Browsing by Subject "regime shift"

Now showing 1 - 3 of 3
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    Data and R code supporting "A hidden Markov model for ecosystems exhibiting alternative stable states"
    (2021-01-20) Vitense, Kelsey; Hanson, Mark A; Herwig, Brian R; Zimmer, Kyle D; Fieberg, John R; viten003@umn.edu; Vitense, Kelsey
    This repository contains the data and R code used to conduct the analyses in the article "Using hidden Markov models to inform conservation and management strategies in ecosystems exhibiting alternative stable states" in Journal of Applied Ecology.
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    Data and R code supporting "Uncovering state-dependent relationships in shallow lakes using Bayesian latent variable regression"
    (2017-10-03) Vitense, Kelsey; Hanson, Mark A; Herwig, Brian R; Zimmer, Kyle D; Fieberg, John R; viten003@umn.edu; Vitense, Kelsey
    This repository contains the data and R code used to conduct the analyses in the article "Uncovering state-dependent relationships in shallow lakes using Bayesian latent variable regression" in Ecological Applications.
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    Shallow lakes in Minnesota: Can we predict the good, the bad, and the vulnerable?
    (2018-12) Vitense, Kelsey
    Shallow lakes (i.e., lakes with maximum depth <5 m) provide critical habitat for wildlife and afford recreational opportunities for the public, including fishing and waterfowl hunting. However, many shallow lakes have degraded conditions resulting from anthropogenic disturbances, such as excessive nutrient inputs from land conversion to agriculture and alteration of natural hydrology leading to increased connectivity of surface waters and colonization by disruptive fish species. These degraded shallow lakes experience frequent and sometimes toxic algal blooms, which decrease the utility of lakes to the public. Additionally, reduced water clarity leads to the loss of submerged aquatic vegetation (SAV), which provide an important food source for waterfowl. Mathematical models tell us that the changing conditions of shallow lakes are reflective of alternative stable states, where lakes can be in either a turbid, algae-dominated state with little to no SAV or a clear, healthy state supporting abundant SAV. These states are stable in the sense that lakes will stay in one of the two states due to strong positive feedback loops (e.g., SAV take up nutrients that algae need, release chemicals toxic to algae, and provide a home to zooplankton that eat algae) unless: (1) there is a sudden disturbance to the system that forces the lake into the other state, or (2) a key component of the system slowly but steadily changes until a threshold is reached, at which point the lake “snaps.” The first case is akin to swinging a hammer to break a pencil in half and the second is like bending a pencil with increasing pressure until it breaks. Much is known about the causes of shifts between clear and turbid states in shallow lakes. For instance, we know that increases in phosphorus (P) inputs to lakes (i.e., bending the pencil) and colonization of bottom-feeding fish species (i.e., the hammers) are associated with shifts from the clear to turbid state. Conversely, we have observed that reducing P inputs and eradicating problematic species can sometimes, but not always, cause the reverse shift back to the clear state. Mathematical models have helped us understand that the critical P threshold at which a lake transitions from the clear to turbid state is not the same as the critical P threshold at which the lake transitions from the turbid state back to the clear state. That is, once a lake transitions to the turbid state, P must be reduced far below its previous level in the clear state before SAV reappears and restores water clarity. This phenomenon makes shallow lake restoration challenging, and efforts to force lakes into the clear state from the turbid state frequently fail or have only short-term effects. Although we have a deep qualitative understanding of the mechanisms driving these shifts, we lack essential quantitative knowledge to improve our ability to manage shallow lakes. For instance, there has not previously been a formal statistical framework grounded in mathematical theory for alternative stable states to classify the state of a lake, nor to estimate critical P thresholds. We lack models to quantify the vulnerability of lakes to state shifts given various risk factors, including proximity to P thresholds and the abundance and composition of fish populations. And we do not have a way to quantitatively prioritize lakes for management, especially without expending significant resources to physically visit and sample lakes. For this dissertation, I partnered with researchers at the Minnesota Department of Natural Resources and the University of St. Thomas who collected a wealth of data on approximately 130 lakes around Minnesota to address these knowledge gaps. I developed methods to accurately classify lake states, identify key drivers of state transitions, and quantify state transition risk based on these drivers. In Chapter 1, I develop a modeling framework that provides the foundation for the approaches I use in subsequent chapters. I use relative abundances of algae and SAV, as well as differing relationships between P and algal abundance within each state, to classify lake states as clear or turbid. The model explicitly incorporates the structure of a cusp catastrophe bifurcation diagram to estimate critical P thresholds where shallow lakes transition from the clear to turbid state and vice-versa. Using data simulated from a theoretical model describing shallow lake processes, I show that not only does this framework classify lake states and estimate critical P thresholds with high accuracy, it also performs better than existing methods. Chapter 2 uses P threshold estimates from Chapter 1 to provide a way to categorize lakes that has direct management implications: lakes that have low enough P levels such that only the clear state is possible vs. lakes with P levels where the lake may exist in the turbid state. I developed a model to predict the category of a lake using only geospatial predictor variables, such as the amount of agriculture in a lake’s watershed. This model provides a first step for managers to prioritize lakes for management and future sampling efforts without visiting lakes to collect water samples or conduct plant surveys. In Chapter 3, I extend the modeling framework in Chapter 1 to allow for temporal dynamics and estimation of state transition probabilities. I assess how transition risk depends on both resilience variables (e.g., current nutrient levels) and perturbation variables (e.g., change in fish biomass). The model identifies top predictors and combinations of predictors for anticipating state transitions, informing essential data needs for future lake surveys. Finally, Chapter 4 describes the development of an R shiny application that allows users to input lake data and receive a predicted state classification and estimate of transition risk based on the modeling work of Chapter 3. This tool can be used by shallow lake managers to help prioritize lakes for management actions based on estimated transition risk according to observed or hypothetical changes to nutrient levels and biological communities, including fluctuations in fish abundance.