This archive includes the scripts and data used to run and analyze the simulations involved in th... more This archive includes the scripts and data used to run and analyze the simulations involved in the manuscript, <i>"Interaction network structure and spatial patterns influence invasiveness and invasibility in a stochastic model of plant communities"</i> by Nicole L. Kinlock and Stephan B. Munch.<br><b>Please see the README file for a detailed guide.</b><br>
Model uncertainty and limited data are fundamental challenges to robust management of human inter... more Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state space where such a tipping point might exist. We illustrate how a Bayesian non-parametric approach using a Gaussian process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a stochastic dynamic programming framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favours models without tipping points, leading to harvest policies that guarantee extinction. The Gaussian process dynamic programming (GPDP) performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, as it does not underestimate the uncertainty outside of the observed data
Chaotic dynamics are thought to be rare in natural populations, but this may be due to methodolog... more Chaotic dynamics are thought to be rare in natural populations, but this may be due to methodological and data limitations, rather than the inherent stability of ecosystems. Following extensive simulation testing, we applied multiple chaos detection methods to a global database of 175 population time series and found evidence for chaos in >30%. In contrast, fitting traditional one-dimensional models identified <10% as chaotic. Chaos was most prevalent among plankton and insects and least among birds and mammals. Lyapunov exponents declined with generation time and scaled as the -1/6 power of mass among chaotic populations. These results demonstrate that chaos is not rare in natural populations, indicating that there may be intrinsic limits to ecological forecasting and cautioning against the use of steady-state approaches to conservation and management.
Biological and Chemical Oceanography Data Management Office, 2017
Dataset: Local adaptationOffspring growth rate from experiments testing for local adaptation in t... more Dataset: Local adaptationOffspring growth rate from experiments testing for local adaptation in thermal TGP For a complete list of measurements, refer to the full dataset description in the supplemental file 'Dataset_description.pdf'. The most current version of this dataset is available at: https://www.bco-dmo.org/dataset/704653NSF Division of Ocean Sciences (NSF OCE) OCE-113048
Complex nonlinear dynamics are ubiquitous in marine ecology. Empirical dynamic modelling can be u... more Complex nonlinear dynamics are ubiquitous in marine ecology. Empirical dynamic modelling can be used to infer ecosystem dynamics and species interactions while making minimal assumptions. Although there is growing enthusiasm for applying these methods, the background required to understand them is not typically part of contemporary marine ecology curricula, leading to numerous questions and potential misunderstanding. In this study, we provide a brief overview of empirical dynamic modelling, followed by answers to the ten most frequently asked questions about nonlinear dynamics and nonlinear forecasting.
Compensatory or catch-up growth (CG) is widely observed following periods of resource deprivation... more Compensatory or catch-up growth (CG) is widely observed following periods of resource deprivation. Because of this commonness, it is generally assumed that compensatory growth is adaptive, but most theory to date has explicitly ignored considerations of fitness. Following a period of deprivation, when resources become plentiful again, individuals may not respond at all and continue on a "normal" trajectory from a smaller size at age, may exhibit faster-than-normal growth immediately following the end of the period, or may adopt a growth strategy that involves faster-than-normal growth at some later time. Compensating individuals may also overtake control individuals who have been growing normally throughout. We hypothesize that the key to understanding CG is that growth leads to the accumulation of damage at the cellular level that is expressed (and thus must be modeled) at the level of the organism. We show that a life-history model incorporating the mortality consequences of both size and damage provides a framework for understanding compensatory growth. We use the theory to classify physiological and life-history characteristics for which CG is predicted to be the optimal response to deprivation.
Fishery management plans ignore the potential for evolutionary change in harvestable biomass. We ... more Fishery management plans ignore the potential for evolutionary change in harvestable biomass. We subjected populations of an exploited fish ( Menidia menidia ) to large, small, or random size-selective harvest of adults over four generations. Harvested biomass evolved rapidly in directions counter to the size-dependent force of fishing mortality. Large-harvested populations initially produced the highest catch but quickly evolved a lower yield than controls. Small-harvested populations did the reverse. These shifts were caused by selection of genotypes with slower or faster rates of growth. Management tools that preserve natural genetic variation are necessary for long-term sustainable yield.
Proceedings of the National Academy of Sciences, 2006
An important task in evolutionary biodemography is to determine the schedule of survival and repr... more An important task in evolutionary biodemography is to determine the schedule of survival and reproduction as the outcome of natural selection acting on life histories. We do this by using a model in which the state of the organism is characterized by mass and accumulated damage, both of which are affected by activity and which affect the rate of mortality. Focusing on growth during the juvenile period, we determine the level of activity that maximizes reproductive value. Given this, we are able to project forward and determine the trajectory of mortality for an individual following the optimal life history, given the physiological and reproductive parameters. We show that there are two main classes of juvenile mortality trajectories: U-shaped (such as recently reported for prereproductive humans) and steadily declining and we are able to connect the shape of the mortality trajectory with the physiological and reproductive parameters characterizing the life history. Our work shows th...
Recruitment dynamics are complicated in species in which multiple cohorts of young-of-the-year (Y... more Recruitment dynamics are complicated in species in which multiple cohorts of young-of-the-year (YOY) are produced each year. Each summer, two cohorts of YOY bluefish (Pomatomus saltatrix), representing fish spawned in spring and summer, recruit to Mid-Atlantic Bight estuaries, but little is known about their interannual variability, environmental forcing, and relative contributions to later life stages. We addressed these questions by examining the distribution and abundance of YOY on the continental shelf of the US east coast in autumn from 1973 through 1995. Abundance on the continental shelf increased in autumn owing to emigration from estuaries. We found clear evidence of two cohorts in autumn length-frequency distributions in most years and used this information to construct cohort-specific indices of abundance, which were then compared with relevant environmental variables. Spring-spawned fish dominated the catch in 20 of the years examined. The summer cohort dominated only in 1992. The abundance of the two cohorts was positively correlated, rejecting the hypothesis that dominance of the spring cohort is the result of cannibalism on the summer cohort. Spring cohort abundance was not correlated with either shelf warming-rate or warm-core ring streamer activity. A strong relationship was found between winds in April and May and the abundance of spring-spawned bluefish, possibly indicating that wind-driven surface flow aids the transport of larvae and/or juveniles across the shelf-slope region.
Several recent studies have demonstrated that rapid growth early in life leads to decreased physi... more Several recent studies have demonstrated that rapid growth early in life leads to decreased physiological performance. Nearly all involved experiments over short time periods (Ͻ1 day) to control for potentially confounding effects of size. This approach, however, neglects the benefits an individual accrues by growing. The net effect of growth can only be evaluated over a longer interval in which rapidly growing individuals are allowed the time required to attain the expected benefits of large size. We used two populations of Menidia menidia with disparate intrinsic growth rates to address this issue. We compared growth and survivorship among populations subject to predation in mesocosms under ambient light and temperature conditions for a period of up to 30 days to address two questions: Do the growth rates of fish in these populations respond differently to the presence of predators? Is the previously demonstrated survival cost of growth counterbalanced by the benefits of increased size? We found that growth was insensitive to predation risk: neither population appeared to modify growth rates in response to predation levels. Moreover, the fast-growing population suffered significantly higher mortality throughout the trials despite being 40% larger than the slow-growing population at the experiment's end. These results confirm that the costs of rapid growth extend over prolonged intervals and are not ameliorated merely by the attainment of large size.
Analyses of changes in size distributions over time frequently suggest that mortality rates depen... more Analyses of changes in size distributions over time frequently suggest that mortality rates depend on body size. Such observations, however, are probably confounded with changes in size due to growth. We describe a parametric method by which the size dependence of both mortality and growth may simultaneously be inferred from pairs of size distributions collected at different times. The method is tested in a Monte Carlo study and found to have sampling properties similar to those of other methods that require more data. Survival of the first winter of life appears to be size dependent in a diverse array of taxa, although few prior studies have accounted for growth. Analysis of sizes of Menidia menidia (Atlantic silverside) from three different latitudes revealed that changes in size distributions through winter resulted from growth in southern populations and mortality in the north. Winter mortality was better described by a power function of size than an exponential. Allometric exponents increased with latitude and were greater than predicted from metabolic-or starvation-based models. The steepness of the estimated survivorship curves imply that winter mortality in M. menidia is more consistent with a threshold effect perhaps attributable to offshore migration.
State-space estimation methods are increasingly used in ecology to estimate productivity and abun... more State-space estimation methods are increasingly used in ecology to estimate productivity and abundance of natural populations while accounting for variability in both population dynamics and measurement processes. However, functional forms for population dynamics and density dependence often will not match the true biological process, and this may degrade the performance of state-space methods. We therefore developed a Bayesian semiparametric state-space model, which uses a Gaussian process (GP) to approximate the population growth function. This offers two benefits for population modeling. First, it allows data to update a specified ''prior'' on the population growth function, while reverting to this prior when data are uninformative. Second, it allows variability in population dynamics to be decomposed into random errors around the population growth function (''process error'') and errors due to the mismatch between the specified prior and estimated growth function (''model error''). We used simulation modeling to illustrate the utility of GP methods in state-space population dynamics models. Results confirmed that the GP model performs similarly to a conventional state-space model when either (1) the prior matches the true process or (2) data are relatively uninformative. However, GP methods improve estimates of the population growth function when the function is misspecified. Results also demonstrated that the estimated magnitude of ''model error'' can be used to distinguish cases of model misspecification. We conclude with a discussion of the prospects for GP methods in other state-space models, including age and length-structured, meta-analytic, and individualmovement models.
Running title: Intrinsic predictability & forecasting 2 3 Title: The intrinsic predictability of ... more Running title: Intrinsic predictability & forecasting 2 3 Title: The intrinsic predictability of 4 ecological time series and its 5 potential to guide forecasting 6 7 Frank Pennekamp1,§, *, Alison C. Iles2,5,6 §, Joshua Garland3, Georgina Brennan4, Ulrich 8 Brose5,6, Ursula Gaedke7, Ute Jacob8, Pavel Kratina9, Blake Matthews10, Stephan Munch11, 12, 9 Mark Novak2, Gian Marco Palamara1,13, Björn C. Rall5,6, Benjamin Rosenbaum5,6, Andrea 10 Tabi1, Colette Ward1, Richard Williams14, Hao Ye15, Owen L. Petchey1 11 12 § F. Pennekamp and A. Iles contributed equally to this work 13
We develop a model for Bayesian selection in high order Markov chains through an extension of the... more We develop a model for Bayesian selection in high order Markov chains through an extension of the mixture transition distribution of Raftery (1985). We demonstrate two uses for the model: parsimonious approximation of high order dynamics by mixing lower order transition models, and model selection through over-specification and shrinkage via priors for sparse probability vectors. We discuss properties of the model and demonstrate its utility with simulation studies. We further apply the model to a data analysis from the high-order Markov chain literature and a novel application to pink salmon abundance time series.
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all ... more Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables. Here we provide an algebraic approach to delay embedding that permits explicit approximation of error. We also provide the asymptotic dependence of the first order approximation error on the system size. More importantly, this formulation of delay embedding can be directly implemented using a Recurrent Neural Network (RNN). This observation expands the interpretability of both delay embedding and RNN and facilitates principled incorporation of structure and other constraints into these approaches.
This archive includes the scripts and data used to run and analyze the simulations involved in th... more This archive includes the scripts and data used to run and analyze the simulations involved in the manuscript, <i>"Interaction network structure and spatial patterns influence invasiveness and invasibility in a stochastic model of plant communities"</i> by Nicole L. Kinlock and Stephan B. Munch.<br><b>Please see the README file for a detailed guide.</b><br>
Model uncertainty and limited data are fundamental challenges to robust management of human inter... more Model uncertainty and limited data are fundamental challenges to robust management of human intervention in a natural system. These challenges are acutely highlighted by concerns that many ecological systems may contain tipping points, such as Allee population sizes. Before a collapse, we do not know where the tipping points lie, if they exist at all. Hence, we know neither a complete model of the system dynamics nor do we have access to data in some large region of state space where such a tipping point might exist. We illustrate how a Bayesian non-parametric approach using a Gaussian process (GP) prior provides a flexible representation of this inherent uncertainty. We embed GPs in a stochastic dynamic programming framework in order to make robust management predictions with both model uncertainty and limited data. We use simulations to evaluate this approach as compared with the standard approach of using model selection to choose from a set of candidate models. We find that model selection erroneously favours models without tipping points, leading to harvest policies that guarantee extinction. The Gaussian process dynamic programming (GPDP) performs nearly as well as the true model and significantly outperforms standard approaches. We illustrate this using examples of simulated single-species dynamics, where the standard model selection approach should be most effective and find that it still fails to account for uncertainty appropriately and leads to population crashes, while management based on the GPDP does not, as it does not underestimate the uncertainty outside of the observed data
Chaotic dynamics are thought to be rare in natural populations, but this may be due to methodolog... more Chaotic dynamics are thought to be rare in natural populations, but this may be due to methodological and data limitations, rather than the inherent stability of ecosystems. Following extensive simulation testing, we applied multiple chaos detection methods to a global database of 175 population time series and found evidence for chaos in >30%. In contrast, fitting traditional one-dimensional models identified <10% as chaotic. Chaos was most prevalent among plankton and insects and least among birds and mammals. Lyapunov exponents declined with generation time and scaled as the -1/6 power of mass among chaotic populations. These results demonstrate that chaos is not rare in natural populations, indicating that there may be intrinsic limits to ecological forecasting and cautioning against the use of steady-state approaches to conservation and management.
Biological and Chemical Oceanography Data Management Office, 2017
Dataset: Local adaptationOffspring growth rate from experiments testing for local adaptation in t... more Dataset: Local adaptationOffspring growth rate from experiments testing for local adaptation in thermal TGP For a complete list of measurements, refer to the full dataset description in the supplemental file 'Dataset_description.pdf'. The most current version of this dataset is available at: https://www.bco-dmo.org/dataset/704653NSF Division of Ocean Sciences (NSF OCE) OCE-113048
Complex nonlinear dynamics are ubiquitous in marine ecology. Empirical dynamic modelling can be u... more Complex nonlinear dynamics are ubiquitous in marine ecology. Empirical dynamic modelling can be used to infer ecosystem dynamics and species interactions while making minimal assumptions. Although there is growing enthusiasm for applying these methods, the background required to understand them is not typically part of contemporary marine ecology curricula, leading to numerous questions and potential misunderstanding. In this study, we provide a brief overview of empirical dynamic modelling, followed by answers to the ten most frequently asked questions about nonlinear dynamics and nonlinear forecasting.
Compensatory or catch-up growth (CG) is widely observed following periods of resource deprivation... more Compensatory or catch-up growth (CG) is widely observed following periods of resource deprivation. Because of this commonness, it is generally assumed that compensatory growth is adaptive, but most theory to date has explicitly ignored considerations of fitness. Following a period of deprivation, when resources become plentiful again, individuals may not respond at all and continue on a "normal" trajectory from a smaller size at age, may exhibit faster-than-normal growth immediately following the end of the period, or may adopt a growth strategy that involves faster-than-normal growth at some later time. Compensating individuals may also overtake control individuals who have been growing normally throughout. We hypothesize that the key to understanding CG is that growth leads to the accumulation of damage at the cellular level that is expressed (and thus must be modeled) at the level of the organism. We show that a life-history model incorporating the mortality consequences of both size and damage provides a framework for understanding compensatory growth. We use the theory to classify physiological and life-history characteristics for which CG is predicted to be the optimal response to deprivation.
Fishery management plans ignore the potential for evolutionary change in harvestable biomass. We ... more Fishery management plans ignore the potential for evolutionary change in harvestable biomass. We subjected populations of an exploited fish ( Menidia menidia ) to large, small, or random size-selective harvest of adults over four generations. Harvested biomass evolved rapidly in directions counter to the size-dependent force of fishing mortality. Large-harvested populations initially produced the highest catch but quickly evolved a lower yield than controls. Small-harvested populations did the reverse. These shifts were caused by selection of genotypes with slower or faster rates of growth. Management tools that preserve natural genetic variation are necessary for long-term sustainable yield.
Proceedings of the National Academy of Sciences, 2006
An important task in evolutionary biodemography is to determine the schedule of survival and repr... more An important task in evolutionary biodemography is to determine the schedule of survival and reproduction as the outcome of natural selection acting on life histories. We do this by using a model in which the state of the organism is characterized by mass and accumulated damage, both of which are affected by activity and which affect the rate of mortality. Focusing on growth during the juvenile period, we determine the level of activity that maximizes reproductive value. Given this, we are able to project forward and determine the trajectory of mortality for an individual following the optimal life history, given the physiological and reproductive parameters. We show that there are two main classes of juvenile mortality trajectories: U-shaped (such as recently reported for prereproductive humans) and steadily declining and we are able to connect the shape of the mortality trajectory with the physiological and reproductive parameters characterizing the life history. Our work shows th...
Recruitment dynamics are complicated in species in which multiple cohorts of young-of-the-year (Y... more Recruitment dynamics are complicated in species in which multiple cohorts of young-of-the-year (YOY) are produced each year. Each summer, two cohorts of YOY bluefish (Pomatomus saltatrix), representing fish spawned in spring and summer, recruit to Mid-Atlantic Bight estuaries, but little is known about their interannual variability, environmental forcing, and relative contributions to later life stages. We addressed these questions by examining the distribution and abundance of YOY on the continental shelf of the US east coast in autumn from 1973 through 1995. Abundance on the continental shelf increased in autumn owing to emigration from estuaries. We found clear evidence of two cohorts in autumn length-frequency distributions in most years and used this information to construct cohort-specific indices of abundance, which were then compared with relevant environmental variables. Spring-spawned fish dominated the catch in 20 of the years examined. The summer cohort dominated only in 1992. The abundance of the two cohorts was positively correlated, rejecting the hypothesis that dominance of the spring cohort is the result of cannibalism on the summer cohort. Spring cohort abundance was not correlated with either shelf warming-rate or warm-core ring streamer activity. A strong relationship was found between winds in April and May and the abundance of spring-spawned bluefish, possibly indicating that wind-driven surface flow aids the transport of larvae and/or juveniles across the shelf-slope region.
Several recent studies have demonstrated that rapid growth early in life leads to decreased physi... more Several recent studies have demonstrated that rapid growth early in life leads to decreased physiological performance. Nearly all involved experiments over short time periods (Ͻ1 day) to control for potentially confounding effects of size. This approach, however, neglects the benefits an individual accrues by growing. The net effect of growth can only be evaluated over a longer interval in which rapidly growing individuals are allowed the time required to attain the expected benefits of large size. We used two populations of Menidia menidia with disparate intrinsic growth rates to address this issue. We compared growth and survivorship among populations subject to predation in mesocosms under ambient light and temperature conditions for a period of up to 30 days to address two questions: Do the growth rates of fish in these populations respond differently to the presence of predators? Is the previously demonstrated survival cost of growth counterbalanced by the benefits of increased size? We found that growth was insensitive to predation risk: neither population appeared to modify growth rates in response to predation levels. Moreover, the fast-growing population suffered significantly higher mortality throughout the trials despite being 40% larger than the slow-growing population at the experiment's end. These results confirm that the costs of rapid growth extend over prolonged intervals and are not ameliorated merely by the attainment of large size.
Analyses of changes in size distributions over time frequently suggest that mortality rates depen... more Analyses of changes in size distributions over time frequently suggest that mortality rates depend on body size. Such observations, however, are probably confounded with changes in size due to growth. We describe a parametric method by which the size dependence of both mortality and growth may simultaneously be inferred from pairs of size distributions collected at different times. The method is tested in a Monte Carlo study and found to have sampling properties similar to those of other methods that require more data. Survival of the first winter of life appears to be size dependent in a diverse array of taxa, although few prior studies have accounted for growth. Analysis of sizes of Menidia menidia (Atlantic silverside) from three different latitudes revealed that changes in size distributions through winter resulted from growth in southern populations and mortality in the north. Winter mortality was better described by a power function of size than an exponential. Allometric exponents increased with latitude and were greater than predicted from metabolic-or starvation-based models. The steepness of the estimated survivorship curves imply that winter mortality in M. menidia is more consistent with a threshold effect perhaps attributable to offshore migration.
State-space estimation methods are increasingly used in ecology to estimate productivity and abun... more State-space estimation methods are increasingly used in ecology to estimate productivity and abundance of natural populations while accounting for variability in both population dynamics and measurement processes. However, functional forms for population dynamics and density dependence often will not match the true biological process, and this may degrade the performance of state-space methods. We therefore developed a Bayesian semiparametric state-space model, which uses a Gaussian process (GP) to approximate the population growth function. This offers two benefits for population modeling. First, it allows data to update a specified ''prior'' on the population growth function, while reverting to this prior when data are uninformative. Second, it allows variability in population dynamics to be decomposed into random errors around the population growth function (''process error'') and errors due to the mismatch between the specified prior and estimated growth function (''model error''). We used simulation modeling to illustrate the utility of GP methods in state-space population dynamics models. Results confirmed that the GP model performs similarly to a conventional state-space model when either (1) the prior matches the true process or (2) data are relatively uninformative. However, GP methods improve estimates of the population growth function when the function is misspecified. Results also demonstrated that the estimated magnitude of ''model error'' can be used to distinguish cases of model misspecification. We conclude with a discussion of the prospects for GP methods in other state-space models, including age and length-structured, meta-analytic, and individualmovement models.
Running title: Intrinsic predictability & forecasting 2 3 Title: The intrinsic predictability of ... more Running title: Intrinsic predictability & forecasting 2 3 Title: The intrinsic predictability of 4 ecological time series and its 5 potential to guide forecasting 6 7 Frank Pennekamp1,§, *, Alison C. Iles2,5,6 §, Joshua Garland3, Georgina Brennan4, Ulrich 8 Brose5,6, Ursula Gaedke7, Ute Jacob8, Pavel Kratina9, Blake Matthews10, Stephan Munch11, 12, 9 Mark Novak2, Gian Marco Palamara1,13, Björn C. Rall5,6, Benjamin Rosenbaum5,6, Andrea 10 Tabi1, Colette Ward1, Richard Williams14, Hao Ye15, Owen L. Petchey1 11 12 § F. Pennekamp and A. Iles contributed equally to this work 13
We develop a model for Bayesian selection in high order Markov chains through an extension of the... more We develop a model for Bayesian selection in high order Markov chains through an extension of the mixture transition distribution of Raftery (1985). We demonstrate two uses for the model: parsimonious approximation of high order dynamics by mixing lower order transition models, and model selection through over-specification and shrinkage via priors for sparse probability vectors. We discuss properties of the model and demonstrate its utility with simulation studies. We further apply the model to a data analysis from the high-order Markov chain literature and a novel application to pink salmon abundance time series.
Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all ... more Complex nonlinear dynamics are ubiquitous in many fields. Moreover, we rarely have access to all of the relevant state variables governing the dynamics. Delay embedding allows us, in principle, to account for unobserved state variables. Here we provide an algebraic approach to delay embedding that permits explicit approximation of error. We also provide the asymptotic dependence of the first order approximation error on the system size. More importantly, this formulation of delay embedding can be directly implemented using a Recurrent Neural Network (RNN). This observation expands the interpretability of both delay embedding and RNN and facilitates principled incorporation of structure and other constraints into these approaches.
Uploads
Papers by Stephan Munch