Efficient sampling designs to assess biodiversity spatial autocorrelation : should we go fractal ?

Abstract

Evaluating the autocorrelation range of species distribution in space is necessary for many applied ecological questions like implementing protected area networks or monitoring programs. The autocorrelation range can be inferred from observations, based on a spatial sampling design. However, there is a trade-off between estimating the autocorrelation range of a species distribution and estimating fixed effects affecting the mean species abundance or occupancy among sites. The random sampling design is considered as a good heuristic to estimate autocorrelation range, for it contains contrasted pairwise distances that cover a wide array of possible range values. The grid design is viewed as a better choice for estimating fixed effects, for it eliminates small pairwise distances that are more prone to pseudo-replication. Mixing random and grid (`hybrid' designs) has been presented as a way to navigate between both conflicting objectives. We postulated that fractal designs --- which have a self-similarity property and well-identified scales --- could make a compromise, for they preserve some regularity reminiscent of grid at each scale, but also browse a wide array of possible autocorrelation range values across scales. We used maximum likelihood estimation within an optimal design of experiments approach to compare the accuracy of hybrid and fractal designs at estimating the fixed intercept and the autocorrelation range of a spatial field of values. We found that hybrid designs were Pareto-optimal intermediary strategies between grid and random for small autocorrelation range values only, while classic grid design should always be preferred when autocorrelation is large. Fractal designs yielded Pareto-optimal stra\-tegies specifically good at estimating small autocorrelation ranges. However, they were generally not Pareto-optimal for higher values of autocorrelation range. At last, when the surveyed area could be changed, random designs were sufficient to reach the Pareto front in any context. Fractal designs seemed relevant when specifically aiming at improving the estimation of small autocorrelation ranges in a fixed surveyed area with a limited sampling budget, which is a quite circumscribed scenario. However, they may prove more clearly advantageous to analyse biodiversity patterns when covariates are included in the analysis and ecological processes differ among spatial scales.