mapply_calc_obs_like: Mapply version of calc_obs_like()

Description

This function applies calc_obs_like to all cells of the input matrices obs_target_species and obs_all_species. These matrices obviously must have the same dimensions.

Usage

mapply_calc_obs_like(truly_present = TRUE, obs_target_species, obs_all_species, mean_frequency = 0.1, dp = 1, fdp = 0)

Arguments

truly_present

Is the OTU of interest known/conditionally assumed to be truly present (TRUE) or truly absent (FALSE)?

obs_target_species

A scalar or column/vector/matrix of detection counts, e.g. as produced from the output from read_detections.

obs_all_species

A scalar or column/vector/matrix of detection counts, e.g. as produced from the output from read_controls.

mean_frequency

This is the proportion of samples from the taphonomic control group that will truly be from this OTU, GIVEN that the OTU is present. This could be estimated, but a decent first guess is (total # samples of OTU of interest / total # of samples in the taphonomic control group where the OTU is known to be present). All that is really needed is some reasonable value, such that more sampling without detection lowers the likelihood of the data on the hypothesis of true presence, and vice versa. This value can only be 1 when the number of detections = the number of taphonomic control detections, for every OTU and area. This is the implicit assumption in e.g. standard historical biogeography analyses in LAGRANGE or BioGeoBEARS.

The detection probability. This is the per-sample probability that you will correctly detect the OTU in question, when you are looking at it. Default is 1, which is the implicit assumption in standard analyses.

fdp

The false detection probability. This is probability of falsely concluding a detection of the OTU of interest occurred, when in fact the specimen was of something else. The default is 0, which assumes zero error rate, i.e. the assumption being made in all historical biogeography analyses that do not take into account detection probability. These options are being included for completeness, but it may not be wise to try to infer mean_frequency, dp and fdp all at once due to identifiability issues (and estimation of fdp may take a very large amount of data). However, fixing some of these parameters to reasonable values can allow the user to effectively include beliefs about the uncertainty of the input data into the analysis, if desired.

Value

pp_df A matrix of the natural log-likelihood of the data, given the model & assumption of true presence or absence.

Details

The inputs are the same as for calc_obs_like, except that obs_target_species and obs_all_species can be matrices.

References

http://phylo.wikidot.com/matzke-2013-international-biogeography-society-poster http://en.wikipedia.org/wiki/Bayes'_theorem

Matzke_2012_IBS

Bottjer_Jablonski_1988

Bayes_1763

Examples

Run this code

test=1
# Calculate likelihood of data, given presence in an area,
# given a dp (detection probability) and detection model.

# soft-coded input files
extdata_dir = np(system.file("extdata", package="BioGeoBEARS"))
detects_fn = np(paste(extdata_dir, "/Psychotria_detections_v1.txt", sep=""))
controls_fn = np(paste(extdata_dir, "/Psychotria_controls_v1.txt", sep=""))

OTUnames=NULL
areanames=NULL
tmpskip=0

detects_df = read_detections(detects_fn, OTUnames=NULL, areanames=NULL, tmpskip=0)
controls_df = read_controls(controls_fn, OTUnames=NULL, areanames=NULL, tmpskip=0)

detects_df
controls_df
detects_df / controls_df


# Calculate data likelihoods, and posterior probability of presence=TRUE
mean_frequency=0.1
dp=1
fdp=0

mapply_calc_obs_like(truly_present=TRUE, obs_target_species=detects_df,
obs_all_species=controls_df, mean_frequency, dp, fdp)

mapply_calc_obs_like(truly_present=FALSE, obs_target_species=detects_df,
obs_all_species=controls_df, mean_frequency, dp, fdp)

mapply_calc_post_prob_presence(prior_prob_presence=0.01,
obs_target_species=detects_df,
obs_all_species=controls_df, mean_frequency, dp, fdp)

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