Upcoming Seminar
- Thursday, February 19, 2026
- 9:30-10:30 am · MSB 318
- Jason Harmon will speak on “Impact of varying dispersal in metapopulation models: A new type of Sherman-Morrison formula“
- Abstract: For population and disease distributed across patches in heterogeneous environments, meta-population models are a useful tool. It is of particular interest whether populations and diseases will persist depending on dispersal rates and network connectivity. In particular, we investigate how changes in network structure and dispersal intensity impact the long-term population growth rate and determine the population persistence threshold. The population growth rate can be found via the largest real part of the eigenvalues of the Jacobian. This eigenvalue can be approximated using an expansion in terms of the Group Inverse. The Group Inverse is a generalized inverse for a specific class of matrices including the discrete Laplacian. We propose a Sherman-Morrison type formula that can be used to find an updated group Inverse for varying dispersal. Using this formula, we explore how changes in dispersal affect the population growth rate.
To be added in our mailing list, please send a request to shuai@ucf.edu
Previous Seminars
- Thursday, February 12, 2026, 9:30–10:30 am · MSB 318
- Poroshat Yazdanbakhsh: “From Slow to Fast Dispersal: Impacts on Species Persistence and Infectious Disease Invasion“
- Abstract: In heterogeneous environments, populations of species and infectious diseases are often distributed across patches with different environmental conditions that are connected through dispersal. As dispersal can play a crucial role in determining whether populations and pathogens persist or go extinct in such spatially structured systems, understanding how movement among patches interacts with environmental heterogeneity is a central problem in ecology and epidemiology. In this talk, we use analytical tools from perturbation theory and group inverse to investigate how slow and fast dispersal influence population dynamics. Our analysis highlights the combined effect of environmental heterogeneity, network connectivity, and dispersal rates.
- Thursday, February 5, 2026, 9:30–10:30 am · MSB 318
- Christen Fleming: “Spatial Distributions for Animal Movement Processes“
- Abstract: Spatial distributions represent a relative frequency at a specified location in two dimensions. Here, I cover a number of biologically relevant spatial distributions, and related concepts, that derive from movement processes—including home ranges, territories, and corridors. I pay special attention to the frequent conflation between prediction and estimation and the commonly misapplied biological concepts of “space use” and “utilization”; and I delineate stronger linkages between important biological concepts and well-defined mathematical objects.
- Thursday, January 29, 2026, 9:30–10:30 am · MSB 318
- B Sagar: “Dynamics of a two-stage epidemiological model with post-infection mortality and transmission heterogeneity“
- Abstract: Many diseases naturally progress from an initial mild infectious phase to a more severe stage (e.g., Influenza and COVID-19). This motivates us to formulate a two-stage epidemiological model that incorporates key post-infection features, including reinfection and post-infection mortality (PIM). The model emphasizes the role of transmission heterogeneity in shaping disease dynamics, influencing both endemic levels and oscillatory behaviors. Numerical simulations show that late-stage hyper-infectivity leads to higher endemic infection levels with long-period oscillations, while early-stage hyper-infectivity results in lower infection levels with shorter-period oscillations.
- Wednesday, November 5, 2025, 1:00–2:00 pm · MSB 110
- Christen Fleming: “Kernel Density Estimation in Spatial Ecology”
- Abstract: Kernel Density Estimation (KDE) is a cornerstone technique in statistics for estimating a probability density function when its parameterized form is unknown. KDE is widely used in spatial ecology for calculating animal home ranges and species distributions where the assumptions behind conventional KDE are often pushed beyond their limits. In this seminar I will present over a decade of research that now allows for accurate kernel density estimates to be computed from irregularly sampled times-series data that are sampled from heterogeneous populations.
- Wednesday, October 1, 2025, 1:00–2:00 pm · MSB 110
- Erika Lin: “Improving statistical methods for wildlife corridor estimation”
- Nozomu Hirama: “Methods for quantifying nocturnality and human impacts using animal tracking data”
- Abstracts
Methods for quantifying nocturnality and human impacts using animal tracking data
Diel activity patterns often reflect an animal’s adaptations and strategies to optimize their fitness. However, these patterns can be disturbed by human influence, potentially forcing individuals to be active during less optimal times of the day. To better understand such effects, we introduce a new method for estimating nocturnality from tracking data, along with a new metric of the overlap and distance between the home range and Human Footprint Index (HFI). First, we have developed a continuous-time movement model (ctmm) that switches between high and low levels of movement according to solar time. Using this model, we can accurately estimate the proportion of nighttime activity from irregularly sampled tracking data. Second, we have developed a novel approach to quantifying HFI levels, or other index, both within an individual’s home range and in the proximal surrounding areas by using log expectation values. Importantly, this metric increases with increasing disturbance within the home range, with increasing disturbance in the neighborhood of the home range, and with increasing proximity to said disturbances, which makes this a suitable predictor for examining any response to human influence. With our new metrics, we explore the impacts of human disturbance on nocturnality for the common raccoon (Procyon lotor), coyote (Canis latrans), and Temminck’s ground pangolin (Smutsia temminckii). Our work is implemented in the ctmm R package, providing accessible tools to better inform conservation and management in an increasingly anthropized environment.
Improving statistical methods for wildlife corridor estimation
Habitat connectivity is essential to conserving biodiversity, by allowing animals to search across landscapes for resources and mates. This is particularly important for migration and dispersal, which can be impeded by human activities that degrade and fragment habitats. To maintain connectivity, it is imperative that we identify wildlife corridors—areas where animals traverse frequently to move between suitable environments. Traditionally, connectivity has been modeled via two main methods: resistance circuit models and Brownian bridges. However, these methods do not target a “well-calibrated” probabilistic corridor distribution—i.e., where 95% of animals pass through the 95% cross-section. We have developed a new statistical method for corridor estimation, using cross-sectional kernel density estimation (KDE) to model corridors as “range distributions” from animal tracking data. We define the corridor by the distribution of repeated passages between two areas in a landscape. To ensure that this method is robust and offers improvements, we conducted a comparative sensitivity analysis across parameters that impact performance, such as sampling frequency and passage count, using GPS-tracked mule deer (Odocoileus hemionus) and jaguars (Panthera onca). We found that cross-sectional KDE is insensitive to the sampling frequency and produces consistent distribution estimates regardless of the location-recording interval, thus demonstrating that our method provides more rigorous estimates of corridor space needed by migrating animals even with few tracking points available. Our research, implemented in the ctmm R package, contributes a novel statistical tool that ecologists can directly apply to conservation management, through designating new wildlife corridors and evaluating the impact of existing ones.