# ecocbo-guide

## ecocbo: Calculating Optimum Sampling Effort in Community Ecology

ecocbo is an R package that helps scientists determine the optimal sampling effort for community ecology studies. It can be used to calculate the minimum number of samples needed to achieve a desired level of precision, or to fit within a set economic budget as proposed by Underwood (1997, ISBN 0 521 55696 1). ecocbo is based on the principles of ecological simulation as done in the SSP package. A pilot study can be used to estimate the natural variability of the system, which in turn is used to calculate the optimal sampling effort. ecocbo is a valuable tool for scientists who need to design efficient sampling plans. It can save time and money by ensuring that scientists collect the minimum amount of data necessary to achieve their research goals.

ecocbo is composed of four main functions:

• sim_beta() computes the statistical power at different sampling efforts.
• plot_power() allows the user to visualize the changes in statistical power given the certain number of sampling units or sites. .
• scompvar() calculates the components of variation among sites and within samples. This information is necessary for calculating the optimal sampling effort.
• sim_cbo() estimates the optimal number of replicated units and replicates per unit depending on the major constrains of budget or precision to be achieved.

## Functions and sequence

### 0. Preparing the data

As it was stated in the introduction, ecocbo uses simulated ecological communities as produced by SSP:simdata() to take advantage of the considerations of natural variability that it produces. As such, it is necessary to prepare the data using the tools provided by SSP.

To get a feeling of the functionality of ecocbo, you can follow the next basic example.

The provided data epiDat is a subset of the original epibionts (Guerra-Castro, et al., 2021). It was prepared by looking for communities that were as different as possible within the dataset. The first step or preparing the data is to save it in two different objects: epiH0 in which the data is treated as if it came from the same site thus accepting the null hypothesis, and epiHa in which the opposite is true, so that the samples come from different sites and portray different characteristics. The defining variable for doing so is site which will be set to a single label for epiH0, and left as-is for epiHa.

The workflow fir SSP requires the computation of simulation parameters, this is done with SSP::assempar() and using the same arguments for both datasets. Both datasets are then used for the simulation of ecological communities, which is done by SSP::simdata(), and that results in the data that we will use to work with ecocbo.

To ensure that the resulting datasets are the same size, the parameters sites and N for SSP::simdata(parH0, ...) must be set to 1 and the product of sites and N in SSP::simdata(parHa, ...), respectively. For this example, the values used to calculate simH0 are sites=1 and N=1000, and then sites=10 and N=100 for simHa, which results in 3 matrices (cases=3) of 1000 rows and 95 columns (the number of columns depends on the simulation parameters from SSP::assempar()) for both of the resulting datasets.

# Load data and adjust it.
data(epiDat)

epiH0 <- epiDat
epiH0[,"site"] <- as.factor("T0")
epiHa <- epiDat
epiHa[,"site"] <- as.factor(epiHa[,"site"])

# Calculate simulation parameters.
parH0 <- SSP::assempar(data = epiH0, type = "counts", Sest.method = "average")
parHa <- SSP::assempar(data = epiHa, type = "counts", Sest.method = "average")

# Simulation.
simH0Dat <- SSP::simdata(parH0, cases = 3, N = 1000, sites = 1)
simHaDat <- SSP::simdata(parHa, cases = 3, N = 100, sites = 10)

### 1. sim_beta()

sim_beta() computes the statistical power for a combination of up to m sites and n samples per site. Its arguments are:

Argument Description
simH0 Simulated community from SSP::simdata() in which there is only one site.
simHa Simulated community from SSP::simdata() in which there are more than one site.
n Maximum number of samples to consider.
m Maximum number of sites.
k Number of resamples the process will take. Defaults to 50.
alpha Level of significance for Type I error. Defaults to 0.05.
transformation Mathematical function to reduce the weight of very dominant species. Options are: ‘square root’, ‘fourth root’, ‘Log (X+1)’, ‘P/A’, ‘none’
method The appropriate distance/dissimilarity metric that will be used by vegan::vegdist() (e.g. Gower, Bray–Curtis, Jaccard, etc).
dummy Logical. It is recommended to use TRUE in cases where there are observations that are empty.
useParallel Logical. Should R call to several cores to work on parallel computing? This is done to speed up the processing time.

The value of k defines the number of times that the combination of sites and samples will be considered to form a statistical distribution that will establish, along with alpha, the probability of type I error from the simulated data. Higher values of k will increase the computational intensity of the process, which may result in slower execution times.

The function returns an object of class ecocbo_beta which prints to a table showing the statistical power at different sampling efforts. The object, however, is a list that contains two data frames, one comprising the information about power and beta, and a second one that lists the results of the resampling of values indicated by k.

betaResult <- sim_beta(simH0Dat, simHaDat, n = 5, m = 4, k = 30, alpha = 0.05,
transformation = "square root", method = "bray", dummy = FALSE,
useParallel = FALSE)
betaResult
#> Power at different sampling efforts (m x n):
#>       n = 2 n = 3 n = 4 n = 5
#> m = 2  0.27  0.71  0.72  0.75
#> m = 3  0.23  0.73  0.88  0.95
#> m = 4  0.50  0.84  0.99  1.00

### 2. plot_power()

plot_power() makes plots for either a power curve, a density plot, or both. Its parameters are:

Argument Description
data Object of class “ecocbo_beta” that results from sim_beta().
n Defaults to NULL, and then the function computes the number of samples (n) that results in a sampling effort close to 95% in power. If provided, said number of samples will be used.
m Site label to be used as basis for the plot.
method The desired plot. Options are “power”, “density” or “both”.

The power curve plot shows that the power of the study increases as the sample size increases, and the density plot shows the overlapping areas where alpha and beta are significant.

The argument n is set to NULL by default, if it is left like that, the the function looks for a number of samples that allows for a power that is close to $$(1-alpha)$$, otherwise it uses the value stated by the user. In either case, the computed or provided value is marked in red in the plot.

plot_power(data = betaResult, n = NULL, m = 3, method = "both")

### 3. scompvar()

scompvar() calculates the components of variation within sites and among replicates. Its arguments are:

Argument Description
data Object of class “ecocbo_beta” that results from sim_beta().
n Site label to be used as basis for the computation. Defaults to NULL.
m Number of samples to be considered. Defaults to NULL.

If m or n are left as NULL, the function will calculate the components of variation using the largest available values as set in the experimental design in sim_beta().

compVar <- scompvar(data = betaResult)
compVar
#>     compVarA  compVarR
#> 1 0.07687087 0.3280817

### 4. sim_cbo()

sim_cbo() estimates the optimal number of sites and replicates per site to perform based on either available budget or desired precision.

Argument Description
comp.var Data frame as obtained from scompvar().
multSE Optional. Required multivariate standard error for the sampling experiment.
ct Optional. Total cost for the sampling experiment.
ck Cost per replicate.
cj Cost per unit.

It is necessary to indicate one of the two optional arguments, as that parameter dictates if the function will work either based on budget or precision.

cboCost <- sim_cbo(comp.var = compVar, ct = 20000, ck = 100, cj = 2500)
cboCost
#>   nOpt mOpt
#> 1   10    5
cboPrecision <- sim_cbo(comp.var = compVar, multSE = 0.10, ck = 100, cj = 2500)
cboPrecision
#>   nOpt mOpt
#> 1   10   10

## References

• Underwood, A. J. (1997). Experiments in ecology: their logical design and interpretation using analysis of variance. Cambridge university press.

• Underwood, A. J., & Chapman, M. G. (2003). Power, precaution, Type II error and sampling design in assessment of environmental impacts. Journal of Experimental Marine Biology and Ecology, 296(1), 49-70.

• Anderson, M. J. (2017). Permutational Multivariate Analysis of Variance (PERMANOVA). Wiley StatsRef: Statistics Reference Online. John Wiley & Sons, Ltd.

• Guerra-Castro, E. J., J. C. Cajas, F. N. Dias Marques Simoes, J. J. Cruz-Motta, and M. Mascaro. (2020). SSP: An R package to estimate sampling effort in studies of ecological communities. bioRxiv:2020.2003.2019.996991.