Non-Linear Model Fitting of Time Distribution of Biological Phenomena

Fit biologically meaningful distribution functions to time-sequence data (phenology), estimate parameters to draw the cumulative distribution function and probability density function and calculate standard statistical moments and percentiles. These methods are described in Steer et al. (2019) .

nlstimedist fits a biologically meaningful distribution function to time-sequence data (phenology), estimates parameters to draw the cumulative distribution function and probability density function and calculates standard statistical moments and percentiles.

Installation

You can install:

• the latest released version from CRAN with

install.packages("nlstimedist")

• the latest development version from GitHub with

devtools::install_github("nathaneastwood/nlstimedist")

Usage

Preparing the data

Data should be in tidy format. nlstimedist provides three example tidy datasets: lobelia, pupae and tilia.

head(tilia)
#> 1  94     0
#> 2  95     0
#> 3  96     1
#> 4 103     1
#> 5 104     0
#> 6 105     3

We first need to calculate the cumulative number of trees as well as the proportions. We do this using the tdData function.

tdTilia <- tdData(tilia, x = "Day", y = "Trees")
tdTilia
#> # A tibble: 26 × 4
#>      Day Trees  cumN    propMax
#>    <int> <dbl> <dbl>      <dbl>
#> 1     96     1     1 0.01538462
#> 2    103     1     2 0.03076923
#> 3    105     3     5 0.07692308
#> 4    107     1     6 0.09230769
#> 5    110     4    10 0.15384615
#> 6    111     7    17 0.26153846
#> 7    112     3    20 0.30769231
#> 8    114     1    21 0.32307692
#> 9    115     3    24 0.36923077
#> 10   116     6    30 0.46153846
#> # ... with 16 more rows

Fitting the model

We fit the model to the proportion of the cumulative number of trees (propMax) in the tdTilia data using the timedist function.

model <- timedist(data = tdTilia, x = "Day", y = "propMax", r = 0.1, c = 0.5, t = 120)
model
#> Nonlinear regression model
#>   model: propMax ~ 1 - (1 - (r/(1 + exp(-c * (Day - t)))))^Day
#>    data: data
#>         r         c         t 
#>   0.02721   0.17126 124.84320 
#>  residual sum-of-squares: 0.01806
#> 
#> Number of iterations to convergence: 10 
#> Achieved convergence tolerance: 1.49e-08

Extracting the moments

We can extract the mean, variance, standard deviation, skew, kurtosis and entropy of the model as follows.

model$m$getMoments()
#>       mean variance       sd     skew kurtosis entropy
#> 1 118.0325 180.7509 13.44436 4.324762 46.82073 5.36145

Extracting the RSS

Similarly we can extract the RSS of the model

model$m$rss()
#> [1] 0.9930469

Plotting the PDF and CDF

The pdf and cdf of the model have their own plotting functions.

tdPdfPlot(model)

tdCdfPlot(model)

Citation

Franco, M. (2012). The time-course of biological phenomenon - illustrated with the London Marathon. Unpublished manuscript. Plymouth University.