island: Stochastic Island Biogeography Theory Made Easy

Description

Tools to develop stochastic models based on the Theory of Island Biogeography (TIB) of MacArthur and Wilson (1967) and extensions. The package allows the calculation of colonization and extinction rates (including environmental variables) given presence-absence data, the simulation of community assembly and model selection.

Details

In the simplest stochastic model of Island Biogeography, there is a pool of species that potentially can colonize a system of islands. When we sample an island in time, we obtain a time-series of presence-absence vectors for the different species of the pool, which allows us to estimate colonization (c) and extinction (e) rates under perfect detectability. These are actual rates (in T^{-1} units).
The simplest stochastic model of island biogeography assumes a single colonization-extinction pair for the whole community. This model implicitly assumes: first, neutrality of the species in the community, that is, all species in the community share the same values for those rates; and second, all species colonize and become extinct independently from each other. The "species neutrality assumption" can be relaxed easily, for example, calculating different rates for different groups or on a per-species basis. In addition, we can make these rates depend on environmental variables measured at the same time that we took our samples. For more information of the basic model, please see the references.

Data entry

The data should be organized in dataframes with consecutive presence-absence data of each sample ordered cronologically, being the data associated with a single species in a row. Additional columns can contain the filiations of every species to a group, i. e. a phylogenetic group or a guild.

Author(s)

Maintainer: Vicente Jimenez vicente.jimenez.ontiveros@gmail.com

Authors:

• David Alonso dalonso@ceab.csic.es

References

Alonso, D., Pinyol-Gallemi, A., Alcoverro T. and Arthur, R.. (2015) Fish community reassembly after a coral mass mortality: higher trophic groups are subject to increased rates of extinction. Ecology Letters, 18, 451–461.

Simberloff, D. S., and Wilson, E. O.. (1969). Experimental Zoogeography of Islands: The Colonization of Empty Islands. Ecology, 50(2), 278–296. doi:10.2307/1934856

Simberloff, D. S.. (1969). Experimental Zoogeography of Islands: A Model for Insular Colonization. Ecology, 50(2), 296–314. doi:10.2307/1934857

Akaike Information Criterion

Description

akaikeic calculates the Akaike Information Criterion (AIC) of a model.
akaikeicc calculates the corrected Akaike Information Criterion (AICc) for small samples.

Usage

akaikeic(NLL, k)

akaikeicc(NLL, k, n)

Arguments

Details

AIC = 2 * k + 2 * NLL

AICc = 2 * k - 2 * lnL + 2 * k * (k + 1) / (n - k - 1)

Value

A number with the AIC value for a model with k parameters and negative log-likelihood NLL, or the AICc value for a model with k parameters, negative log-likelihood NLL and sample size n.

See Also

weight_of_evidence

Examples

akaikeic(1485.926, 3)
akaikeicc(736.47, 6, 15)
akaikeicc(736.47, 6, 100)

Environmental fit for a single dataset

Description

all_environmental_fit estimates the best expressions for colonization and extinction rates given their dependency on environmental variables.
greedy_environmental_fit estimates expressions for colonization and extinction rates given their dependency on environmental variables using a greedy algorithm.
custom_environmental_fit estimates the m.l.e. of the parameters describing the relationship between colonization and extinction rates and environmental variables.
NLL_env returns the Negative Log-Likelihood of a pair of colonization and extinction rates for a given dataset with an specific relationship with environmental variables.

Usage

all_environmental_fit(dataset, vector, env, c, e, aic, verbose = FALSE)

custom_environmental_fit(dataset, vector, params, c_expression, e_expression)

NLL_env(dataset, vector, params, c_expression, e_expression)

greedy_environmental_fit(dataset, vector, env, c, e, aic, verbose = FALSE)

Arguments

Details

all_environmental_fit calculates all the combinations of parameters, that increase exponentially with the number of parameters. We advise to keep low the number of parameters.
greedy_environmental_fit adds sequentially environmental variables to the expressions of colonization and extinction rates and fix one at a time until termination, when only adding one variable does not improve the AIC of the last accepted model.

Value

A list with three components: a expression for colonization, a expression for extinction and the output of the optimization function, or the output of the optimization function in the custom environmental fit.
In the case of NLL_env, returns the NLL of an specific set or parameters describing the relationship of environmental covariates with colonizaiton and extinction.

Note

AIC is recommended to be higher than the AIC of the most simple model (i.e. not including environmental variables).

See Also

rates_calculator

Examples

all_environmental_fit(idaho[[1]],3:23,c("idaho[[2]]$TOTAL.ppt",
"idaho[[2]]$ANNUAL.temp"),0.13,0.19,100000)
greedy_environmental_fit(idaho[[1]],3:23,c("idaho[[2]]$TOTAL.ppt",
"idaho[[2]]$ANNUAL.temp"),0.13,0.19,100000)

custom_environmental_fit(idaho[[1]], 3:23, c(-0.00497925, -0.01729602,
0.19006501, 0.93486956), expression(params[1] * idaho[[2]]$TOTAL.ppt[i] +
params[3]), expression(params[2] * idaho[[2]]$ANNUAL.temp[i] + params[4]))
NLL_env(idaho[[1]], 3:23, c(-0.00497925, -0.01729602,
0.19006501, 0.93486956), expression(params[1] * idaho[[2]]$TOTAL.ppt[i] +
params[3]), expression(params[2] * idaho[[2]]$ANNUAL.temp[i] + params[4]))

Lakshadweep Archipelago coral fish community reassembly

Description

A list with three datasets containing presence-absence data for the reassembly proccess of coral fish communities in three atolls (Agatti, Kadmat and Kavaratti) of the Lakshadweep Archipelago (India).

Format

A list with 3 dataframes, each corresponding to the survey of a different atoll. Dataframes have in columns:

Species

Name of the species found

Trophic.Level

A number indicating the trophic level of the surveyed species

Presence-absence data

Several columns with letters (indicating the atoll surveyed) and the year in which the surveys were done

Guild

Guild of the surveyed species

Details

Surveys were conducted from 2000 to 2011 in order to follow community reassembly after a coral mass mortality event in the relatively unfished Lakshadweep Archipelago. Results indicated that higher trophic groups suffer an increased extinction rate even without fishing targeting them.

Note

Kavaratti atoll was not surveyed in 2000 and 2010.

Source

Alonso, D., Pinyol-Gallemi, A., Alcoverro T. and Arthur, R.. (2015) Fish community reassembly after a coral mass mortality: higher trophic groups are subject to increased rates of extinction. Ecology Letters, 18, 451–461.

From rates to probabilities

Description

cetotrans calculates transition probabilities from colonization and extinction rates for a determined interval of time, when provided.

Usage

cetotrans(c, e, dt = 1)

Arguments

Details

Given a pair of colonization and extinction rates, we can calculate the transition probabilities with the following equations:

T_{01} = (e / (c + e)) * (1 - exp( - (c + e) * dt))

T_{10} = (c / (c + e)) * (1 - exp( - (c + e) * dt))

Value

A matrix with the transition probabilities T_{01} and T_{10} of the Markov chain associated with the specified colonization and extinction rates.

Examples

cetotrans(0.13, 0.19)
cetotrans(0.2, 0.2, 2)

Data simulation of colonization-extinction dynamics

Description

data_generation simulates species richness data according to the stochastic model of island biogeography
PA_simulation simulates presence-absence data according to the stochastic model of island biogeography

Usage

data_generation(x, column, transitions, iter, times)

PA_simulation(x, column, transitions, times = 1)

Arguments

Details

To simulate community assembly, we need an initial vector of presence-absence, from which the subsequent assembly process will be simulated. This initial vector is considered as x[, column].

Value

A matrix with species richness representing each row consecutive samples and each column a replica of the specified dynamics or a matrix with presence-absence data for the specified dynamics, each row representing a species and each column consecutive samplings.

Note

You can simulate not only with a colonization and extinction pair, but with the pairs obtained from the environmental fit. In this case, you still have to indicate exactly the number of temporal steps that you are going to simulate.

See Also

cetotrans to obtain the transition probabilities associated with a colonization-extinction pair.

Examples

data_generation(as.data.frame(rep(0, 100)), 1,
matrix(c(0.5, 0.5), ncol = 2), 5, 25)
data_generation(alonso15[[1]], 3, matrix(c(0.5, 0.5), ncol = 2), 5, 25)
PA_simulation(as.data.frame(c(rep(0, 163), rep(1, 57))), 1, c(0.13, 0.19),
20)

Inmigration, birth, death- models

Description

ibd_models simulates population dynamics under three different inmigration, birth and death models.

Usage

ibd_models(n0, beta, delta, mu, K = NULL, time_v, type)

Arguments

Details

We have included three different stochastic models: Kendall (1948) seminal work, Alonso & McKane (2002) mainland-island model, and Haegeman & Loreau (2010) basic population model with denso-dependent deaths. These models are different formulations of a population dynamics with three basic processes: birth, death and inmigration of individuals. For the specifics, please refer to the original articles.

Value

A data.frame with two columns: one with the time vector and the other with the number of individuals at those times.

Note

Haegeman & Loreau model specification breaks for high values of n0 when the birth rate is lower than the death rate.

References

Kendall, D. G. (1948). On some modes of population growth leading to R. A. Fishers logarithmic series distribution. Biometrika, 35, 6–15.

Haegeman, B. and Loreau, M. (2010). A mathematical synthesis of niche and neutral theories in community ecology. Journal of Theoretical Biology, 269(1), 150–165.

Alonso, D. and McKane, A (2002). Extinction Dynamics in Mainland–Island Metapopulations: An N -patch Stochastic Model. Bulletin of Mathematical Biology, 64, 913–958.

Examples

ibd_models(n0 = 0, beta = 0.4, delta = 0.3, mu = 0.2,
time_v = 0:20, type = "Kendall")
ibd_models(n0 = 0, beta = 0.4, delta = 0.3, mu = 0.1, K = 30,
time_v = 0:20, type = "Alonso")

Mapped plant community time series, Dubois, ID

Description

A list with two datasets containing presence-absence and environmental data for a plant community of sagebrush steppe in Dubois, Idaho, USA

Format

A list with 2 dataframes, one corresponding to the presence-absence data and the other to the environmental variables. The first dataframe has in columns:

quad

Name of the quadrat surveyed

species

Name of the species found

Presence-absence data

Several columns with the year in which the surveys were conducted

The second dataframe has the following columns:

YEAR

Year in which surveys were conducted

Environmental variables

Data of the recorded environmental variables in the form XXX.YYY, where XXX denotes a month (or a total) and YYY can refer to snow (in inches), temperature (fahrenheit degrees) or precipitation (in inches)

Details

A historical dataset consisting of a series of permanent 1-m^2 quadrats located on the sagebrush steppe in eastern Idaho, USA, between 1923 and 1973. It also contains records of monthly precipitation, mean temperature and snowfall. Total precipitation, total snowfall, and mean annual temperature have been calculated from the original data.

Note

Only quadrats Q1, Q2, Q3, Q4, Q5, Q6, Q25 and Q26 are included here. The surveys were conducted annually from 1932 to 1955 with some gaps for the quadrats included here.

Source

https://knb.ecoinformatics.org/#view/doi:10.5063/AA/lzachmann.6.36

References

Zachmann, L., Moffet, C., and Adler, P.. (2010). Mapped quadrats in sagebrush steppe long-term data for analyzing demographic rates and plant-plant interactions. Ecology, 91(11), 3427–3427. doi:10.1890/10-0404.1

c/e rates for irregular samplings in multiple datasets

Description

irregular_multiple_datasets estimates colonization and extinction rates for data in several datasets.
NLL_imd returns the Negative Log-Likelihood of a pair of colonization and extinction rates for irregular sampling schemes in several single dataset.

Usage

irregular_multiple_datasets(
  list,
  vectorlist,
  c,
  e,
  column = NULL,
  n = NULL,
  step = NULL,
  assembly = FALSE,
  jacobian = FALSE,
  verbose = FALSE,
  CI = FALSE
)

NLL_imd(list, vectorlist, c, e, assembly = FALSE)

Arguments

Value

irregular_multiple_datasets returns a dataframe with colonization and extinction rates and their upper and lower confidence interval, and if needed, the names of the groups to which colonization and extinction rates have been calculated. NLL_imd gives the NLL for a multiple datasets with irregular sampling schemes given a specific c and e.

Note

The columns with the presence-absence data should have the day of that sampling on the name of the column in order to calculate colonization and extinction.

See Also

regular_sampling_scheme, irregular_single_dataset

Examples

irregular_multiple_datasets(simberloff, list(3:17, 3:18, 3:17,
3:19, 3:17, 3:16), 0.001, 0.001)

irregular_multiple_datasets(simberloff, list(3:17, 3:18, 3:17, 3:19, 3:17,
 3:16), 0.001, 0.001, "Tax. Unit 1", n = 13)
irregular_multiple_datasets(simberloff, list(3:17, 3:18, 3:17, 3:19, 3:17,
 3:16), 0.001, 0.001, "Tax. Unit 1", n = 13, CI = TRUE)
 
 NLL_imd(simberloff, list(3:17, 3:18, 3:17, 3:19, 3:17, 3:16), 0.0051, 0.0117)

c/e rates for irregular samplings in a dataset

Description

irregular_single_dataset estimates colonization and extinction rates in a single dataset with irregular sampling scheme.
NLL_isd returns the Negative Log-Likelihood of a pair of colonization and extinction rates for an irregular sampling scheme in a single dataset.

Usage

irregular_single_dataset(
  dataframe,
  vector,
  c,
  e,
  column = NULL,
  n = NULL,
  step = NULL,
  assembly = FALSE,
  jacobian = FALSE,
  verbose = FALSE,
  CI = FALSE
)

NLL_isd(dataframe, vector, c, e, assembly = FALSE)

Arguments

Value

irregular_single_dataset returns a dataframe with colonization and extinction rates and their upper and lower confidence interval, and if needed, the names of the groups to which colonization and extinction rates have been calculated. NLL_isd gives the NLL for a single dataset in an irregular sampling scheme given a specific c and e.

Note

The columns with the presence-absence data should have the day of that sampling on the name of the column in order to calculate colonization and extinction.

See Also

regular_sampling_scheme, irregular_multiple_datasets

Examples

irregular_single_dataset(simberloff[[1]], 3:17, 0.001, 0.001)
irregular_single_dataset(simberloff[[1]], 3:17, column = "Tax. Unit 1",
0.001, 0.001, 3)

irregular_single_dataset(simberloff[[1]], 3:17, column = "Tax. Unit 1",
0.001, 0.001, 3, 0.00001)

NLL_isd(simberloff[[1]], 3:17, 0.0038, 0.0086)

Lakshadweep Archipelago coral fish community reassembly data (expanded)

Description

A list with three data frames containing presence-absence data for the reassembly proccess of coral fish communities in three atolls (Agatti, Kadmat and Kavaratti) of the Lakshadweep Archipelago in India. These data contains a number of replicates (transects) per sampling time. It is in this respect that expands alonso community data (see island R package).

Format

A list with three dataframes from the 3 different atoll. The dataframe has in columns:

Species

Name of the species found

Atoll

Atoll surveyed

Guild

Feeding strategy of the surveyed species

Presence-absence data

Several columns corresponding to the year in which the surveys were done. Year repetition means repeated sampling of the same atoll at the same time. Presences are represented by 1 and true absencestrue or undetected presences by 0.

Details

Surveys were conducted from 2000 to 2013 in order to follow community reassembly after a coral mass mortality event in the relatively unfished Lakshadweep Archipelago. For most years, transects were taken in four locations per atoll. Although there might be some underlying heterogeneity, these transects are approximately taken as true replicates.

Note

Detectability per transect results to be of about 0.5, which means that the parameter 'Detectability' per atoll goes up to almost 0.94 if four transects per sampling time are taken (1-0.5^4).

Source

Alonso, D., Pinyol-Gallemi, A., Alcoverro T. and Arthur, R.. (2015) Fish community reassembly after a coral mass mortality: higher trophic groups are subject to increased rates of extinction. Ecology Letters, 18, 451–461.

Lakshadweep Archipelago coral fish community reassembly data in a single data frame

Description

A list with only one data frame containing presence-absence data for the reassembly proccess of coral fish communities in three atolls (Agatti, Kadmat and Kavaratti) of the Lakshadweep Archipelago in India. These data contains a number of replicates per sampling time. The data matrix marks missing data with a flag. It is in this respect that differs from lakshadweep.

Format

A list of a single dataframe with data from the 3 different atoll. The dataframe has in columns:

Species

Name of the species found

Atoll

Atoll surveyed

Guild

Feeding strategy of the surveyed species

Presence-absence data

Several columns corresponding to the year in which the surveys were done. Year repetition means repeated sampling of the same atoll at the same time. Presences are represented by 1 and true absencestrue or undetected presences by 0.

Details

Surveys were conducted from 2000 to 2013 in order to follow community reassembly after a coral mass mortality event in the relatively unfished Lakshadweep Archipelago. For most years, transects were taken in four locations per atoll. Although there might be some underlying heterogeneity, these transects are approximately taken here as true replicates.

Note

Detectability per transect results to be of about 0.5, which means that the parameter 'Detectability' per atoll goes up to almost 0.94 if four transects per sampling time are taken (1-0.5^4). The sampling structure differs from atoll to to atoll. Certain columns are filled with 0.1. This is the missing value flag.

Source

Alonso, D., Pinyol-Gallemi, A., Alcoverro T. and Arthur, R.. (2015) Fish community reassembly after a coral mass mortality: higher trophic groups are subject to increased rates of extinction. Ecology Letters, 18, 451–461.

Likelihood approach for estimating colonization/extinction with perfect or imperfect detectability

Description

mss_cedp conducts maximum likelihood estimation of colonization/extinction parameters of different data sets. This function can handle imperfect detectability and missing data defining a heterogeneous sampling structure across input data matrix rows.

Usage

mss_cedp(
  Data,
  Time,
  Factor,
  Tags,
  Colonization = 1,
  Extinction = 1,
  Detectability_Value = 0.5,
  Phi_Time_0_Value = 0.5,
  Tol = 1e-08,
  MIT = 100,
  C_MAX = 10,
  C_min = 0,
  E_MAX = 10,
  E_min = 0,
  D_MAX = 0.99,
  D_min = 0,
  P_MAX = 0.99,
  P_min = 0.01,
  I_0 = 0,
  I_1 = 1,
  I_2 = 2,
  I_3 = 3,
  z = 2,
  Minimization = 1,
  Verbose = 0,
  MV_FLAG = 0.1,
  PerfectDetectability = TRUE
)

Arguments

Details

The input is a data frame containing presence data per time (in cols). Different factors (for instance, OTU, location, etc) can slide the initial data frame accordingly. Model parameters will be estimated for each of these groups independently that correspond to each level of the chosen factor. If Minimization is 0, then no maximum likelihood estimation is performed and only the likelihood evaluation at the input model parameter values is returned. Searches are based on the Nelder-Mead simplex method, but conducted in a bounded parameter space which means that in case a neg loglikelihood (NLL) evaluation is called out from these boundaries, the returned value for this NLL evaluation is artifically given as the maximum number the machine can hold. Each group is named by a short-length-character label (ideally, 3 or 4 characters). All labels should have the same character length to fulfill memmory alignment requirements of the shared object called by .C(...) function. I_0, I_1, I_2, I_3 are model parameter keys. They are used to define a 4D-vector (Index). The search will take place on the full parameter space defined by model parameters (I_0, I_1) if PefectDetectability is TRUE or, alternatively, defined by (I_0, I_1, I_2, I_3) if PerfectDetectability is FALSE. Model parameter keys correspond to colonization (0), extinction (1), detectability (2), and P_0 (3) model parameters. For instance, if (I_0, I_1) is (1, 0), the search will take place whitin the paremeter space defined by extinction, as the first axis, and colonization, as the second.

Value

The function generates, as an output, either a 3-column matrix (Colonization, Extinction, Negative LogLikelihood) or 5-column matrix (Colonization, Extinction, Detectability, P_0, Negative LogLikelihood), depending on the value of the input parameter PerfectDetectability (either TRUE or FALSE).

Examples

Data <- lakshadweepPLUS[[1]]
Guild_Tag = c("Alg", "Cor", "Mac", "Mic", "Omn", "Pis", "Zoo")
Time <- as.vector(c(2000, 2000, 2001, 2001, 2001, 2001, 2002, 2002, 2002,
2002, 2003, 2003, 2003, 2003, 2010, 2010, 2011, 2011, 2011, 2011, 2012,
2012, 2012, 2012, 2013, 2013, 2013, 2013))
R <- mss_cedp(Data, Time, Factor = 3, Tags = Guild_Tag,
PerfectDetectability = FALSE, z = 4)
Guild_Tag = c("Agt", "Kad", "Kvt")
R <- mss_cedp(Data, Time, Factor = 2, Tags = Guild_Tag,
PerfectDetectability = FALSE, z = 4)

Model prediction error

Description

r_squared evaluates R^2 for our simulated dynamics.
simulated_model Error of the stochastic model.
null_model Error of the null model.

Usage

r_squared(observed, simulated, sp)

null_model(observed, sp)

simulated_model(observed, simulated)

Arguments

Details

The importance of assessing how well a model predicts new data is paramount. The most used metric to assess this model error is R^2. R^2 is always refered to a null model and is defined as follows:

R^{2} = 1 - \epsilon^{2} / \epsilon^{2}_0

where \epsilon^2 is the prediction error defined as the mean squared deviation of model predictions from actual observations, and \epsilon^2_0 is a null model error, in example, an average of squared deviations evaluated with a null model.

Our null model corresponds with a random species model with no time correlations, in which we draw randomly from a uniform distribution a number of species between 0 and number of species observed in the species pool. The expectation of the sum of squared errors under the null model is evaluated analytically in Alonso et al. (2015).

Value

r_squared gives the value of R^2 for the predictions of the model.

null_model gives the average of squared deviations of the null model predictions from actual observations, \epsilon^2_0.

simulated_model gives the average of squared deviations of the model predictions from the actual observations, \epsilon^2.

Note

The value of R^2 depends critically on the definition of the null model. Note that different definitions of the null model will lead to different values of R^2.

References

Alonso, D., Pinyol-Gallemi, A., Alcoverro T. and Arthur, R.. (2015) Fish community reassembly after a coral mass mortality: higher trophic groups are subject to increased rates of extinction. Ecology Letters, 18, 451–461.

Examples

idaho.sim <- data_generation(as.data.frame(c(rep(0, 163),
rep(1, 57))), 1, matrix(c(0.162599, 0.111252), ncol = 2), 250, 20)
idaho.me <- c(57, apply(idaho.sim, 1, quantile, 0.5))
r_squared(colSums(idaho[[1]][,3:23]), idaho.me, 220)

null_model(colSums(idaho[[1]][,3:23]), 220)

simulated_model(colSums(idaho[[1]][,3:23]), idaho.me)

Colonization and extinction rates calculator for expressions.

Description

rates_calculator Calculate colonization and extinction rates depending of their expressions.

Usage

rates_calculator(params, c_expression, e_expression, t)

Arguments

Value

A matrix with the colonization and extinction rates.

See Also

all_environmental_fit

Examples

rates_calculator(c(-0.00497925, -0.01729602, 0.19006501,
0.93486956), expression(params[1] * idaho[[2]]$TOTAL.ppt[i] + params[3]),
expression(params[2] * idaho[[2]]$ANNUAL.temp[i] + params[4]), 21)

c/e rates for a regular sampling scheme

Description

regular_sampling_scheme estimates colonization and extinction rates for a community or groups in a community.
NLL_rss returns the Negative Log-Likelihood of a pair of colonization and extinction rates for a regular sampling scheme.

Usage

regular_sampling_scheme(
  x,
  vector,
  level = NULL,
  n = NULL,
  step = NULL,
  CI = FALSE
)

NLL_rss(x, vector, c, e)

Arguments

Details

The confidence intervals are calculated with a binary search seeded with the hessian of the estimated rates.

Value

regular_sampling_scheme returns a dataframe with colonization and extinction rates along with their lower and upper confidence intervals (optional), for each group if specified, and its number of rows and NLL. NLL_rss gives the NLL for a dataframe given a specific c and e.

See Also

irregular_single_dataset, irregular_multiple_datasets

Examples

regular_sampling_scheme(alonso15[[1]], 3:6)
regular_sampling_scheme(alonso15[[1]], 3:6, "Guild", n = 5)
regular_sampling_scheme(alonso15[[1]], 3:6, "Guild", n = 5, CI = TRUE)
NLL_rss(alonso15[[1]], 3:6, 0.52, 0.39)

Simberloff and Wilson original defaunation experiment data

Description

A list of datasets containing the presence-absence data gathered originally by Simberloff and Wilson in their defaunation experiment of six mangrove islands in the Florida Keys.

Format

A list with 6 dataframes, each corresponding to the survey of a different island. Dataframes have in columns:

Taxa

Taxa considered

PRE

Presence-absence before the defaunation process

Integers (e.g. 21, 40, 58...)

Several columns with presence-absence data for the day specified

Tax. Unit 1

Highest taxonomical unit considered

Tax. Unit 2

Second highest taxonomical unit considered

Genera

Genera of the identified taxon

Island

Island of identification of the taxon

Details

The defaunation experiment of Simberloff and Wilson was aimed to test experimentally the Theory of Island Biogeography. The approach sought was eliminating the fauna of several islands and following the recolonization proccess.

After some trials, six red mangrove islets of Florida Bay were chosen for the task. These islets had to be stripped of all arthropofauna without harming the vegetation and then all the colonists were identified. The result of these defaunation experiments supported the existence of species equilibria and were consistent with the basic MacArthur-Wilson equilibrium model.

Note

The shaded entries in the original dataset, for taxa inferred to be present from other evidence rather than direct observation, are considered as present in these datasets.

Source

Simberloff, D. S., & Wilson, E. O.. (1969). Experimental Zoogeography of Islands: The Colonization of Empty Islands. Ecology, 50(2), 278–296. doi:10.2307/1934856

References

Wilson, E. O.. (2010). Island Biogeography in the 1960s: THEORY AND EXPERIMENT. In J. B. Losos and R. E. Ricklefs (Eds.), The Theory of Island Biogeography Revisited (pp. 1–12). Princeton University Press.

Simberloff, D. S., and Wilson, E. O.. (1969). Experimental Zoogeography of Islands: The Colonization of Empty Islands. Ecology, 50(2), 278–296. doi:10.2307/1934856

Wilson, E. O., and Simberloff, D. S.. (1969). Experimental Zoogeography of Islands: Defaunation and Monitoring Techniques. Ecology, 50(2), 267–278. doi:10.2307/1934855

Simberloff, D. S.. (1969). Experimental Zoogeography of Islands: A Model for Insular Colonization. Ecology, 50(2), 296–314. doi:10.2307/1934857

MacKenzie etal (2003) likelihood approach for estimating colonization/extinction parameters (with imperfect detectability)

Description

sss_cedp conducts a maximum likelihood estimation of model parameters (Colonization, Extinction, Detectability, and Phi_Time_0) of MacKenzie et al (2003) colonization-extinction model. This function is an alternative to mss_cedp that takes a different input (a 2D array), and requires the same sampling structure for all input data matrix rows, this is, no missing data defining a heterogeneous sampling structure across rows are allowed. As an advantage, it may run faster than mss_cedp.

Usage

sss_cedp(
  Data,
  Time,
  Transects,
  Colonization = 0.1,
  Extinction = 0.1,
  Detectability = 0.99,
  Phi_Time_0 = 0.5,
  Tol = 1e-06,
  MIT = 100,
  C_MAX = 2,
  C_min = 0,
  E_MAX = 2,
  E_min = 0,
  D_MAX = 0.999,
  D_min = 0.001,
  P_MAX = 0.999,
  P_min = 0.001,
  I_0 = 0,
  I_1 = 1,
  I_2 = 2,
  I_3 = 3,
  z = 4,
  Verbose = 0,
  Minimization = TRUE
)

Arguments

Details

Maximum likelihood parameter estimation is conducted through bounded searches. This is the reason why the minimum and maximum values for each axis should be given as input arguments. The optimization procedure is the simplex method. A bounded parameter space implies that in case a neg loglikelihood (NLL) evaluation is required outside from these boundaries, the returned value for this NLL evaluation is artifically given as the maximum number the machine can hold. The array Parameters (I_0, I_1, I_2, I_3) has to be a permutation of (0, 1, 3, 4). This parameter indeces along with the imput parameter 'z' are used to define a subparameter space where the search will be conducted. If z = 2, then the search will take place on the plane defined by model parameters (I_0, I_1). These indeces are model parameter keys: colonization (0), extinction (1), detectability (2), and Phi_Time_0 (3). For instance, if (I_0, I_1, I_2, I_3) is (2, 3, 1, 0), and z = 2, then the search will take place whithin the subparemeter space defined by the detection probability (Detectability) and the probability of presence at time 0 (Phi_Time_0). If Minimization is TRUE (default value), then the whole mle is conducted. If FALSE, the function only return the NLL value at the input model parameter values. Likelihood evaluations are exact provided the number of 'absences' corresponding to either true absences or undetected presences in the input data matrix is not to high.

Value

A list with five components (Colonization, Extinction, Detectability, P_0, and Negative Log-Likelihood).

Examples

Data1 <- lakshadweep[[1]]
Name_of_Factors <- c("Species","Atoll","Guild")
Factors <- Filter(is.factor, Data1)
No_of_Factors <- length(Factors[1,])
n <- No_of_Factors + 1
D1 <- as.matrix(Data1[1:nrow(Data1),n:ncol(Data1)])
Time <- as.double(D1[1,])
P1 <- as.matrix(D1[2:nrow(D1),1:ncol(D1)])
# Dealing with time.
Time_Vector <- as.numeric(names(table(Time)))
Transects   <- as.numeric((table(Time)))
R1 <- sss_cedp(P1, Time_Vector, Transects,
                       Colonization=0.5, Extinction=0.5, Detectability=0.5,
                       Phi_Time_0=0.5,
                       Tol=1.0e-8, Verbose = 1)

Model selection function based on a upgma grouping algorithm

Description

upgma_model_selection function conducts a model selection procedure intended to find an optimal partition that mimimize AIC values. Maximum likelihood estimation of model parameters (Colonization, Extinction) or (Colonization, Extinction, Detectability, P_0) is performed assuming either perfect detectability or imperfect detectability, respectively. In the latter case, the input data frame should contain multiple transects per sampling time. This function can handle missing data defining a heterogeneous sampling structure across the rows of the input data matrix.

Usage

upgma_model_selection(
  Data,
  Time,
  Factor,
  Tags,
  Colonization = 1,
  Extinction = 1,
  Detectability_Value = 0.5,
  Phi_Time_0_Value = 0.5,
  Tol = 1e-08,
  MIT = 100,
  C_MAX = 10,
  C_min = 0,
  E_MAX = 10,
  E_min = 0,
  D_MAX = 0.99,
  D_min = 0,
  P_MAX = 0.99,
  P_min = 0.01,
  I_0 = 0,
  I_1 = 1,
  I_2 = 2,
  I_3 = 3,
  z = 2,
  Verbose = 0,
  MV_FLAG = 0.1,
  PerfectDetectability = TRUE
)

Arguments

Details

The output matrix contains a row for the S different binary partitions of the set of S groups. Searches are conducted using Nelder-Mead simplex method in a bounded parameter space which means that in case a neg loglikelihood (NLL) evaluation is called out from these boundaries, the returned value for this NLL evaluation is artifically given as the maximum number the machine can hold. The input is a data frame containing presence data per time (in cols) and sites (in rows). Different factors (for instance, OTU, location, etc) can slide the initial data frame in their different levels, accordingly. Each initial group (usually, species, OUTs, factors, ...) is named by a short-length-character label (ideally, 3 or 4 characters). The length of Tags array should match the number of levels in which the given factor is subdivided. All labels should have the same character length to fulfill memmory alignment requriement of the shared object called by .C(...) function. I_0, I_1, I_2, and I_3 are model parameter keys. They are used to define a 4D-vector (Index). The model parameter keys correspond to the colonization (0), extinction (1), detectability (2), and Phi_0 (3) model parameters in case detectability is imperfect or, alternatively, only colonization (0) and extinction (1) in case detectability is perfect. For instance, if (I_0, I_1) is (1, 0), searches will take place within the paremeter space defined by extinction, as the first axis, and colonization, as the second.

Value

The function generates, as an output, a Sx6 matrix with the following 6 columns (for the S different partitions): (No of Model Parameters, NLL, AIC, AIC_c, AIC_d, AIC_w) which compares all upgma-generarated partitions. It also produces .tex code to generate a table of the best grouping and a summary of the model selection process.

Examples

## Not run: 
Data <- lakshadweepPLUS[[1]]
Guild_Tag = c("Alg", "Cor", "Mac", "Mic", "Omn", "Pis", "Zoo")
Time <- as.vector(c(2000, 2000, 2001, 2001, 2001, 2001, 2002, 2002, 2002,
2002, 2003, 2003, 2003, 2003, 2010, 2010, 2011, 2011, 2011, 2011, 2012,
2012, 2012, 2012, 2013, 2013, 2013, 2013))
R <- upgma_model_selection(Data, Time, Factor = 3, Tags = Guild_Tag,
PerfectDetectability = FALSE, z = 4)
Guild_Tag = c("Agt", "Kad", "Kvt")
R <- upgma_model_selection(Data, Time, Factor = 2, Tags = Guild_Tag,
PerfectDetectability = FALSE, z = 4)

## End(Not run)

Weight of evidence

Description

weight_of_evidence calculates the weight of evidence of a set of nested models.

Usage

weight_of_evidence(data)

Arguments

Details

Calculates the weight of evidence in favor of model i being the actual Kullback-Leibler best model given a set of models R for your data.

w_i = exp( - 1/2 * \Delta_i) / \Sigma exp( - 1/2 * \Delta_r)

r = 1, R

Value

A dataframe with the names of the analysed models, their AIC differences with respect to the best model and the w_i of each one.

References

K. P. Burnham, D. R. Anderson. Model selection and multimodel inference: a practical information-theoretic approach (New York:Springer, ed. 2, 2002).

See Also

akaikeic

Examples

models <- c("Best_3k", "Best_4k", "Best_5k", "Best_6k", "Best_7k",
  "Best_8k", "Best_9k")

  aks <- c(2977.852, 2968.568, 2957.384, 2952.618,
  2949.128, 2947.038, 2943.480)

  weight_of_evidence(cbind(models, aks))