Research  Interests

My research interests lie in developing numerical/statistical models and quantitative methods for a better understanding of mechanisms responsible for different ecological system processes and behaviors. Currently, I am active in five areas of research:1) modeling of vegetation dynamics under climatic change; 2) modeling of vector-borne disease dynamics;3) methodology development for uncertainty and sensitivity analysis; 4) methodology development for elasticity and loop analysis; and 5) remote sensing.

 1.    Dynamic Vegetation modeling under climatic change

Two key challenges of simulating global vegetation dynamics is to correctly simulate the water and nitrogen limitation for plant growth. My research is to improve our understanding and predictability of these two important limitations. For nitrogen limitation, I have developed/improved models of nitrogen limitation based on optimization of nitrogen investment of key biological processes (photosynthesis, respiration and storage). For water limitation, I have developed a vegetation-soil model (ARCHY-ED) that mechanistically simulate soil/leaf water potential and conductivity. Carbon starvation and hydrological failure due to water limitation are implemented in the model to mechanistically simulate tree mortality.

 2.  Vector-borne disease dynamic modeling

Aedes aegypti is one of the most important disease vectors in the world. The development of spatial mosquito models for aedes. aegypti and spatial models of disease transmission provides a promising start toward model-based pest control and risk assessment. One key challenge of that is to understand the reliability of population and disease dynamics predicted from these models, which can be measured by the uncertainties in model predictions. As a post-doctor jointly advised by Professor Fred Gould and Professor Alun Loyd (2009 May -2010 May), I am specifically exploring the following topics:

1)        Quantifying uncertainties in the equilibrium population dynamics predicted from a spatial model of mosquito population (Skeeter-Buster) in its application to the Iquitos city in Peru. Uncertainties in the model predictions result from uncertainties in the estimation of 67 parameters accounting for mosquito survival, development, fecundity, environmental thresholds, and spatial dispersals, which are estimated from literature, expert knowledge and data re-estimation using Markov-Chain Monte Carlo approach (Xu et al. 2010);

2)        Quantifying uncertainties in allele frequency distribution predicted from a spatial model of mosquito population (Skeeter-Buster) targeted for releasing genetically modified mosquitoes carrying anti-pathogen genes;

3)        Assessing the effect of spatial heterogeneity of human and vector population on dengue fever transmission dynamics;

4)        Parameter estimation for spatial population models based on entomological survey data.


3.        Uncertainty and sensitivity analysis

Uncertainty and sensitivity analysis is a statistical method to assess how much uncertainty there is in the model prediction and where the uncertainty comes from. Uncertainty and sensitivity analysis can help scientists target at processes/parameters that make large contributions to ecological/environmental system prediction, which can be very useful for natural resources conservation, management, and general understanding of ecological processes. The previous methods for model uncertainty and sensitivity analysis are commonly based on assumptions of parameter independence. However, for most of the realistic model applications, the parameters are correlated. Coauthoring with my advisor, we proposed two uncertainty and sensitivity methods for models with correlated parameters: one method for linear models (Xu and Gertner 2008e) and another method for general models based on an extension to the popular Fourier Amplitude Sensitivity Test (FAST) (Xu and Gertner 2007, 2008b). We have also extended the approach of FAST to accounting for interactions among parameters (Xu and Gertner 2009c), decoupling correlated and uncorrelated effects (Xu and Gertner 2009a), theoretically assessing the reliability of sensitivity indices based on FAST (Xu and Gertner 2009b). The new method based on our work can promote a more realistic model analysis for both spatial and non-spatial models. We applied the new improved method to different systems including transient population dynamics using a matrix population model (Xu and Gertner 2008d), forest landscape response to global climatic change (Xu et al. 2008a), and LiDAR-based forest inventory system (Xu et al. 2008b).

In addition to uncertainties in model parameters (scalar variables), there are also uncertainties for spatial and temporal inputs for spatial-temporal dynamics models. For uncertainty analysis of spatial model inputs, I introduced the Latin hypercube sampling into geostatistical stochastic simulation to account for uncertainties in spatial model inputs for a more efficient spatial sample space exploration (Xu et al. 2005) and assessed the effect of uncertainty in the initial species composition map on forest landscape prediction at different scales using a Monte-Carlo simulation approach (Xu et al. 2004). For the uncertainty analysis of temporal inputs, I have introduced a profile based approach to incorporate uncertainty in time-series predictions of climate accounting for auto-correlation through time and cross-correlation among different time series predictions (Xu et al. 2008a). 

I am also very familiar with hierarchical Bayesian model and Bayesian belief network, which can incorporate the uncertainty when we build our models. However, uncertainty and sensitivity analysis is still necessary for understanding the pathways of uncertainty propagation from the parameters to the model predictions.

4.        Elasticity and loop analysis

The elasticity and loop analyses are prevalent approaches in demographic study of individual species in ecology. Elasticity and loop analysis has already been important tools to understand the underlying mechanism of simulated dynamics in matrix population model (Caswell 2001) and system dynamics models (Güneralp 2006). Collaborating with Dr. Burak Güneralp (Lecturer at Yale University), we proposed a novel application of these approaches as a formal method to quantitatively measure the importance of different transition pathways in the forest landscape response to climatic change (Xu et al. 2009a). Such a formal method allows for more informed assessments of the differential response to external perturbation such as climatic change not only for forest landscape dynamics but also for any ecosystem or landscape whose dynamics can be represented in the form of transition matrices. The ability to evaluate landscape responses in a quantitative and consistent manner is especially noteworthy when uncertainty in these responses is likely to be high. By quantifying the importance of specific processes (transitions among forest types) to forest composition dynamics, the proposed approach can be a valuable tool for a more quantitative understanding of the relationship between processes and landscape composition / patterns.


5.        Remote sensing

Remote sensing is an essential tool for large scale ecological study. I have coupled an Ecosystem Demography (ED) model with a Forest Reflectance and Transmittance (FRT) model to detect tree mortality by fitting ED-FRT to remote sensed reflectance values (Xu et al in prep).  Ensemble Kalman Filter is employed for data-model integration. This is a very novel approach that could potentially make the global detection of tree mortality possible, a key challenge of benchmarking of dynamic vegetation  models .