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- Creators: Grimm, Nancy
- Creators: Li, Ziqi
- Creators: Lu, Xuetao
An understanding of the formation of spatial heterogeneity is important because spatial heterogeneity leads to functional consequences at the ecosystem scale; however, such an understanding is still limited. Particularly, research simultaneously considering both external variables and internal feedbacks (self-organization) is rare, partly because these two drivers are addressed under different methodological frameworks. In this dissertation, I show the prevalence of internal feedbacks and their interaction with heterogeneity in the preexisting template to form spatial pattern. I use a variety of techniques to account for both the top-down template effect and bottom-up self-organization. Spatial patterns of nutrients in stream surface water are influenced by the self-organized patch configuration originating from the internal feedbacks between nutrient concentration, biological patchiness, and the geomorphic template. Clumps of in-stream macrophyte are shaped by the spatial gradient of water permanence and local self-organization. Additionally, significant biological interactions among plant species also influence macrophyte distribution. The relative contributions of these drivers change in time, responding to the larger external environments or internal processes of ecosystem development. Hydrologic regime alters the effect of geomorphic template and self-organization on in-stream macrophyte distribution. The relative importance of niche vs. neutral processes in shaping biodiversity pattern is a function of hydrology: neutral processes are more important in either very high or very low discharge periods. For the spatial pattern of nutrients, as the ecosystem moves toward late succession and nitrogen becomes more limiting, the effect of self-organization intensifies. Changes in relative importance of different drivers directly affect ecosystem macroscopic properties, such as ecosystem resilience. Stronger internal feedbacks in average to wetter years are shown to increase ecosystem resistance to elevated external stress, and make the backward shifts (vegetation loss) much more gradual. But it causes increases in ecosystem hysteresis effect. Finally, I address the question whether functional consequences of spatial heterogeneity feed back to influence the processes from which spatial heterogeneity emerged through a conceptual review. Such feedbacks are not likely. Self-organized spatial patterning is a result of regular biological processes of organisms. Individual organisms do not benefit from such order. It is order for free, and for nothing.
In the first part, nonlinear regression models were embedded into a multistage workflow to predict the spatial abundance of reef fish species in the Gulf of Mexico. There were two challenges, zero-inflated data and out of sample prediction. The methods and models in the workflow could effectively handle the zero-inflated sampling data without strong assumptions. Three strategies were proposed to solve the out of sample prediction problem. The results and discussions showed that the nonlinear prediction had the advantages of high accuracy, low bias and well-performed in multi-resolution.
In the second part, a two-stage spatial regression model was proposed for analyzing soil carbon stock (SOC) data. In the first stage, there was a spatial linear mixed model that captured the linear and stationary effects. In the second stage, a generalized additive model was used to explain the nonlinear and nonstationary effects. The results illustrated that the two-stage model had good interpretability in understanding the effect of covariates, meanwhile, it kept high prediction accuracy which is competitive to the popular machine learning models, like, random forest, xgboost and support vector machine.
A new nonlinear regression model, Gaussian process BART (Bayesian additive regression tree), was proposed in the third part. Combining advantages in both BART and Gaussian process, the model could capture the nonlinear effects of both observed and latent covariates. To develop the model, first, the traditional BART was generalized to accommodate correlated errors. Then, the failure of likelihood based Markov chain Monte Carlo (MCMC) in parameter estimating was discussed. Based on the idea of analysis of variation, back comparing and tuning range, were proposed to tackle this failure. Finally, effectiveness of the new model was examined by experiments on both simulation and real data.
model spatially non-stationary relationships. Classic GWR is considered as a single-scale model that is based on one bandwidth parameter which controls the amount of distance-decay in weighting neighboring data around each location. The single bandwidth in GWR assumes that processes (relationships between the response variable and the predictor variables) all operate at the same scale. However, this posits a limitation in modeling potentially multi-scale processes which are more often seen in the real world. For example, the measured ambient temperature of a location is affected by the built environment, regional weather and global warming, all of which operate at different scales. A recent advancement to GWR termed Multiscale GWR (MGWR) removes the single bandwidth assumption and allows the bandwidths for each covariate to vary. This results in each parameter surface being allowed to have a different degree of spatial variation, reflecting variation across covariate-specific processes. In this way, MGWR has the capability to differentiate local, regional and global processes by using varying bandwidths for covariates. Additionally, bandwidths in MGWR become explicit indicators of the scale at various processes operate. The proposed dissertation covers three perspectives centering on MGWR: Computation; Inference; and Application. The first component focuses on addressing computational issues in MGWR to allow MGWR models to be calibrated more efficiently and to be applied on large datasets. The second component aims to statistically differentiate the spatial scales at which different processes operate by quantifying the uncertainty associated with each bandwidth obtained from MGWR. In the third component, an empirical study will be conducted to model the changing relationships between county-level socio-economic factors and voter preferences in the 2008-2016 United States presidential elections using MGWR.