@article{banks_banks_bommarco_laubmeier_myers_rundlof_tillman_2017, title={Modeling bumble bee population dynamics with delay differential equations}, volume={351}, ISSN={["1872-7026"]}, DOI={10.1016/j.ecolmodel.2017.02.011}, abstractNote={Bumble bees are ubiquitous creatures and crucial pollinators to a vast assortment of crops worldwide. Bumble bee populations have been decreasing in recent decades, with demise of flower resources and pesticide exposure being two of several suggested pressures causing declines. Many empirical investigations have been performed on bumble bees and their natural history is well documented, but the understanding of their population dynamics over time, causes for observed declines, and potential benefits of management actions is poor. To provide a tool for projecting and testing sensitivity of growth of populations under contrasting and combined pressures, we propose a delay differential equation model that describes multi-colony bumble bee population dynamics. We explain the usefulness of delay equations as a natural modeling formulation, particularly for bumble bee modeling. We then introduce a particular numerical method that approximates the solution of the delay model. Next, we provide simulations of seasonal population dynamics in the absence of pressures. We conclude by describing ways in which resource limitation, pesticide exposure and other pressures can be reflected in the model.}, journal={ECOLOGICAL MODELLING}, author={Banks, H. T. and Banks, J. E. and Bommarco, Riccardo and Laubmeier, A. N. and Myers, N. J. and Rundlof, Maj and Tillman, Kristen}, year={2017}, month={May}, pages={14–23} }
 @article{banks_banks_rosenheim_tillman_2017, title={Modelling populations of Lygus hesperus on cotton fields in the San Joaquin Valley of California: the importance of statistical and mathematical model choice}, volume={11}, ISSN={["1751-3766"]}, DOI={10.1080/17513758.2016.1143533}, abstractNote={ABSTRACT Understanding the population dynamics of herbivorous insects is critical to developing and implementing effective pest control protocols. In the context of inverse problems, we explore the dynamic effects of pesticide treatments on Lygus hesperus, a common pest of cotton in the western United States. Fitting models to field data, we explore the topic of model selection for an appropriate mathematical model and corresponding statistical models, and use techniques including ANOVA-based model comparison tests and residual plot analysis to make the best selections. In addition we explore the topic of data information content: in this example, we are testing the question of whether data, as it is currently collected, can support time-dependent parameter estimation. Furthermore, we investigate the statistical assumptions often haphazardly made in the process of parameter estimation and consider the implications of unfounded assumptions.}, number={1}, journal={JOURNAL OF BIOLOGICAL DYNAMICS}, author={Banks, H. T. and Banks, J. E. and Rosenheim, Jay and Tillman, Kristen}, year={2017}, month={Mar}, pages={25–39} }
 @article{banks_banks_link_rosenheim_ross_tillman_2015, title={Model comparison tests to determine data information content}, volume={43}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2014.11.002}, abstractNote={In the context of inverse or parameter estimation problems we demonstrate the use of statistically based model comparison tests in several examples of practical interest. In these examples we are interested in questions related to information content of a particular given data set and whether the data will support a more complicated model to describe it. In the first example we compare fits for several different models to describe simple decay in a size histogram for aggregates in amyloid fibril formation. In a second example we investigate whether the information content in data sets for the pest Lygus hesperus in cotton fields as it is currently collected is sufficient to support a model in which one distinguishes between nymphs and adults. Finally in a third example with data for patients having undergone an organ transplant, we question whether the data content is sufficient to estimate more than 5 of the fundamental parameters in a particular dynamic model.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Banks, J. E. and Link, Kathryn and Rosenheim, J. A. and Ross, Chelsea and Tillman, K. A.}, year={2015}, month={May}, pages={10–18} }
 @article{banks_banks_rinnovatore_jackson_2015, title={Optimal sampling frequency and timing of threatened tropical bird populations: A modeling approach}, volume={303}, ISSN={["1872-7026"]}, DOI={10.1016/j.ecolmodel.2015.02.005}, abstractNote={Abstract Conservation of threatened or endangered species relies critically on accurate population counts over time. In practice, many population censuses are conducted by non-governmental organizations or volunteer citizen scientists who are constrained by fiscal and temporal resources. Less than optimal sampling regimens (characterized by infrequent and/or irregular schedules) for conducting population censuses can result in woefully misleading population estimates – and thus have dire consequences for management and conservation. We illustrate this using an East African case study in which 14 years of bird data was collected in the Arabuko-Sokoke Forest in coastal Kenya. We first estimate life history parameters in a discrete matrix model. Desiring a data collection protocol which would lessen observation error and lend to a deeper understanding of population projections and dynamics of a threatened species, we carry out mathematical and statistical modeling efforts with an adaptation of a Leslie model for simulated population estimates stemming from different population sampling schemes. We illustrate how resource managers might take a strategic approach, using simple quantitative models, to develop an optimal sampling scheme that considers important species traits, such as breeding season, and balances the tradeoff between resources and accuracy.}, journal={ECOLOGICAL MODELLING}, author={Banks, J. E. and Banks, H. T. and Rinnovatore, K. and Jackson, C. M.}, year={2015}, month={May}, pages={70–77} }