Comparing model types

1 Purpose

The purpose of this site is to contrast a few different approaches to modelling broad scale spatio-temporal that are suitable for both very large and small sample data sets in the context of the upcoming GCRMN report. More specifically, we have identified the following modelling challenges for which analyses of simulated data will hopefully provide model choice guidance:

• Site replacements: when monitored sites are removed from a design and replaced with alternative sites. Of particular concern is the situation in which a poor site is discontinued (perhaps it becomes so degraded it no longer functions as a coral reef) and is replaced by a relatively good new site (with the argument that there is no value in establishing a new poor site that might similarly disappear in the near future). Unfortunately, this shifts the bias and has the potential to confound the timeseries.

• Unsampled years: when the timeseries are punctuated with missing years. Ideally, it is important that the analyses are able to estimate trends across the full timeseries. Hence estimates are necessary, even when data are unavailable.

• Use of covariates: whilst other covariates (such as sea surface temperature and cyclones could be used to inform trends at locations and times for which observed data are lacking, they also have the potential to induce new biases. For example, if models are “trained” with wave energy (or wind) data in which no major storms occurred and coral cover grew, it is possible that the model could “learn” that coral cover is positively correlated with wave energy. When predicting to a different area that did experience substantial stores (that might be expected to have a negative impact on coral cover), such a model might erroneously predict substantial increases in coral cover.

There are also additional complications of using covariates that are likely to represent acute impacts. Whilst, coral cover can decline rapidly in response to a disturbance, it typically takes time to recover (if at all) to its pre-disturbance state. As a result, the state of coral at any specific time is the result of an accumulation of conditions over the past and not just the most recent conditions. To account for this in a modelling perspective, is likely to require either:

Inclusion of the previous years cover estimate in a model (which effectively means the model is parameterised on changes in cover). This is obviously infeasible for the first year of a monitoring program or a program without fixed sites and also becomes a proportionally bigger issue with shorter the time series. Inclusion of multiple lagged versions of each of the covariates that are likely to represent causal disturbances.

2 Approach

To explore the above challenges, we have elected to take two approaches:

1. create exemplar datasets from a simulated landscape and apply a range of candidate models to each of these datasets. Since the landscape is fully simulated, the modelled outcomes can be compared to the “truth”. Furthermore, this approach permits us to explore the suitability of different modelling approaches to very specific challenges (such as site replacements or temporal gaps) in complete isolation.
2. select exemplar cases from the real collated data and apply a range of candidate models. Whilst less controlled, this approach allows us to explore the impact of modelling decisions on real situation.

The current site will focus on the former of these approaches as it does not require the dissemination of real data for which there might be embargoes or other restrictions in place.

3 The simulated landscape

To simulate a coral reef landscape, we are making use of an R package (synthos). This package starts with a spatial array representing the state of a coral reef (hard coral, soft coral and algae cover) at time 0. Realistic spatio-temporal footprints for three broad types of disturbances (cyclones, ocean temperature and an “other”) are also defined. These disturbances are then used to perturb the coral reef benthos over time and space in conjunction with some growth. The net result is a full spatio-temporal grid of each of hard coral cover, soft coral cover and algae cover to act as the “truth”.

The synthos package also permits us to apply different monitoring sampling designs to mimic the collection of observational data over space and time. For example, we could nominate a sampling design comprised of 25 randomly selected reefs, each of which are monitored over a 12 year period and comprise of samples collected from 50 photos along five transects in each of three sites from each reef.

We used the synthos package to construct specific datasets that each focused on one of the modelling challenges outlined above. Details of the codes used to create the base of those datasets (e.g. the full spatio-temporal landscape and the observed monitoring datasets) are outlined here.

4 Investigation of modelling approaches

The following table describes each of the modelling challenges along with the associated dataset and link to the modelling outcomes. Note, the first case in each challenge represents the ideal full spatio-temporal observation grid and is there for comparison.

Challenge	Dataset name	Description	Link
Reef replacement			site_replacements.html
	benthos_fixed_locs_obs	Full monitoring sample 25 sites, 12 years complete	Model
	benthos_fixed_locs_obs_1	25 sites, 12 years complete, poorest site replaced by strongest after 9 years	Model
	benthos_fixed_locs_obs_2	5 sites, 12 years complete, poorest site replaced by strongest after 9 years	Model
Missing years			missing_years.html
	benthos_fixed_locs_obs	Full monitoring sample 25 sites, 12 years complete	Model
	benthos_fixed_locs_obs_3	25 sites, 12 years, 5 site with gap between years 2 and 6	Model
	benthos_fixed_locs_obs_4	5 sites, 12 years, 5 site with gap between years 2 and 6	Model