Estimating natural scales of ecological systems

A fundamental goal in ecology is to identify the appropriate scales at which to observe trends in ecosystem behavior. Researchers often rely on intuition to choose a sampling scale, which if too large or too small potentially obscures the real system trends. A characteristic length scale (CLS) is a natural scale of a system at which the underlying deterministic dynamics are most clearly observed over stochasticity. The overarching aim of this research was to develop, examine and apply a robust technique to detect CLSs of real ecological systems. In this thesis, I first compared the robustness of two CLS methods, both of which account for complex oscillatory dynamics of ecological systems using attractor reconstruction from long time series of data. I applied these techniques to estimate CLSs of spatial multispecies systems of varying complexity, showing that for more complex models, the prediction r2 metric of Pascual and Levin (1999) is a robust method. I then used an alternative method of CLS estimation, based on prediction r2 but where repetition in space is largely substituted for repetition in time in attractor reconstruction, to determine the CLS of a natural marine fouling system. The new technique, requiring only a short temporal sequence of as few as three highly resolved spatial maps, enabled unambiguous length scales to be estimated for this system. Importantly, the estimated CLS was similarly based on analysis of several species representing a spectrum of phyla and life history patterns, indicating the adequacy of this method for objectively determining optimal scales of observation for real systems. Moreover, the CLS estimates of this system remained surprisingly consistent despite changes in time intervals between the spatial maps, changes in the number of maps used in the temporal sequence, and varying start dates of map sequences. When the field results were compared to those derived from a spatially explicit individual-based model of a similar marine community nearby, the average CLSs of the two communities were strikingly similar (~ 0.35 m), suggesting that dynamical trends of like systems may be best observed on similar scales. I also considered whether the approach could be extended to identify trends based on the dynamics of interactions among habitat types as opposed to interactions among species groups. Analysis of maps produced from remote sensing data at the habitat level successfully revealed unambiguous characteristic length scales of a coral reef. Habitats distinct in their species assemblages, abundances and morphologies provided similar length scales (~ 300 m), suggesting that the system-level CLS detected is independent of the habitat type used for its estimation. Different species within the same system indicated dissimilar CLSs in some spatial model communities where species were only weakly connected, either due to the topology of network interactions or through spatial isolation as a result of spatial self-organization and patchiness. I finally evaluated the sensitivity of CLS estimates to varying levels of species connectivity and found that when species were weakly connected in terms of their network topology, the estimates of scale were likely to be dissimilar. The results contained within this thesis illustrate that the new method developed to detect natural scales of complex systems (1) can be applied to natural dynamical systems with a reasonable quantity of data, (2) is robust to changes in parameters that should not affect the scale of observation (e.g. initial configuration of the landscape), but (3) is sensitive to variations that would likely affect the spatial scale at which trends can be observed (e.g. connectivity). Species or habitat level data can be used to estimate CLSs, which will be critical for choosing the scale at which to sample real ecosystems to distinguish trends from random variation. Characteristic length scales can now be implemented to objectively guide the choice of observation scale, and I expect that in the future, they will become a part of every assiduous ecologist's toolbox.