Kenneth A. Rose

Skill assessment for coupled biological/physical models of marine systems

Coupled biological/physical models of marine systems serve many purposes including the synthesis of information, hypothesis generation, and as a tool for numerical experimentation. However, marine system models are increasingly used for prediction to support high-stakes decision-making. In such applications it is imperative that a rigorous model skill assessment is conducted so that the models capabilities are tested and understood. Herein, we review several metrics and approaches useful to evaluate model skill. The definition of skill and the determination of the skill level necessary for a given application is context specific and no single metric is likely to reveal all aspects of model skill. Thus, we recommend the use of several metrics, in concert, to provide a more thorough appraisal. The routine application and presentation of rigorous skill assessment metrics will also serve the broader interests of the modeling community, ultimately resulting in improved forecasting abilities as well as helping us recognize our limitations.

Super-individuals a simple solution for modelling large populations on an individual basis

Modelling populations on an individual-by-individual basis has proven to be a fruitful approach. Many complex patterns that are observed on the population level have been shown to arise from simple interactions between individuals. However, a major problem with these models is that the typically large number of individuals needed requires impractically large computation times. The common solution, reduction of the number of individuals in the model, can lead to loss of variation, irregular dynamics, and large sensitivity to the value of random generator seeds. As a solution to these problems, we propose to add an extra variable feature to each model individual, namely the number of real individuals it actually represents. This approach allows zooming from a real individual-by-individual model to a cohort representation or ultimately an all-animals-are-equal view without changing the model formulation. Therefore, the super-individual concept offers easy possibilities to check whether the observed behaviour is an artifact of following a limited number of individuals or of lumping individuals, and also to verify whether individual variability is indeed an essential ingredient for the observed behaviour. In addition the approach offers arbitrarily large computational advantages. As an example the super-individual approach is applied to a generic model of the dynamics of a size-distributed consumer cohort as well as to an elaborate applied simulation model of the recruitment of striped bass.

Individual variability and spatial heterogeneity in fish population models

SummaryFish populations consist of non-identical individuals inhabiting heterogeneous environments and moving about the environment in a manner that maximizes their individual fitness. No study has fully integrated these characteristics of fish populations into a single model. In this paper we propose a new class of model that includes each characteristic in a unified description of populations. To lay the foundation for these models we review models concerning (1) population dynamics in heterogeneous environments, (2) the effects of individual variability on population dynamics, and (3) individual movement and habitat selection rules. The models that we propose allow investigators to explore the population-level consequences of novel changes in the environment, and of different individual fitness maximization strategies. The strengths of our proposed class of model lie in their mechanistic, individual-level description of fish growth, movement and survival. Correctly depicting these mechanisms presents important challenges in developing such models. Despite these challenges, mechanistic models like those we propose should greatly increase our understanding of the interaction between environmental heterogeneity and fish population dynamics and distributions.

Interactions between Size-Structured Predator and Prey Populations: Experimental Test and Model Comparison

Abstract Because predation mortality is often size-dependent, the survival and size structure of prey populations may vary substantially depending on the size structure of the predator assemblage. We tested this hypothesis in a replicated pond experiment in which a bimodal size distribution of young-of-year spot Leiostomus xanthurus was exposed to two sizes of southern flounder Paralichthvs lethostigina, each predator size-group present alone or together, at densities providing equal predation pressure, After 3 weeks, we examined cohort survival and size distributions of remaining spot. In the no-predator controls, spot size-frequency distributions were essentially unchanged, and survival of the large- and small-spot cohorts was similar. However, the size distribution of survivors, and the relative survival of large- and small-spot cohorts, differed markedly with the size structure of the predator assemblage, In the presence of small southern flounders, the large-spot cohort survived 4 times better than t...

Individual-Based Approach to Fish Population Dynamics: An Overview

Abstract Individual-based simulation modeling tracks the attributes of individual fish through time and aggregates them to generate insights into population function. By seeking to understand how fish of differing phenotypes respond to variations in physicochemical and biological environments, analysts hope to improve predictions of population trends. A review ofeight accompanying papers highlights the promise and current limitations of the individual-based approach. Among the challenges to be faced are accurately representing feeding encounter rates, extending models to account for spatial heterogeneity and transgenerational responses, dealing with practical limits to the amount of data on individuals that can be measured and managed, more fully conceptionalizing natural processes, and acquiring appropriate field data with which to formulate and test the models.

INDIVIDUAL‐BASED MODEL OF YELLOW PERCH AND WALLEYE POPULATIONS IN ONEIDA LAKE

Predator–prey dynamics and density dependence are fundamental issues in ecology. We use a detailed, individual-based model of walleye and yellow perch to investigate the effects of alternative prey and compensatory responses on predator and prey population dynamics. Our analyses focus on the numerical and developmental responses of the predator, rather than the traditional emphasis on functional responses. The extensive database for Oneida Lake, New York, USA was used to configure the model and ensure its realism. The model follows the daily growth, mortality, and spawning of individuals of each species through their lifetime. Three ecologically distinct periods in the history of Oneida Lake were simulated: baseline, high mayfly densities, and high forage fish densities. Mayflies and forage fish act as alternative prey for walleye. For model corroboration, the three periods were simulated sequentially as they occurred in Oneida Lake. Model predictions of abundances, size at age, and growth and survival ra...

Model goodness-of-fit analysis using regression and related techniques

Four related approaches for assessing model goodness-of-fit (GOF) are discussed in this paper: linear regression of observed versus predicted values, the sum of squared prediction errors, a reliability index summarizing predictions as being within a factor Ks of observed values, and correlation-like measures of fit that normalize the sum of squared prediction error to be between zero and one. Relationships among the four measures are derived and alternative decompositions of the measures into components relating to bias, variance, and consistency are presented. The measures are extended to include lack-of-fit terms when multiple observations are available for each prediction, and except for the reliability index, extended to include the multivariate case of multiple prediction variables. Application of the GOF measures to model predictions and observed radon-222 concentrations (a univariate example) showed significant lack-of-fit for high concentrations. Application of the GOF measures to predicted and observed mean lengths and densities of winter flounder larvae (a multivariate example) showed predicted densities were good with most of the lack-of-fit attributed to ∼ 0.44 mm bias in predicted mean lengths. The role of GOF analysis in evaluating model performance is discussed.

FISH COHORT DYNAMICS: APPLICATION OF COMPLEMENTARY MODELING APPROACHES

The recruitment to the adult stock of a fish population is a function of both environmental conditions and the dynamics of juvenile fish cohorts. These dynamics can be quite complicated and involve the size structure of the cohort. Two types of models,i-state distribution models (e.g., partial differential equations) and/-state configuration models (computer simulation models following many individuals simultaneously), have been developed to study this type of question. However, these two model types have not to our knowledge previously been compared in detail. Analytical solutions are obtained for three partial differential equation models of early life-history fish cohorts. Equivalent individual-by-individual computer simulation models are also used. These two approaches can produce similar results, which suggests that one may be able to use the approaches interchangeably under many circumstances. Simple uncorrelated stochasticity in daily growth is added to the individual-by-individual models, and it is shown that this produces no significant difference from purely deterministic situations. However, when the stochasticity was temporally correlated such that a fish growing faster than the mean I d has a tendency to grow faster than the mean the next day, there can be great differences in the outcomes of the simulations.

Individual-Based Model of Young-of-the-Year Striped Bass Population Dynamics. I. Model Description and Baseline Simulations

Abstract An individual-based model of population dynamics of age-0 striped bass Morone saxatilis is described and model predictions are analyzed. The model begins with spawning and simulates the daily growth and mortality of the progeny from each egg clutch as the fish develop through the life stages of egg, yolk-sac larva, feeding larva, and juvenile during their first year of life in a single, well-mixed compartment. Day of spawning and development rates of eggs and yolk-sac larvae depend on temperature. Daily growth of feeding individuals is represented by a bioenergetics equation, for which consumption is based on random encounters by individuals with different types of prey. Larvae feed on four zooplankton types and juveniles feed exclusively on size-classes of four benthic types. Mortality of eggs and yolk-sac larvae has both temperature-dependent and constant terms; mortality of feeding larvae and juveniles depends on an individuals weight and length. Most of the computations in the simulation inv...

Individual-based model of stream-resident rainbow trout and brook char: model description, corroboration, and effects of sympatry and spawning season duration

Abstract An individual-based model of the population dynamics of sympatric rainbow trout ( Oncorhynchus mykiss ) and brook char ( Salvelinus fontinalis ) is described and analyzed. The model simulates daily growth, mortality, movement, and spawning over the full life cycle of each species for 100 years in a compartmentalized, hypothetical stream configured for the southern Appalachian mountains, USA. Egg and alevin development is temperature-dependent with mortality having constant, spatial, and temperature-dependent components. Daily growth of fry, juveniles, and adults is based on bioenergetics and consumption of drift prey. Mortality rate of fry through adults decreases with length. Model predictions of densities, growth, age, and size structure were similar to those observed in southern Appalachian streams. Five different conditions were simulated to explore the population dynamics and competition between the two species: (1) sympatric populations (baseline), (2) allopatric brook char, (3) allopatric rainbow trout, (4) and (5) sympatric populations with reduced or increased spawning season durations. Results indicated that density-dependence mainly operated during the fry and juvenile stages. Brook char were more affected by interspecific competition than rainbow trout, and crowding of fry negatively affected brook char (with little effect on rainbow trout), whereas low fry density favored brook char.