Abstract:Complex dynamics are often shown by simple ecological models and have been clearly demonstrated in laboratory and natural systems. Yet many classes of theoretically possible dynamics are still poorly documented in nature. Here we study long-term time-series data of a midge, Tanytarsus gracilentus (Diptera: Chironomidae), in Lake Myvatn, Iceland. The midge undergoes density fluctuations of almost six orders of magnitude. Rather than regular cycles, however, these fluctuations have irregular periods of 4-7 years… Show more
“…If sufficient information exists about a system, a potentially better strategy is to fit system-specific, nonlinear, biologically explicit models in order to investigate the possibility of alternative states (e.g., Ives et al 2008, Schooler et al 2011). This typically requires time series that are rich in dynamical patterns taken from systems that are biologically well-understood.…”
Citation: Ives, A. R., and V. . Detecting dynamical changes in nonlinear time series using locally linear statespace models. Ecosphere 3(6):58. http://dx.doi.org/10.1890/ES11-00347.1Abstract. Interest is growing in methods for predicting and detecting regime shifts-changes in the structure of dynamical processes that cause shifts among alternative stable states. Here, we use locally linear, autoregressive state-space models to statistically identify nonlinear processes that govern the dynamics of time series. We develop both time-varying and threshold models. In time-varying autoregressive models with p time lags, AR( p), and vector autoregressive models for n-dimensional systems of order p ¼ 1, VAR(1), we assume that coefficients vary with time. We can infer an approaching regime shift if the coefficients indicate critical slowing down of the local dynamics of the system. In selfexcited threshold models, we assume that the time series is governed by two autoregressive processes; the state variable switches between them when the time series crosses a threshold value. We use the existence of a statistically significant threshold as an indicator of alternative stable states. All models are fit to data using a state-space form that incorporates measurement error, and maximum likelihood estimation allows for statistically testing alternative hypotheses about the processes governing dynamics. Our model-based approach for forecasting regime shifts and identifying alternative stable states overcomes limitations of other common metric-based approaches and is a useful addition to the toolbox of methods for analyzing nonlinear time series.
“…If sufficient information exists about a system, a potentially better strategy is to fit system-specific, nonlinear, biologically explicit models in order to investigate the possibility of alternative states (e.g., Ives et al 2008, Schooler et al 2011). This typically requires time series that are rich in dynamical patterns taken from systems that are biologically well-understood.…”
Citation: Ives, A. R., and V. . Detecting dynamical changes in nonlinear time series using locally linear statespace models. Ecosphere 3(6):58. http://dx.doi.org/10.1890/ES11-00347.1Abstract. Interest is growing in methods for predicting and detecting regime shifts-changes in the structure of dynamical processes that cause shifts among alternative stable states. Here, we use locally linear, autoregressive state-space models to statistically identify nonlinear processes that govern the dynamics of time series. We develop both time-varying and threshold models. In time-varying autoregressive models with p time lags, AR( p), and vector autoregressive models for n-dimensional systems of order p ¼ 1, VAR(1), we assume that coefficients vary with time. We can infer an approaching regime shift if the coefficients indicate critical slowing down of the local dynamics of the system. In selfexcited threshold models, we assume that the time series is governed by two autoregressive processes; the state variable switches between them when the time series crosses a threshold value. We use the existence of a statistically significant threshold as an indicator of alternative stable states. All models are fit to data using a state-space form that incorporates measurement error, and maximum likelihood estimation allows for statistically testing alternative hypotheses about the processes governing dynamics. Our model-based approach for forecasting regime shifts and identifying alternative stable states overcomes limitations of other common metric-based approaches and is a useful addition to the toolbox of methods for analyzing nonlinear time series.
“…Kendall et al 2005;Ives et al 2008), large-scale changes, such as consumer-resource cycles, are especially revealing about potential effects of rapid contemporary evolution. Several types of natural large-scale ecological dynamics have offered opportunities for studying rapid evolution in the wild, including invasions (e.g.…”
Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or a sexual phase reshuffles the genetic material. When clones differ in traits affecting interspecific interactions, within-species clonal dynamics can have major effects on the population dynamics. We first consider a simple predator-prey system with two prey genotypes, parametrized with data from a well-studied experimental system, and explore how the extent of differences in defence against predation within the prey population determine dynamic stability versus instability of the system. We then explore how increased potential for evolution affects the community dynamics in a more general community model with multiple predator and multiple prey genotypes. These examples illustrate how microevolutionary 'details' that enhance or limit the potential for heritable phenotypic change can have significant effects on contemporaneous community-level dynamics and the persistence and coexistence of species.
“…In addition, anthropogenic disturbances, such as dredging, causing changes in the hydrology of lakes, may reduce algae and detritus inputs to midge habitats, and thus, leading to higher-amplitude fluctuations of midge populations. Consequently, the fish and bird populations that feed on midges were negatively influenced [159]. However, not only do subsidy flux is influenced by hydrology, riparian consumers are also driven by hydrological pressures of the stream because they are required to possess some specific traits.…”
Section: The Role Of Water Availability In Shaping Riparian Trophic Smentioning
Riparian zone provides a variety of resources to organisms, including availability of water and subsidies. Water availability in riparian areas influences species distribution and trophic interaction of terrestrial food webs. Cross-ecosystem subsidies as resource flux of additional energy, nutrients, and materials benefit riparian populations and communities (e.g. plants, spiders, lizards, birds and mammals). However, aquatic ecosystems and riparian zones are prone to anthropogenic disturbances, which change water availability and affect the flux dynamics of cross-system subsidies. Yet, we still lack sufficient empirical studies assessing impacts of disturbances of land use, climate change and invasive species individually and interactively on aquatic and riparian ecosystems through influencing subsidy resource availability. In filling this knowledge gap, we can make more effective efforts to protect and conserve riparian habitats and biodiversity, and maintain riparian ecosystem functioning and services.
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