Research Themes

I have broad research interests that cover a wide-range of areas, including spatiotemporal statistics, robust estimation, forecasting, disease modeling, Bayesian estimation, and causal inference for ecological data. For the most part, they can be grouped into two main goals:

  • Developing statistical methods for non- and semi-parametric models for high-dimensional data to explore the effects of climate change on population dynamics
  • Expanding causal inference for large ecosystem networks while ameliorating weaknesses in causal analysis techniques for ecological data

Robust estimation for non- and semi-parametric models

Plot of estimated coefficient functions from a single-index varying coefficient model
Estimated coefficient functions for the log transformed data with outliers. Top: LS estimators. Bottom: Rank estimators.

My research focuses on developing and applying robust and efficient nonparametric statistical procedures for nonlinear modeling of climate change effects on groundfish communities in the northern Pacific Ocean. Working with non- and semi-parametric models to explore the effects of climate changes on populations has highlighted the inadequacy of current methods to appropriately calculate effect size measures for predictors in high-dimensional model structures. As model structures become complex in order to accommodate more ecological interactions, accurately measuring the size of such effects becomes equally convoluted. I am therefore interested in creating robust effect size measures suitable for such model structures to expand the usability of these models to scientists who require appropriate inference to develop ecological theory and make management decisions.

Otlaadisa, M., Bindele, H. F., Abebe, A. & Correia, H. E. (2022) Varying coefficient single-index regression model with missing responses under rank-based modeling. Journal of Nonparametric Statistics. 34(2), 319-343.

Correia, H. E. & Abebe, A. (2021) Regularised rank quasi-likelihood estimation for generalised additive models. Journal of Nonparametric Statistics. 33(1).

Sun, W., Bindele, H. F., Abebe, A., & Correia, H. E. (2021) Robust functional selection for the single-index varying coefficients regression model. Journal of Statistical Computation and Simulation. 91(8), 1681-1697.

Sun, W., Bindele, H. F., Abebe, A., & Correia, H. E. (2019) General local rank estimation for single-index varying coefficient models. Journal of Statistical Planning and Inference. 202(September 2019):57-79.

Spatiotemporal effects of climate change on population dynamics

An important factor that should be considered in modeling large-scale population dynamics is spatial information. My research has highlighted a need to improve methods for modeling and forecasting of heterogeneous spatiotemporal data. Devising optimized statistical procedures for these types of data will contribute to the explanation and projection of the impacts of anthropogenic processes and climate change on large populations. With information from these forecasting procedures, optimal strategies can be planned to intervene at critical junctions in population and community dynamics. I develop statistical methods for forecasting of spatial data and employ the latest climate models to predict population-level responses to climate change in keystone species. These techniques can also be expanded to determine and quantify the effects of climate change on commercially important marine and terrestrial species, agricultural crop output, and spread of infectious diseases.

Plot of loess smooths of fish CPUE and sea surface temperature
Loess smooths of CPUE and winter SST by management area over time for each of the four species. Solid line is CPUE; dashed line is the coefficient of variation of winter SST; shaded regions are confidence intervals for each smooth.

Correia, H. E., Tveraa,T. , Stien, A., & Yoccoz, N. (2022). Nonlinear spatial and temporal decomposition provides insight for climate change effects on sub-Arctic herbivore populations. Oecologia. 198:889–904.

Buley, R. P., Correia, H. E., Abebe, A., Issa, T. B., & Wilson, A. E. (2021). Predicting microcystin occurrence in freshwater lakes and reservoirs: assessing environmental variables. Inland Waters. 11(3):430-444.

Correia, H. E. (2021). Selecting environmental covariates related to adult groundfish catches and weights in the Gulf of Alaska. Scientific Reports. 11, 9949.

Correia, H. E. & Abebe, A. (2021) Capturing spatiotemporal dynamics of Alaskan groundfish catch using signed-rank estimation for varying coefficient models. Journal of Applied Statistics. 49:8, 2137-2156.

Correia, H. E. (2018) Spatiotemporally explicit model averaging for forecasting of Alaskan groundfish catch. Ecology & Evolution. 8(24):12308–12321.

Exploring multiple paternity across clades

Estimated frequency of multiple paternity across litter sizes ranging from 2 to 10 for mammals
Bayesian MCMC estimated frequency of multiple paternity across litter sizes for mammalian species (red points). The solid red line is the predicted frequency of multiple paternity using a zero-truncated binomial distribution.

Studies of multiple paternity in mammals and other animal species generally report proportion of multiple paternity among litters, mean litter or clutch sizes, and mean number of sires per litter or clutch. I collaborate with a population ecologist and a statistician to estimate a null model for multiple paternity across a variety of animals using Bayesian regression models. We show how these variables can be used to produce an estimate of the probability of reproductive success for a male that has mated with a female. This estimate of male success is more closely aligned to the intensity of sexual selection and is more informative about the mating system that alternative measures, like the proportion of litters with multiple paternity or the number of sires. The probability of success for a mated male can be measured both theoretically and empirically, and gives an estimate of a male’s “confidence of paternity” upon mating.

Dobson, F. S., Correia, H. E., & Abebe, A. (2022+) How much multiple paternity should we expect? A study of birds and contrast with mammals. Submitted.

Correia, H. E., Abebe, A., & Dobson, F. S. (2021) Multiple paternity and the number of offspring: A model reveals two major groups of species. BioEssays. 43(4).

Abebe, A., Correia, H. E., & Dobson, F. S. (2019) Estimating a key parameter of mammalian mating systems: the chance of siring success for a mated male. BioEssays. 41(12).

Dobson, F. S., Abebe, A., Correia, H. E., Kasumo, C., & Zinner, B. (2018) Multiple paternity and number of offspring in mammals. Proceedings of the Royal Society B: Biological Sciences. 285.

Mathematical models

As part of the Masamu Advanced Study Institute (MASI), I collaborate with the mathematical biology working group on two main projects: modeling the effects of climate variability on population dynamics of elephants in Kenya and modeling the effects of stigma on HIV/AIDS prevalence and spread in eastern Africa.

Plot of total, male, and female numbers of elephants in Amboseli, Kenya from 1973 to 1999
Population trends for Amboseli elephants from 1972 to 1999, sex-specific and total population size by year. From Moss, C. J.(2001) in J. Zool., Lond.

Levy, B., Correia, H. E., Chirove, F., Ronoh, M., Abebe, A., Kgosimore, M., Chimbola, O., Machingauta, M. H., Lenhart, S., White, K. A. J. (2021) Modelling the effect of HIV/AIDS stigma on HIV infection dynamics in Kenya. Bulletin of Mathematical Biology. 83(55).

Levy, B., Burton, D., Abebe, A., Kgosimore, M., Lenhart, S., Yakubu, A.-A., Edholm, C., Correia, H. E., Lungu, E., Dobson, F. S., Evans, K., & Washington, M. (2022+) Modeling population dynamics of the Amboseli elephants in Kenya. In prep.

Causal inference in ecology

While causality is a highly explored area of research in biostatistics and epidemiology, it has not been explored extensively for ecological data. Causal analysis has the potential to establish direct causal links and uncover indirect casual links in large ecosystem networks, however many methods used to establish causality require separability, which is not possible to establish in nonlinear systems common in nature. Causal inference has the potential to be exceedingly informative in identifying causes behind population fluctuations linked to climate change and planning interventions to reduce the impacts of climate change on community dynamics. I work to expose and ameliorate weaknesses in causal analysis techniques for ecological data and test the performance of such methods in detecting multiple causal influences in dynamic, nonlinear systems. I also apply such methods to well-studied ecological systems using intuitive model frameworks to encourage wider examination, modification and utilization of causal analysis techniques for ecological data.

Plot of cross correlation as a function of time series length from convergent cross mapping
Unidirectional forcing of process A (red) on process B (black) determined by convergent cross mapping.

Correia, H. E. (2022+) Spatial convergent cross mapping for a marine predator-prey system in the North Pacific. In prep.