=0.20, pe=0.01, fr=0, int=0) ## End(Not run)## Not run: comCompete(tmax=1000, rw=100, cl=100, S=10, fi=1, fsp1=0.20, pe=0.01, fr=0, int=0) ## End(Not run)
Simulate the Lotka-Volterra competition model for two populations.
compLV(n01, n02, tmax, r1, r2, k1, k2, alfa, beta)compLV(n01, n02, tmax, r1, r2, k1, k2, alfa, beta)
n01 |
initial population for the superior competitor species. |
n02 |
initial population for the inferior competitor species. |
tmax |
maximum simulation time. |
r1 |
intrinsic growth rate for the superior competitor species. |
r2 |
intrinsic growth rate for the inferior competitor species. |
k1 |
carrying capacity for the superior competitor species. |
k2 |
carrying capacity for the inferior competitor species. |
alfa |
alfa coefficient. |
beta |
beta coefficient |
The Lotka-Volterra competition model follows the equations:
SP1:
SP2:
'compLV' returns a graph of the population size in time, and a graph with the isoclines of the equilibrium for both species. 'compLV' also returns an invisible matrix with the population size of each species in time.
Alexandre Adalardo de Oliveira [email protected]
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp. Hastings, A. 1980. Disturbance, coexistence, history and competition for space. Theoretical Population Biology, 18:363-373. Stevens, M.H.H. 2009. A primer in ecology with R. New York, Springer.
## Not run: compLV(n01=10, n02=10,r1=0.05, r2=0.03, k1=80, k2=50, alfa=1.2, beta=0.5, tmax=200) ## End(Not run)## Not run: compLV(n01=10, n02=10,r1=0.05, r2=0.03, k1=80, k2=50, alfa=1.2, beta=0.5, tmax=200) ## End(Not run)
Functions to simulate population dynamic models.
popExp(N0, lamb, tmax, intt = 1) estEnv(N0, lamb, tmax, varr, npop = 1, ext = FALSE) BDM(tmax, nmax = 10000, b, d, migr = 0, N0, barpr = FALSE) simpleBD(tmax = 10, nmax = 10000, b = 0.2, d = 0.2, N0 = 10, cycles = 1000, barpr = FALSE) estDem(N0 = 10, tmax = 10, nmax = 10000, b = 0.2, d = 0.2, migr = 0, nsim = 20, cycles = 1000, type = c("simpleBD", "BDM"), barpr = FALSE) popLog(N0, tmax, r, K, ext = FALSE) popStr(tmax, p.sj, p.jj, p.ja, p.aa, fec, ns, nj, na, rw, cl) logDiscr(N0, tmax, rd, K) bifAttr(N0, K, tmax, nrd, maxrd = 3, minrd = 1)popExp(N0, lamb, tmax, intt = 1) estEnv(N0, lamb, tmax, varr, npop = 1, ext = FALSE) BDM(tmax, nmax = 10000, b, d, migr = 0, N0, barpr = FALSE) simpleBD(tmax = 10, nmax = 10000, b = 0.2, d = 0.2, N0 = 10, cycles = 1000, barpr = FALSE) estDem(N0 = 10, tmax = 10, nmax = 10000, b = 0.2, d = 0.2, migr = 0, nsim = 20, cycles = 1000, type = c("simpleBD", "BDM"), barpr = FALSE) popLog(N0, tmax, r, K, ext = FALSE) popStr(tmax, p.sj, p.jj, p.ja, p.aa, fec, ns, nj, na, rw, cl) logDiscr(N0, tmax, rd, K) bifAttr(N0, K, tmax, nrd, maxrd = 3, minrd = 1)
N0 |
number of individuals at start time. |
lamb |
finite rate of population growth. |
tmax |
maximum simulation time. |
intt |
interval time size. |
varr |
variance. |
npop |
number of simulated populations. |
ext |
extinction. |
nmax |
maximum population size. |
b |
birth rate. |
d |
death rate. |
migr |
migration. logical. |
barpr |
show progress bar. |
cycles |
number of cycles in simulation. |
nsim |
number of simulated populations. |
type |
type of stochastic algorithm. |
r |
intrinsic growth rate. |
K |
carrying capacity. |
p.sj |
probability of seed survival. |
p.jj |
probability of juvenile survival. |
p.ja |
probability of transition from juvenile to adult phase. |
p.aa |
probability of adult survival. |
fec |
mean number of propagules per adult each cycle. |
ns |
number of seeds at initial time. |
nj |
number of juveniles at initial time. |
na |
number of adults at initial time. |
rw |
number of rows for the simulated scene. |
cl |
number of columns for the simulated scene. |
rd |
discrete growth rate. |
nrd |
number of discrete population growth rate to simulate. |
maxrd |
maximum discrete population growth rate. |
minrd |
minimum discrete population growth rate. |
popExp simulates discrete and continuous exponential population growth.
estEnv simulates a geometric population growth with environmental stochasticity.
BDM simulates simple stochastic birth death and immigration dynamics of a population (Renshaw 1991). simpleBD another algorithm for simple birth dead dynamics. This is usually more efficient than BDM but not implemented migration.
estDem creates a graphic output based on BDM simulations.
Stochastic models uses lambda values taken from a normal distribution with mean lambda and variance varr.
popLog simulates a logistic growth for continuous and discrete models.
popStr simulates a structured population dynamics, with Lefkovitch matrices.
In popStr the number of patches in the simulated scene is defined by rw*cl.
logDiscr simulates a discrete logistic growth model.
bifAttr creates a bifurcation graphic for logistic discrete models.
The functions return graphics with the simulation results, and a matrix with the population size for deterministic and stochastic models.
Alexandre Adalardo de Oliveira and Paulo Inacio Prado [email protected]
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp. Renshaw, E. 1991. Modelling biological populations in space and time Cambridge University Press. Stevens, M.H.H. 2009. A primer in ecology with R. New York, Springer.
metaComp, http://ecovirtual.ib.usp.br
## Not run: popStr(p.sj=0.4, p.jj=0.6, p.ja=0.2, p.aa=0.9, fec=0.8, ns=100,nj=40,na=20, rw=30, cl=30, tmax=20) ## End(Not run)## Not run: popStr(p.sj=0.4, p.jj=0.6, p.ja=0.2, p.aa=0.9, fec=0.8, ns=100,nj=40,na=20, rw=30, cl=30, tmax=20) ## End(Not run)
Simulates a zero-sum game between two competitors with a fixed amount of resource.
extGame(bet = 1, total = 100, tmax = 2)extGame(bet = 1, total = 100, tmax = 2)
bet |
bet size of each competitor on each time. |
total |
total amount of resource. |
tmax |
maximum game time. |
A zero-sum game is a mathematical representation of a situation in which a participant's gain (or loss) of resource is exactly balanced by the losses (or gains) of the resource of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.
'extGame' returns a graphic with the amount of resource of each competitor on each time.
'extGame' also returns an invisible vector with the results of the loser on each time.
Alexandre Adalardo de Oliveira and Paulo Inacio Prado [email protected]
http://en.wikipedia.org/wiki/Zero-sum_game
simHub, randWalk,
http://ecovirtual.ib.usp.br
## Not run: extGame(bet=1,total=20) extGame(bet=1,total=100) ## End(Not run)## Not run: extGame(bet=1,total=20) extGame(bet=1,total=100) ## End(Not run)
Simulate a metapopulation dynamics with two competing species, a superior and an inferior competitor. Includes the possibility of habitat destruction in the model.
metaComp(tmax, rw, cl, f01, f02, i1, i2, pe, D = 0, anima = TRUE)metaComp(tmax, rw, cl, f01, f02, i1, i2, pe, D = 0, anima = TRUE)
tmax |
maximum simulation time. |
rw |
number of rowns for the simulated landscape. |
cl |
number of columns for the simulated landscape. |
f01 |
initial fraction of patches occupied by the superior competitor. |
f02 |
initial fraction of patches occupied by the inferior competitor. |
i1 |
colonization coefficient for the superior competitor. |
i2 |
colonization coefficient for the inferior competitor. |
pe |
probability of extinction (equal for both species). |
D |
proportion of habitat destroyed. |
anima |
logical; if TRUE, show simulation frames. |
This function uses the metapopulationa model with internal colonization
(see function metaCi in metapopulation) for the superior
competitor. The inferior competitor can only occupy empty patches and is
displaced by the superior competitor if it occupies the same patch.
The argument 'D' inserts the influences of habitat destruction in the model.
The number of patches in the simulated landscape is defined by rw*cl.
'metaComp' returns a graphic with the simulated landscapes and the results of the proportion of patch occupied by both species.
This function also return an invisible array with the simulation results.
Alexandre Adalardo de Oliveira and Paulo Inacio Prado [email protected]
Stevens, M.H.H. 2009. A primer in ecology with R. New York, Springer.
Gotelli, N.J. 1991. Metapopulation models: the rescue effect, the propagule rain, and the core-satellite hypothesis. The American Naturalist 138:768-776.
comCompete, http://ecovirtual.ib.usp.br
## Not run: metaComp(tmax=100,cl=20,rw=20,f01=0.1,f02=0.4,i1=0.4,i2=0.5,pe=0.25) metaComp(tmax=100,cl=20,rw=20,f01=0.1,f02=0.4,i1=0.4,i2=0.5,pe=0.25, D=0.1) ## End(Not run)## Not run: metaComp(tmax=100,cl=20,rw=20,f01=0.1,f02=0.4,i1=0.4,i2=0.5,pe=0.25) metaComp(tmax=100,cl=20,rw=20,f01=0.1,f02=0.4,i1=0.4,i2=0.5,pe=0.25, D=0.1) ## End(Not run)
Simulate metapopulation dynamics with propagules seed rain, internal colonization and rescue effect.
metaPop(cl, rw, f0, pi, pe, tmax, anima = TRUE) metaCi(cl, rw, f0, ci, pe, tmax, anima = TRUE) metaEr(cl, rw, f0, pi, ce, tmax, anima = TRUE) metaCiEr(cl, rw, f0, ci, ce, tmax, anima = TRUE)metaPop(cl, rw, f0, pi, pe, tmax, anima = TRUE) metaCi(cl, rw, f0, ci, pe, tmax, anima = TRUE) metaEr(cl, rw, f0, pi, ce, tmax, anima = TRUE) metaCiEr(cl, rw, f0, ci, ce, tmax, anima = TRUE)
cl |
number of columns for the simulated landscape. |
rw |
number of rows for the simulated landscape. |
f0 |
initial proportion of occupied patches. |
pi |
probability of colonization. |
pe |
probability of extinction. |
tmax |
maximum simulation time. |
anima |
show animation frames. |
ci |
colonization coefficient, represents the maximum probability of colonization (when f=1) and should be a number between 0 and 1. |
ce |
coefficient of extinction, represents the maximum probability of extinction (when f=0) and should be a number between 0 and 1. |
'metaPop' is the seed rain metapopulation model, including only propagules seed rain from a external pool (no extinction).
'metaCi' is the Internal Colonization model, where number of propagules depends on number of occupied patches, there is no external pool.
'metaEr' is the Rescue Effect model, where extinction probability is negatively associated with number of occupied patches.
'metaCiEr' includes both effects: Rescue Effect and Internal Colonization.
The number of patches in the simulated landscape is defined by rw*cl.
Metapopulation functions return graphics with the simulation results. These functions also return an invisible array with the simulation data.
Alexandre Adalardo de Oliveira and Paulo Inacio Prado [email protected]
Gotelli, N.J. 1991. Metapopulation models: the rescue effect, the propagule rain, and the core-satellite hypothesis. The American Naturalist 138:768-776.
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp.
## Not run: metaPop(cl=10,rw=10,f0=0.5,pi=0.3,pe=0.15, tmax=100) metaCi(cl=10,rw=10,f0=0.1,ci=1,pe=0.5, tmax=100) metaEr(cl=10, rw=10, f0=0.2, pi=0.2, ce=0.15, tmax=100) metaCiEr(cl=10, rw=10, f0=0.2, ci=0.2, ce=0.15, tmax=100) ## End(Not run)## Not run: metaPop(cl=10,rw=10,f0=0.5,pi=0.3,pe=0.15, tmax=100) metaCi(cl=10,rw=10,f0=0.1,ci=1,pe=0.5, tmax=100) metaEr(cl=10, rw=10, f0=0.2, pi=0.2, ce=0.15, tmax=100) metaCiEr(cl=10, rw=10, f0=0.2, ci=0.2, ce=0.15, tmax=100) ## End(Not run)
Simulates random walk models.
randWalk(S = 1, step = 1, tmax = 1e+05, x1max = 200, alleq = FALSE)randWalk(S = 1, step = 1, tmax = 1e+05, x1max = 200, alleq = FALSE)
S |
number of individuals. |
step |
step size (number of steps on each time) |
tmax |
maximum simulation time. |
x1max |
maximum initial distance from absorption surface. |
alleq |
logical; if TRUE, all initial distance are equal. if FALSE, initial distances for each individual is a sample between 1 and maximum initial distance(x1max). |
Random walk is a stochastic process of a succession of random steps.
Zero is the absorption surface. When an individual simulation reaches zero, it means that the individual is dead.
See http://en.wikipedia.org/wiki/Random_walk.
'randWalk' returns a graphic with the simulated trajectories of each individual.
'randWalk' also returns an invisible matrix with the distance from de edge for each individual on each time.
Alexandre Adalardo de Oliveira and Paulo Inacio Prado [email protected]
http://en.wikipedia.org/wiki/Random_walk
extGame, simHub,
http://ecovirtual.ib.usp.br
## Not run: randWalk(S=100,step=2,tmax=2e5) randWalk(S=10,step=1,tmax=1e4, x1max=300, alleq=TRUE) ## End(Not run)## Not run: randWalk(S=100,step=2,tmax=2e5) randWalk(S=10,step=1,tmax=1e4, x1max=300, alleq=TRUE) ## End(Not run)
Simulates the process of niche succession by successional stages in a community with 2 species (a superior and an inferior competitor), following the model of Pacala and Rees (1998).
regNicho(tmax, rw, cl, c1, c2, ec, dst, er, sc, mx, rs, anima = TRUE)regNicho(tmax, rw, cl, c1, c2, ec, dst, er, sc, mx, rs, anima = TRUE)
tmax |
maximum simulation time. |
rw |
number of rows for the simulated landscape. |
cl |
number of columns for the simulated landscape. |
c1 |
colonization rate for the late successional species (superior competitor). |
c2 |
colonization rate for the early successional species (inferior competitor). |
ec |
rate of competitive exclusion. |
dst |
disturbance rate. |
er |
inicial proportion of patches in early stage. |
sc |
inicial proportion of patches in susceptible stage. |
mx |
initial proportion of patches in mixed stage. |
rs |
initial proportion of pathces in resistant stage. |
anima |
show animation frames. |
There are five possible states of this model:
free - open, unoccupied space;
early - occupied by only the early successional species;
susceptible - occupied by only the late succesional species and susceptible to invasion by the early succesional species;
mixed - occupied by both species;
resistant - occupied by only the late successional species.
The early successional species is the inferior competitor in the model, and the later successional species is the superior competitor.
The number of patches in the simulated landscape is defined by rw*cl.
'dst' is the proportion of patches in any stage that turns empty, it represents a disturbance in the landscape.
'ec' is the probability of succeptible and mixed stages turns resistant stage.
'regNicho' returns the simulation results of patch occupancy in time for each successional stage.
'regNicho' also returns an invisible array with the simulation results per time.
Alexandre Adalardo de Oliveira [email protected]
Pacala, S & Rees, M. 1998. Models suggesting field experiments to test two hypotheses explaining successional diversity. The American Naturalist 152(2): 729:737.
Stevens, MHH. 2009. A primer in ecology with R. New York, Springer.
comCompete, http://ecovirtual.ib.usp.br
## Not run: regNicho(tmax=50, rw=100, cl=100, c1=0.2, c2=0.8, ec=0.5, dst=0.04, er=0.08, sc=0.02, mx=0, rs=0) ## End(Not run)## Not run: regNicho(tmax=50, rw=100, cl=100, c1=0.2, c2=0.8, ec=0.5, dst=0.04, er=0.08, sc=0.02, mx=0, rs=0) ## End(Not run)
Count the number of species (species richness) from a vector with a species list.
rich(x)rich(x)
x |
a vector with names. |
This function is used internally in the functions 'simHub1', simHub2', and 'simHub3'.
returns the number of species (species richness).
Alexandre Adalardo de Oliveira [email protected]
lsp <- sample(LETTERS,50,replace=TRUE) lsp rich(lsp)lsp <- sample(LETTERS,50,replace=TRUE) lsp rich(lsp)
Simulates Community Dynamics as in the Neutral Theory of Biogeography
simHub1(S = 100, j = 10, D = 1, cycles = 10000, m.weights = 1, anima = TRUE) simHub2(S = 100, j = 10, D = 1, cycles = 10000, m = 0.01, anima = TRUE) simHub3(Sm = 200, jm = 20, S = 100, j = 10, D = 1, cycles = 10000, m = 0.01, nu = 0.001, anima = TRUE)simHub1(S = 100, j = 10, D = 1, cycles = 10000, m.weights = 1, anima = TRUE) simHub2(S = 100, j = 10, D = 1, cycles = 10000, m = 0.01, anima = TRUE) simHub3(Sm = 200, jm = 20, S = 100, j = 10, D = 1, cycles = 10000, m = 0.01, nu = 0.001, anima = TRUE)
S |
number of species in the community. |
j |
individuals per species in the metacommunity. |
D |
number of deaths per cycle. |
cycles |
number of cycles in the simulation. |
m.weights |
Mortality weights for each species. Mortality rates of individuals of each species is proportional to species' abundances multiplied by these weights as in Yu et al. (1998). In neutral dynamics all weigths are equal. If length(m.weights)<S then species are divided in groups of (approximately) S/length(m.weights) and species of each group have a value in m.weights. This allows to create groups of species with different mortality probabilities and compare to the neutral dynamics. |
anima |
logical; if TRUE, the simulation frames of the metacommunity are shown. |
m |
colonization/immigration rate. |
Sm |
number of species in the metacommunity. |
jm |
individuals per species in the metacommunity. |
nu |
speciation rate. |
'simHub1' is the model without immigration.
'simHub2' incorporates immigration rate from the metacommunity
'simHub3' incorporates immigration and speciation rates in the metacommunity.
These functions returns a graph with the number of species in time (cycles) in the metacommunity.
They also return an invisible matrix with the results of species richness on each community per time.
Alexandre Adalardo de Oliveira and Paulo Inacio Prado [email protected]
Hubbell, S.P. 2001. The Unified Neutral Theory of Biodiversity and Biogeography. Princeton University Pres, 448p.
Yu, D. W., Terborgh, J. W., and Potts, M. D. 1998. Can high tree species richness be explained by Hubbell's null model?. Ecology Letters, 1(3): 193–199.
extGame, randWalk,
http://ecovirtual.ib.usp.br
## Not run: simHub1(S=10,j=10, D=1, cycles=5e3) simHub2(j=2,cycles=2e4,m=0.1) simHub3(Sm=200, jm=20, S= 10, j=100, D=1, cycles=1e4, m=0.01, nu=0.001, anima=TRUE) ## End(Not run)## Not run: simHub1(S=10,j=10, D=1, cycles=5e3) simHub2(j=2,cycles=2e4,m=0.1) simHub3(Sm=200, jm=20, S= 10, j=100, D=1, cycles=1e4, m=0.01, nu=0.001, anima=TRUE) ## End(Not run)
Simulates a successional model based on a transitional matrix of stages and its initial proportion of occurence in the landscape.
sucMatrix(mat.trans, init.prop, rw, cl, tmax)sucMatrix(mat.trans, init.prop, rw, cl, tmax)
mat.trans |
a matrix of stage transition probabilites. |
init.prop |
a vector with the initial proportions of each stage. |
rw |
number of rows to build the simulated landscape. |
cl |
number of columns to build the simulated landscape. |
tmax |
maximum simulation time. |
The number of patches in the simulated landscape is defined by rw*cl.
'sucMatrix' return a simulation graphic with the proportions of stages in the landscape in time, and a stage distribution graphic with the results of the simulation with the number o patches in time for each stage.
'sucMatrix' also return an invisible array with the simulation results.
Alexandre Adalardo de Oliveira [email protected]
Gotelli, N.J. 2008. A primer of Ecology. 4th ed. Sinauer Associates, 291pp.
## Not run: sucMatrix(mat.trans=matrix(data=c(0.5,0.5,0.5,0.5), nrow=2), init.prop=c(0.5,0.5),rw=20,cl=20, tmax=100) ## End(Not run)## Not run: sucMatrix(mat.trans=matrix(data=c(0.5,0.5,0.5,0.5), nrow=2), init.prop=c(0.5,0.5),rw=20,cl=20, tmax=100) ## End(Not run)