14-eco.Rmd

# Geocomputation for Ecology: A case study of fog oases {#eco}

## Prerequisites {-}

This chapter assumes you have a strong grasp of spatial data analysis and processing, covered in chapters 2-5.
In it you will make use of R's interfaces to dedicated GIS software, and spatial cross validation, topics covered in chapters \@ref(gis) and \@ref(spatial-cv) respectively.

## Introduction

keywords: species distribution modeling, floristic modeling, spatial cross-validation, spatial autocorrelation, ordination (NMDS, Isomap), predictive mapping

structure:

1. intro ecological modeling and related applications beyond ecology
2. introduce research question, shortly the dataset and the planned approach
3. ordination
4. retrieving predictors and quick data exploration
5. modeling ordination scores most likely using machine-learning since we are mostly interested in spatial predictions, and because the mlr spatial cv approach is new, and finally because Alain Zuur's books cover statistical inference broadly
6. predictive mapping of floristic composition including spatial cross-validation
7. discussion: what could be done better or alternatives and again emphasizing that the methods shown
finally, point to books on ecological modeling especially emphasizing Alain Zuur's books


## Background

Fog oases are one of the most fascinating vegetation formations I have ever encountered. 
These formations, locally termed *lomas*, develop on mountains along the coastal deserts of Peru and Chile.
The desert's extreme conditions and remoteness provide the habitat for a unique ecosystem, including species endemic to the fog oases.
Despite the arid conditions and low levels of precipitation of around 30-50 mm per year, plants can survive, by 'combing out' fog.
This fog, which develops below the temperature inversion caused by the cold Humboldt current in austral winter, provides the name for this habitat.
Every few years, the El Niño weather pattern brings torrential rainfall to this sun-baked environment [@dillon_lomas_2003].
This causes the desert to bloom, and provides tree seedlings a chance to develop roots long enough to survive the following arid conditions.

Unfortunately fog oases are heavily endangered.
This is mostly due to human activity (agriculture and climate change).
To effectively protect the last remnants of this unique vegetation ecosystem, evidence is needed on the composition and spatial distribution of the native flora [@muenchow_predictive_2013; @muenchow_soil_2013].
*Lomas* mountains also have economic value as a tourist destination, and can contribute to the wellbeing of local people via recreation.
For example, most Peruvians live in the coastal desert, and *lomas* mountains are frequently the closest "green" destination.

In this chapter we will demonstrate ecological applications of some of the techniques learned in the previous chapters.
This case study will involve analyzing the composition and the spatial distribution of the vascular plants on the southern slope of Mt. Mongón, a *lomas* mountain near Casma on the central northern coast of Peru (Fig. \@ref(fig:study-area-mongon)).

```{r study-area-mongon, echo = FALSE, fig.cap = "The Mt. Mongón study area (taken from @muenchow_rqgis:_2017; Landsat image: path 9, row 67, acquisition date 09/22/2000; @usgs_u.s._2016)."}
knitr::include_graphics("https://user-images.githubusercontent.com/1825120/38989956-6eae7c9a-43d0-11e8-8f25-3dd3594f7e74.png")
```

During a field study to Mt. Mongón we recorded all vascular plants living in 100 randomly sampled 4x4 m^2^ plots in the austral winter of 2011 [@muenchow_predictive_2013].
The sampling coincided with a strong La Niña event that year (see ENSO monitoring of the [NOASS Climate Prediction Center](http://origin.cpc.ncep.noaa.gov/products/analysis_monitoring/ensostuff/ONI_v5.php)).
This led to even higher levels of aridity than usual in the coastal desert.
By contrast, it increased fog activity on the southern slopes of Peruvian *lomas* mountains.

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The first hypothesis is that four plant belts will be found along the altitudinal gradient: a low-elevation *Tillandsia* belt, a herbaceous belt, a bromeliad belt, and an uppermost succulent belt [@muenchow_soil_2013].
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Ordinations are dimension-reducing techniques which allow the extraction of the main gradients from a (noisy) dataset, in our case the floristic gradient developing along the southern mountain slope.
In this chapter we will try to model the first ordination axis, i.e., the floristic gradient, as a function of environmental predictors such as altitude, slope, catchment area and NDVI.
The corresponding model will allow us to make spatial predictions of the floristic composition anywhere in the study area.
When doing the spatial predictions, we will of course account for the likely presence of spatial autocorrelation with the help of spatial cross-validation (see chapter \@ref(spatial-cv)).

## Reducing dimensionality

Ordinations are a popular tool in vegetation science to extract the main information, frequently corresponding to ecological gradients, from large species-plot matrices mostly filled with 0s. 
However, they are also used in remote sensing (spectral bands + hyperspectral), the soil sciences, geomarketing, etc.
If you are unfamiliar with ordination techniques or in need of a refresher, have a look at Michael W. Palmers [webpage](http://ordination.okstate.edu/overview.htm) for a short introduction to popular ordination techniques in ecology and at @borcard_numerical_2011 for a deeper look how to apply these techniques in R. 
**vegan**'s package documentation is also very helpful (`vignette(package = "vegan")`).

Principal component analysis (PCA) is probably the most famous ordination technique. 
It is a great tool to reduce dimensionality if one can expect linear relationships between variables, and if the joint absence of a variable (for example calcium) in two plots (observations) can be considered a similarity.
This is barely the case with vegetation data.

For one, relationships are usually non-linear along environmental gradients.
That means the presence of a plant usually follows a unimodal relationship along a gradient (e.g., humidity, temperature or salinity) with a peak at the most favorable conditions and declining ends towards the unfavarable conditions. 

Secondly, the joint absence of a species in two plots is often hardly an indication for similarity.
Suppose a plant species is absent from the driest (e.g., an extreme desert) and the most moist locations (e.g., a tree savannah) of our sampling.
Then we really should refrain from counting this as a simlilarity because it is very likely that the only thing these two completely different environmental settings have in common in terms of floristic composition is the shared absence of species (except for rare ubiquist species). 

## Exercises