README.md
In PhillRob/PopulationGrowthR: Linear Population Growth Scenarios

title: "PopulationGrowthR" output: html_document: default pdf_document: default word_document: default bibliography: man/bibliography.bib csl: man/apa-5th.csl

Population development scenarios

Rob Hyndman developed an R function to estimate the existence and length of the time lag in species populations based on species occurrence time series. The method published in Biological Invasions detects a period of stagnant population growth prior to an increase. While the original script distinguishes species with a biphasic population growth, this update fits a piece-wise model to differentiate between multiple scenarios. The script fits a maximum of 5 linear splines and determines the slope. The number of splines depends on the best model (highest AIC). Lag phases are reported if one or more splines have a slope of 0.

You can install the Population Growth package from github with:

# install.packages("devtools")
devtools::install_github("PhillRob/PopulationGrowthR")
library(PopulationGrowthR)

Raw GBIF data is included as test data is included along with formatted input data.

data(rawdata)
cleandata = raw2freqdata(rawdata) # Convert the raw GBIF data
fdata = cleandata$data # Frequency data for each specimen by year
yeardata = cleandata$yeardata # Frequency data for all specimens by year

One can make use of the example data provided with the package as well

data(fdata)
data(yeardata)

This is a basic example that fits the model to the test data.

# Run lagfit for 1 species only
Species = unique(fdata$Species) # List of all species
fit1 = lagfit(data = fdata, yeardata = yeardata, species = Species[1])

# Run lagfit for multiple species
fit2 = lagfit(data=fdata, yeardata=yeardata, species=Species[1:3])
fitdata = fit2$fitdata  # Dataframe containing fits
fitcoefs = fit2$fitcoefs # List containing slopes of the fitted splines

# Run lagfit for the whole dataset
fitall = lagfit(data = fdata, yeardata = yeardata)

To plot observed and predicted frequencies for a species against year

freqplot(fit1$fit)

To plot the fitted growth curve with confidence bands

growthplot(fit1$fit)

Alternatively, one can use the following to plot all species

fit1 = lagfit(fdata, yeardata, species = Species, plotlag = TRUE, plotfreq = TRUE)

You can use raw2freqdata.R to wrap GBIF data downloaded using the rgbif package by @Scott_Chamberlain_Vijay_Barve_Dan_Mcglinn_Damiano_Oldoni_Laurens_Geffert_Karthik_Ram2018-zi into the format required by the lag code.

# get gbif occurences
if (!require(rgbif)) install.packages('rgbif')
library(rgbif)

species <- c("Vachellia farnesiana", "Achyranthes aspera"))
gbifkey <- sapply(species, function(x)
  name_backbone(name = x, kingdom = 'plants'),
  USE.NAMES = FALSE)
gbifkey <- as.data.frame(gbifkey)


gbifocc <- occ_search(taxonKey = gbifkey[1,], limit = 200000, country = "US",  return = "data")
gbifocc <- ldply(gbifocc, data.frame)

# format gbif data to format for lag code
lagdata <- raw2freqdata(x = gbifocc)

This function also allows to specify the number of knots (0-4) and returns the scenario of the fit between the knots. A sequence of 0, + or - is returned. A 0 indicates constant, + indicates a positive slope and a - indicates negative slope. The function fits generalised linear models @Hyndman2015-rt to the Poisson distributed count data and adjusts the collection rate by the overall collection effort. $$n_t \sim Poisson(N_t exp[f(t)])$$ $N_t$ = total number of samples of alien species/year

$n_t$ = number of samples of focal species/year

A lag-phase exists if $f(t)$ is constant until some year, and then increases.

The results return the scenario per species including the slope of every individual splines.

negative sign (-) reflects a negative slope and a decrease in abundance
positive sign (+) reflects a positive slope and a increase in abundance
zero (0) reflects a stagnant growth with a slope of 0

Attached a few examples of single knot scenarios in an plant invasion context.

1. Constant (single-phase, no lag): No biphasic pattern is detected and the abundance remains constantly low/high. A species is managed or only survives in a nurtured human assisted context. The species (sleeper weed) may still be exploring suitable conditions at the margin of their 'niche', with potential for population expansion.

2. Instant increase without delay (single-phase, no lag): No biphasic population change is detected and the species population growth is continuously positive. The species may be nurtured, continuously introduced (high propagule pressure) or introduced at a location with suitable biotic and abiotic conditions.

3. Instant decrease without delay (single-phase, no lag): A decrease can be linked to a successful eradication effort, stopped nurturing or halted introduction of non-naturalized aliens. The species may also rely on biotic interaction (muralists) that are absent in the invaded environment. A change in the survey effort may be linked.

4. Decrease after lag (biphasic, lag): A delayed decrease can occur if a successful establishment is followed by an eradication, halted nurturing efforts or change in biotic or abiotic conditions. A change in the survey effort may be associated to this pattern.

5. Lag phase: The original scenario showing rapid increase after delay (biphasic, lag)

6. Decrease followed by lag (biphasic, lag)

7. Increase before delay (biphasic, lag)

8. Instant increase followed by decrease (biphasic, no lag)

9. Decrease followed by increase (biphasic, no lag)