Ecology of UV
UV introduction and basic optics
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Autoregressive modeling
prepared by Janet
Fischer
Understanding the role of direct and indirect effects in community responses to perturbation is a major challenge in community ecology. The multivariate first order autoregressive (MAR(1)) approach was developed and refined by the Community Dynamics Working Group at the National Center for Ecological Analysis and Synthesis (see http://www.nceas.ucsb.edu). MAR(1) models have been used previously to distinguish the role of direct environmental effects and food web interactions in acidification experiments (Klug et al. 2000, Fischer et al. 2001) and predator manipulations (Ives et al. 1999). In the current project we will use MAR(1) models to distinguish the relative importance of abiotic factors related to UV and climate change from biotic factors related to interactions with other species in a series of mesocosm experiments.
Using time series data from experiments, MAR(1) models will predict the temporal dynamics of major components of the food. The model explicitly separates the direct effects of a perturbation from indirect effects acting through changes in the food web. In each model, biomass of the focal food web component in the next time step (time t+1) is predicted using previous data (time t) for biomass of the focal food web component, other food web components, and abiotic variables. The multivariate linear autoregressive model for a community containing S food web components and V abiotic variables has the form:
where ni(t+1) is the ln(x+1)-transformed biomass of foodweb component i at time t+1, ni(t) and nj(t) are ln(x+1)-transformed biomasses of foodweb components i and j at time t, uj is ln(x+1)-transformed value of abiotic variable j, and e(t) is variability that is not explained by the linear terms of the model. The regression coefficients aij and bij indicate the strength of each effect considered in the model, and ci is a fitted constant.
Recent refinements of the MAR(1) model provides estimates of confidence intervals for regression coefficients (Ives et al. accepted). Environmental variability not captured by abiotic variables in the model is contained within e(t), as is variability associated with possible nonlinear interactions among variables in the model. Although the model cannot account for nonlinear population dynamics, it nonetheless is a first-order approximation that can be used to estimate the main effects of abiotic variables and food web interactions on changes in biomass of focal food web components.
One of the goals of this 5 year project is to use the MAR(1) approach to determine how the interactive effects of UV and temperature affect the dynamics of planktonic communities because community dynamics are driven by food web interactions, as well as abiotic variables such as UV and CDOM.
To learn more about this topic, please refer to the following articles:
Fischer, J.M., T.M. Frost, and A.R. Ives. 2001. Compensatory dynamics in zooplankton community responses to acidification: measurement and mechanisms. Ecological Applications 11: 1060-1072.
Ives, A.R. 1995. Predicting the response of populations to environmental change. Ecology 76: 926-941.
Ives, A.R., S.R. Carpenter, and B. Dennis. 1999. Community interaction webs and zooplankton responses to planktivory manipulations. Ecology 80: 1405-1421.
Ives, A.R., B. Dennis, K.L. Cottingham, and S.R. Carpenter. Accepted. Estimating community stability and ecological interactions from time-series data. Ecological Monographs.
Klug, J.L., J.M. Fischer, A.R. Ives, and B. Dennis. 2000. Compensatory dynamics
in planktonic community responses to pH perturbations. Ecology 81: 387-398.