
Robin Decker
Climatedriven habitat shifts pose challenges for dispersallimited, slowgrowing, latematuring taxa. Older trees are often the most reproductive individuals in the population, but as habitats shift, these individuals are left behind in the trailing range edge, generating â€œzombie forestsâ€? that may persist long after the habitat has shifted. Are these zombie forests vestiges of ecosystems past or do they play an ecological role? I develop a spatially explicit, stagestructured model of tree populations occupying a shifting habitat patch to understand how zombie forests affect tree population persistence in the face of climate change. I show that zombie forests, which experience no recruitment at the trailing patch edge, help the entire population survive high rates of climate change by dispersing seeds to the core population. Over many generations, most of the core population descends from the zombie forest. These results suggest that preserving zombie forests may increase forest persistence in the face of rapid climate change.

Mark Lewis
Classical population dynamics problems assume constant unchanging environments. However, realistic environments fluctuate in both space and time. My lecture will focus on the analysis of population dynamics in environments that shift spatially, due either to advective flow (eg., river population dynamics) or to changing environmental conditions (eg., climate change). The emphasis will be on the analysis of nonlinear advectiondiffusionreaction equations and related models in the case where there is strong advection and environments are heterogeneous. I will use methods of spreading speed analysis, net reproductive rate and inside dynamics to understand qualitative outcomes. Applications will be made to river populations in one and twodimensions and to the genetic structure of populations subject to climate change.

Bo Zhang
Understanding the mechanisms that promote species coexistence is a central topic in ecology. Predicting coexistence in heterogeneous environments where populations are linked by dispersal is a challenge that has attracted attention of ecologists. A particular body of theory, based on LotkaVolterralike equations, has focused on the effects of different relative dispersal rates in the absence of other differences in competing species, and has predicted that the slower disperser always outcompetes the faster one in environments where the limiting resources are heterogeneously distributed. However, this theory has never been rigorously tested empirically, and has generally only considered random diffusion. Here, we extended previous theory to include exploitable resources and an additional component of directed movement, proving qualitatively novel results, which we tested experimentally using laboratory populations of C. elegans. We revealed, both theoretically and emperically, that stable coexistence can occur when two competing species have identical directed components but different diffusive components to their movement. Our results advance understanding of coexistence theory and has important ecological implications, such as the essential of individuals obtaining clues of neighboring environments, to determine where to disperse in changing environments.

Chris Heggerud
Cyanobacterial (CB) blooms are becoming a global concern due to the increasing prevalence of eutrophication. The dependence of CB dynamics on phosphorus and light inputs is modeled via a stoichiometric approach. The dynamics occur in distinct phases that allow us to make use of multiple timescale analysis to uncover the driving mechanisms of each phase. As a result we are able to approximate the length of time a bloom persists. We then couple the CB model to a socioeconomic model governing the anthropogenic nutrient inputs. We assume that the human population is made up of cooperators and defectors and that each strategy has an associated cost dependent on social pressure and norms, concern for CB, and effort. We find that the human population at a single lake exhibits bistability. Further, in considering a network of lakes the level of cooperation is highly dependent on social norms.

Bethany Fowler
Picophytoplankton are the most abundant primary producers in the ocean. Knowledge of their community dynamics is key to understanding their role in marine food webs and global biogeochemical cycles. I will present on the analysis of an ongoing 16year time series from the Marthaâ€™s Vineyard Coastal Observatory. We use a combination of autonomous flow cytometry and sizestructured modeling to estimate taxonspecific vital rates for this picophytoplankton community. The results indicate that the picoeukaryotes reproduce and are lost much more rapidly than cyanobacteria at the same location. The picoeukaryotes appear to be a preferred prey item of the micrograzer community and so contribute more to the regionâ€™s primary productivity than would be inferred from their abundance alone. This work improves our understanding of the economically important Northeast US Shelf ecosystem and provides insight into the response of phytoplankton communities to environmental change across a range of timescales.

Suzanne Lenhart
Optimal control techniques of ordinary and partial differential equations will be introduced to consider management strategies for two different aquatic populations. In the first example, managing invasive species in rivers can be assisted by adjustment of flow rates. Control of a flow rate in a partial differential equation model for a population in a river will be used to keep the population from moving upstream. The second example represents a food chain on the Turkish coast of the Black Sea. Using data from the anchovy landings in Turkey, optimal control of the harvesting rate of the anchovy population in a system of three ordinary differential equations (anchovy, jellyfish and zooplankton) will give management strategies.

Alan Hastings
A challenge for ecological modeling is to focus on appropriate time scales. A caricature of classical ecological theory is that it is typically based on the asymptotic behavior of deterministic systems with constant parameters. Yet answering the questions of interest for many real ecological systems requires approaches that use none of these assumptions. Work over recent decades has focused on just such approaches, with some of the most recent work focusing on transient dynamics and time varying parameters, which raises substantial mathematical challenges. I will give both ecological examples where these ideas are essential and describe some recent work in this area.

Priyanga Amarasekare
I want to argue that a complete understanding of life on earth requires that we look above the ecological level, towards evolution, and below, towards chemistry. The ecological patterns we see today are both the outcome of past evolution and the material of future evolution. They are also the result of the chemical reactions  from DNA synthesis to enzyme kinetics  that occur within individuals. If we are to understand how abiotic factors, and perturbations thereof, influence ecological patterns, we need to first learn how they affect the biochemical processes underlying phenotypes, and how these phenotypic effects translate into population and community patterns. I will resent theory, data, and some conjectures on how temperature, and climate warming, influence the biochemistry, ecology, and evolution of ectothermic organisms.

Yuan Lou
We will discuss several reactiondiffusion models for the spread of disease in heterogeneous environment. The first is an SEIR model in spatially heterogeneous environment, in which we investigate the effect of movement of exposed and infected populations. This is a joint work with Pengfei Song and Yanni Xiao. The second is an SIS model in spatially heterogeneous and timeperiodic environment, and our focus is on the effect of frequency and dispersal. This is a joint work with Shuang Liu.

Sarah Bogen, Sarah Bogen
As climate warms, populations may adapt by shifting poleward to track suitable habitat. The speed of such shifts is influenced by demographic characteristics, such as the species' survival and reproduction rates, and dispersal characteristics, such as the species' mean dispersal distance and dispersal kernel shape. Understanding how temperature influences demography and dispersal is important for understanding how a population will shift in response to climate change. Here, we present an approach for incorporating temperature into mechanistic models for population spread considering ragweed (Ambrosia artemisiiflia) as an empirical example. Ragweed is a strict annual with a longlived seed bank that is of particular interest due to its roles as an allergen and a crop competitor. We propose a stagestructured integrodifference equation model with temperaturedependent demography and dispersal parameters. We assume that survival, growth, and reproduction respond to temperature according to a betadistribution and that the dispersal kernel follows a Laplace distribution with a mean that increases with the size of reproductive adults. Future work will analyze the impact of a variety of temperature variation patterns on population spreading speed in order to assess ability to track suitable habitat under global change.

Noelle Beckman
In response to global change, species must adapt to environmental changes or move to track suitable habitat in order to persist. Interdisciplinary approaches can help us understand and predict a populationâ€™s ability to track changing environments due to global warming and habitat loss. In response to global warming, species shift their ranges poleward to track suitable habitat for growth, survival, and reproduction. Meanwhile, habitat loss results in the loss of both species and functional diversity. We can predict the ability of populations to persist and track suitable habitat in response to different global change scenarios by parameterizing mathematical models with data on dispersal and demography. Data on dispersal and demography are intensive to collect; hence, fundamental research on population dynamics and spread often focus on a few wellparameterized case studies. We can harness the growing availability and accessibility of data in combination with spatial population models to estimate the vulnerability of species to global warming and habitat loss. While data are becoming more available and accessible, the joint data on dispersal and demography tend to be sparse across species. I will discuss several novel approaches to tackle these limitations by synthesizing advances in mathematical models and publiclyavailable data.

Ensheng Weng
Terrestrial vegetation, as a key component of the Earth system, defines the boundary conditions of land surface for the exchange of energy, momentum, and water vapor between land and atmosphere, regulates longterm atmospheric CO2 concentration, and thus deeply shapes Earthâ€™s climate dynamics. Dynamic global vegetation models (DGVMs) are normally used in Earth system models (ESMs) to simulate plant physiological activities, vegetation dynamics, ecosystem biogeochemical cycles, and land surface characteristics for atmospheric components. DGVMs bin vegetation into a small number of plant functional types (PFTs) and predict the geographic distribution of PFTs by bioclimatic and physiological rules. These models are able to track ecosystem carbon and/or nitrogen cycles as pools and fluxes, and predict their feedbacks on climate systems at large spatial scales. However, these models are unable to predict transient vegetation compositional and transient changes because of underrepresentation of functional diversity and lack of detailed demographic processes. Vegetation demographic models (VDMs) are thus developed to explicitly simulate demographic processes and individualbased competition for light and soil resources. In VDMs, the stochastic birth, growth, and mortality processes replace the deterministic carbon processes that are in current DGVMs, potentially altering the representation of vegetation dynamics and carbon cycle. The inclusion of individualbased competition effectively implements adaptive dynamics â€“ a method used in evolutionary game theoretic analysis to determine the best fit strategy in a given context â€“ into ESMs and thus significantly increases the functional diversity of PFTs. In this presentation, I will summarize our studies on the modeling of stochastic disturbance effects on ecosystem carbon dynamics, vegetation demographic processes, and competitively dominant plant traits to show how the fundamental plant physiological and ecological processes are represented in vegetation models and thus significantly increase model predictive skills. With the case studies, I will show how the predictions of vegetation dynamics and carbon cycle are improved by exploring plant competitively dominant strategy in response to elevated CO2, variations of soil nitrogen and precipitation regimes. I will also discuss the possible approaches of bridging the gaps between vegetation modeling and conventional ecological studies for improving Earth system modeling.

Wasiur KhudaBukhsh, Wasiur Rahman Kuda Bukhsh
In many biological systems, chemical reactions or changes in a physical state are assumed to occur instantaneously. For describing the dynamics of those systems, Markov models that require exponentially distributed interevent times have been used widely. However, some biophysical processes such as gene transcription and translation are known to have a significant gap between the initiation and the completion of the processes, which renders the usual assumption of exponential distribution untenable. In this talk, we consider relaxing this assumption by incorporating agedependent random time delays into the system dynamics. We do so by constructing a measurevalued Markov process on a more abstract state space, which allows us to keep track of the "ages" of molecules participating in a chemical reaction. We study the largevolume limit of such agestructured systems. We show that, when appropriately scaled, the stochastic system can be approximated by a system of Partial Differential Equations (PDEs) in the largevolume limit, as opposed to Ordinary Differential Equations (ODEs) in the classical theory. We show how the limiting PDE system can be used for the purpose of further model reductions and for devising efficient simulation algorithms.

Junyi Guo
One of the common mathematical topics of Earth and biological sciences is the treatment of data of global coverage. In many instances, data of global coverage of a quantity, e.g., the atmospheric pressure in Earth science or the density of population of a species in bioscience, are values of the quantity as a function defined on the Earthâ€™s surface. Therefore, the mathematics behind is the representation of functions defined on a sphere. The most primitive representation of the function is to use its values over an array of points, e.g., over the intersection points of parallels of equal latitude intervals and meridians of equal longitude intervals, which are referred to as grid values. However, there should be a need of additional information in the interpretation of the data in the form of grid values: How large area the data are representative? If the data represent the averages of the quantity in some way within an area of, say, 50 km around the grid points, the data are said to have a resolution of 100 km (half wavelength). It is evident that data of higher resolution (with smaller wavelength) can be converted to data of lower resolution (with larger wavelength), but the reverse cannot be done. In this talk, we convert the data into a series and then back, so that lower resolution data can be obtained by truncating the series of the higher resolution data. Two kinds of series on a sphere will be discussed. One is the Cartesian product of a cosine series over the colatitude and a Fourier series over the longitude, and the other is the spherical harmonic series. Each kind of series has its characteristic with advantage and disadvantage for a specific application. Take for example a grid of 1âˆ˜Ã—1âˆ˜, i.e., with equal intervals of 1âˆ˜ in both the latitude and longitude. We have 180Ã—360 grid data (taking 180 grid points over the latitude). We can define a cosineFourier series with the same number of coefficients, and the grid data can be exactly recovered from the series. However, if we use the spherical harmonics, we can only expand to degree and order 179, which has 180Ã—180 coefficients, meaning that the 180Ã—360 grid data cannot be necessarily exactly recovered from the series. The resolution of the cosineFourier series is expressed as an interval in latitude and an interval in longitude; In terms of distance over the sphere, the longitudinal resolution (the length of the parallel in 1âˆ˜ longitude interval) at latitude Â±60âˆ˜ is half of that over the equator (the length of the equator in 1âˆ˜ longitude interval). However, the resolution of the spherical harmonic series is homogeneous and isotropic all over the sphere in terms of distance. The choice of one over the other should be done based on the characteristic of the application.

Karianne Bergen
Many observational studies in the Earth sciences rely on passive sensors to detect and monitor the events or processes of interest. For example, earthquake detection  the extraction of weak earthquake signals from continuous waveform data recorded by sensors in a seismic network â€“ is a fundamental and challenging task in earthquake seismology. These longduration, continuously recorded sensor data require modern, datadriven analysis techniques that are capable of scaling to massive data sets.
In this talk, I will describe the data science challenges associated with event detection in large sensor data sets, focusing on earthquake detection in seismic data. I will discuss how new algorithmic advances in â€œbig dataâ€? and machine learning (ML) are helping to advance the stateoftheart in earthquake monitoring. As a case study, I will present Fingerprint and Similarity Thresholding (FAST), a novel method for largescale earthquake detection inspired by audio recognition technology (Yoon et al, 2015). I will draw parallels between developments in ML for geophysics and emerging research in bio and ecoacoustics.