---
title: "randomTF on spatially structured environments"
author: "Richard J Telford"
date: "`r Sys.Date()`"
output: 
  rmarkdown::html_vignette:
    fig_caption: yes
vignette: >
  %\VignetteIndexEntry{randomTF on spatially structured environments}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---
  
```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

Spatial autocorrelation can severely bias transfer function performance estimates.
If can also bias reconstruction significance tests, but I suspect the bias is not as severe.

This vignette show how to use the `autosim` argument to `randomTF()` to use an autocorrelated simulated environmental variables, instead of the default uniformly distributed independent environmental variables, to make the reference distribution.

```{r}
#| label: load-packages
#| message: false
library(palaeoSig)
library(rioja)
library(sf)
library(gstat)
library(dplyr)
library(tibble)
library(tidyr)
library(purrr)
library(ggplot2)
set.seed(42) # for reproducibility
```


## Data

We use the foraminifera dataset by [Kucera et al. (2005)](https://doi.pangaea.de/10.1594/PANGAEA.227322). 
We use some of the samples to represent a core.

```{r, results='hide', warning=FALSE}
# load data
data(Atlantic)
meta <- c("Core", "Latitude", "Longitude", "summ50")
Atlantic <- as.data.frame(Atlantic) # prevents rowname warnings

# pseudocore as no fossil foram data in palaeoSig
fosn <- Atlantic |>
  filter(between(summ50, 5, 10)) |>
  slice_sample(n = 20)

# remaining samples as training set
Atlantic <- Atlantic |>
  anti_join(fosn, by = "Core") |>
  slice_sample(n = 300) # random subset to speed analysis up

Atlantic_meta <- Atlantic |>
  select(one_of(meta)) # to keep rdist.earth happy
Atlantic <- Atlantic |> # species
  select(-one_of(meta))

fos <- fosn |>
  select(-one_of(meta))
```

## Variogram

We need to convert the meta data into an `sf` object for further calculation.

```{r, message=FALSE, results = 'hide', fig.cap = "Figure 2: Semi-variogram fitted to detrended residuals of a weighted averaging model."}
Atlantic_meta <- st_as_sf(
  x = Atlantic_meta,
  coords = c("Longitude", "Latitude"),
  crs = 4326
)
```


Fitting the variogram is the hardest part.
There are several types of variogram model available, e.g. exponential "Exp", spherical "Sph", gaussian "Gau" and Matérn "Mat". 
These have different shapes. 
It is important to find one that fits the data well.

```{r, fig.cap = "Figure 1: Semi-variogram model (Matérn class) fitted to the Atlantic summer sea temperature at 50 m depth."}
# Estimate the variogram model for the environmental variable of interest
ve <- variogram(summ50 ~ 1, data = Atlantic_meta)
vem <- fit.variogram(
  object = ve,
  model = vgm(40, "Mat", 5000, .1, kappa = 1.8)
)
plot(ve, vem)
vem
```

## Kriging

Now we can use `gstat::krige` to do Gaussian unconditional simulation and make simulated environmental fields with the same spatial structure as the observed variable.
This step is quite slow with large datasets. 

```{r}
#| label: kriging

# Simulating environmental variables
sim <- krige(sim ~ 1,
  locations = Atlantic_meta,
  dummy = TRUE,
  nsim = 100,
  beta = mean(Atlantic_meta$"summ50"),
  model = vem,
  newdata = Atlantic_meta
)

# convert sf back to a regular data.frame
sim <- sim |> st_drop_geometry()
```

Now we can run `randomTF` using the simulated environmental variables.

```{r}
#| label: randomTF-auto
#| fig-cap: "Figure 2. Result of randomTF with an autocorrelated null model."

rtf_auto <- randomTF(
  spp = Atlantic,
  env = Atlantic_meta$summ50,
  fos = fos,
  autosim = sim,
  fun = MAT,
  col = "MAT.wm"
)

plot(rtf_auto)
```

```{r}
#| label: randomTF-independent
#| fig-cap: Figure 3. Result of randomTF with a spatially independent null model.
rtf_ind <- randomTF(
  spp = Atlantic,
  env = Atlantic_meta$summ50,
  fos = fos,
  fun = MAT,
  col = "MAT.wm"
)

plot(rtf_ind)
```


## References
Kucera, M., Weinelt, M., Kiefer, T., Pflaumann, U., Hayes, A., Weinelt, M., Chen, M.-T., Mix, A.C., Barrows, T.T., Cortijo, E., Duprat, J., Juggins, S., Waelbroeck, C. 2005. Reconstruction of the glacial Atlantic and Pacific sea-surface temperatures from assemblages of planktonic foraminifera: multi-technique approach based on geographically constrained calibration datasets. *Quaternary Science Reviews* 24, 951-998 [doi:10.1016/j.quascirev.2004.07.014](https://doi.org/10.1016/j.quascirev.2004.07.014).

Telford, R.J., Birks, H.J.B. 2009. Evaluation of transfer functions in spatially structured environments. *Quaternary Science Reviews* 28, 1309-1316 [doi:10.1016/j.quascirev.2008.12.020](https://doi.org/10.1016/j.quascirev.2008.12.020).  
