MULTISPECIES AND SINGLE‐SPECIES MODELS OF FISH POPULATION DYNAMICS: COMPARING PARAMETER ESTIMATES

Abstract Population features inferred from single‐species, age‐structured models are compared to those inferred from a multispecies, age‐structured model that includes predator‐prey interactions among three commercially harvested fish species—walleye pollock, Atka mackerel, and Pacific cod—on the Aleutian Shelf, Alaska. The multispecies framework treats the single‐species models and data as a special case of the multispecies model and data. The same data from fisheries and surveys are used to estimate model parameters for both single‐species and multispecies configurations of the model. Additionally, data from stomach samples and predator rations are used to estimate the parameters of the multispecies model. One form of the feeding functional response, predator pre‐emption, was selected using AIC from seven alternative models for how the predation rate changes with the densities of prey and possibly other predators. Differences in estimated population dynamics and productivity between the multispecies and single‐species models were observed. The multispecies model estimated lower mackerel population sizes from 1964–2003 than the single‐species model, while the spawning biomass of pollock was estimated to have declined more than three times faster since 1964 by the multispecies model. The variances around the estimates of spawning biomass were smaller for mackerel and larger for pollock in the multispecies model compared to the single‐species model.     

A MICROFOUNDATION OF PREDATOR‐PREY DYNAMICS

ABSTRACT. Predator‐prey relationships account for an important part of all interactions betweenspecies. In this paper we provide a microfoundation for such predator‐prey relations in afood chain. Basic entities of our analysis are representative organisms of species modeled similar to economic households. With prices as indicators of scarcity, organisms are assumed to behave as if they maximize their net biomass subject to constraints which express the organisms' risk of being preyed upon during predation. Like consumers, organisms face a ‘budget constraint’ requiring their expenditure on prey biomass not to exceed their revenue from supplying own biomass. Short‐run ecosystem equilibria are defined and derived. The net biomass acquired by the representative organism in the short term determines the positive or negative population growth. Moving short‐run equilibria constitute the dynamics of the predator‐prey relations that are characterized in numerical analysis. The population dynamics derived here turn out to differ significantly from those assumed in the standard Lotka‐Volterra model.     

A MODEL OF CHINOOK SALMON POPULATION DYNAMICS INCORPORATING SIZE‐SELECTIVE EXPLOITATION AND INHERITANCE OF POLYGENIC CORRELATED TRAITS

Abstract Concern regarding the potential for selective fisheries to degrade desirable characteristics of exploited fish populations is growing worldwide. Although the occurrence of fishery‐induced evolution in a wild population has not been irrefutably documented, considerable theoretical and empirical evidence for that possibility exists. Environmental conditions influence survival and growth in many species and may mask comparatively subtle trends induced by selective exploitation, especially given the evolutionarily short time series of data available from many fisheries. Modeling may be the most efficient investigative tool under such conditions. Motivated by public concern that large‐mesh gillnet fisheries may be altering Chinook salmon in western Alaska, we constructed a stochastic model of the population dynamics of Chinook salmon. The model contained several individually based components and incorporated size‐selective exploitation, assortative mating, size‐dependent female fecundity, density‐dependent survival, and the heritability of size and age. Substantial reductions in mean size and age were observed under all scenarios. Concurrently reducing directional selection and increasing spawning abundance was most effective in stimulating population recovery. Use of this model has potential to improve our ability to investigate the consequences of selective exploitation and aid development of improved management strategies to more effectively sustain fish and fisheries into the future.     

A multi‐stage ‘infection’ model of stock investors' reaction to new product announcement signal

Drawing on viral dynamics theory, this paper presents a differential equations model with time delay to investigate the stock investor behavior driven by new product announcement (NPA) signal. Visually, we look upon investors in stock market as cells in vivo and the NPA signals as free virus. The potential investors will be ‘infected’ by the dissociative NPA signal and then make investment decisions. In order to better understand the ‘infection’ process, we extract and establish a multi‐stage process during which NPA signal is delivered and ‘infects’ the potential investors. A time‐delay effect is employed to reflect the evaluation stage at which potential investors comprehensively evaluate and decide whether to invest or not. In addition, we introduce a set of external and internal factors into the model, including information sensitivity and investor sentiment, and so on, which are pivotal for examining investor behavior. Equilibrium analysis and numerical simulations are employed to check out the properties of the model and highlight the practical application values of the model. Copyright © 2016 John Wiley & Sons, Ltd.     

A STAGE‐STRUCTURED MODEL WITH TWO TIME‐STEPS FOR ANALYZING THE POPULATION DYNAMICS OF RHEA AMERICANA UNDER VARIABLE ENVIRONMENTAL CONDITIONS

ABSTRACT. The Ñandú or Rhea americana is an autochthonous species perfectly adapted to the pampas environment and only distributed in South America. The species exhibits an unusual breeding system combining polygyny, polyandry, communal nests and exclusive male parental care, which seems to contradict the idea of selfish genes. Our aim has been to construct a mathematical model based on the short term population dynamics of Rhea, living in the wild or in semi‐captivity, and taking into account environmental factors that vary from year to year. Due to the characteristics of its life cycle, it was necessary to develop a model that allows us to differentiate between the survival and fertility rates of each age group and the distinct behavior during breeding and non‐breeding seasons. Therefore, a quarterly differentiated stage‐structured discrete model was needed. Time steps of different lengths are used for modeling chicks or “charos' on the one hand, and juveniles and adults on the other. Environmental variables have been incorporated into the model because they affect the reproductive success of the species. Different scenarios are given as illustrations of the model use. Finally, the possibility of harvesting has been introduced in the model. The model is intended as a first step towards more refined models and systematic data gathering with the purpose of leading the way to a computational tool for risk assessment and decision‐making.     

‘Modified Hermitian and skew‐Hermitian splitting methods for non‐Hermitian positive‐definite linear systems’ [Numer. Linear Algebra Appl. 14 (2007) 217–235]

In this note, some errors in the article (Numer. Linear Algebra Appl. 2007; 14 :217–235) are pointed out and some correct results are presented. Copyright © 2011 John Wiley & Sons, Ltd.     

A critical Kirchhoff‐type problem involving the ‐Laplacian

In this paper we provide an existence result for a nonlocal problem of Kirchhoff‐type which involves both the p‐ and the q‐Laplacian and contains a critical term. Our approach is variational: we derive the existence of one non‐trivial solution via the multidimensional mountain pass theorem.     

A STRUCTURALLY BASED ANALYTIC MODEL OF GROWTH AND BIOMASS DYNAMICS IN SINGLE SPECIES STANDS OF CONIFERS

A theoretically based analytic model of plant growth in single species conifer communities based on the species fully occupying a site and fully using the site resources is introduced. Model derivations result in a single equation simultaneously describes changes over both, different site conditions (or resources available), and over time for each variable for each species. Leaf area or biomass, or a related plant community measurement, such as site class, can be used as an indicator of available site resources. Relationships over time (years) are determined by the interaction between a stable foliage biomass in balance with site resources, and by the increase in the total heterotrophic biomass of the stand with increasing tree size. This structurally based, analytic model describes the relationships between plant growth and each species’ functional depth for foliage, its mature crown size, and stand dynamics, including the self‐thinning. Stand table data for seven conifer species are used for verification of the model. Results closely duplicate those data for each variable and species. Assumptions used provide a basis for interpreting variations within and between the species. Better understanding of the relationships between the MacArthur consumer resource model, the Chapman–Richards growth functions, the metabolic theory of ecology, and stand development resulted.     

A TWO‐STAGE INFORMATION‐THEORETIC APPROACH TO MODELING LANDSCAPE‐LEVEL ATTRIBUTES AND MAXIMUM RECRUITMENT OF CHINOOK SALMON IN THE COLUMBIA RIVER BASIN

ABSTRACT. Many anadromous salmonid stocks in the Pacific Northwest are at their lowest recorded levels, which has raised questions regarding their long‐term persistence under current conditions. There are a number of factors, such as freshwater spawning and rearing habitat, that could potentially influence their numbers. Therefore, we used the latest advances in information‐theoretic methods in a two‐stage modeling process to investigate relationships between landscape‐level habitat attributes and maximum recruitment of 25 index stocks of chinook salmon (Onocorhynchus tshawy‐tscha) in the Columbia River basin. Our first‐stage model selection results indicated that the Ricker‐type, stock recruitment model with a constant Ricker a, i.e., recruits‐per‐spawner at low numbers of fish) across stocks was the only plausible one given these data, which contrasted with previous unpublished findings. Our second‐stage results revealed that maximum recruitment of chinook salmon had a strongly negative relationship with percentage of surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and private moderate‐high impact managed forest. That is, our model predicted that average maximum recruitment of chinook salmon would decrease by at least 247 fish for every increase of 33% in surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and privately managed forest. Conversely, mean annual air temperature had a positive relationship with salmon maximum recruitment, with an average increase of at least 179 fish for every increase in 2°C mean annual air temperature.     

A (T,ψ)‐ψe decoupled scheme for a time‐dependent multiply‐connected eddy current problem

The aim of this paper is to develop a fully discrete ( T ,ψ)‐ψ_e finite element decoupled scheme to solve time‐dependent eddy current problems with multiply‐connected conductors. By making ‘cuts’ and setting jumps of ψ_e across the cuts in nonconductive domain, the uniqueness of ψ_e is guaranteed. Distinguished from the traditional T ‐ ψ method, our decoupled scheme solves the potentials T and ψ‐ ψ_e separately in two different simple equation systems, which avoids solving a saddle‐point equation system and leads to a remarkable reduction in computational efforts. The energy‐norm error estimate of the fully discrete decoupled scheme is provided. Finally, the scheme is applied to solve two benchmark problems—TEAM Workshop Problems 7 and IEEJ model. Copyright © 2013 John Wiley & Sons, Ltd.     

A note on the paper ‘Analytical approach to heat and mass transfer in MHD free convection from a moving permeable vertical surface’ by A. Asgharian,D.D. Ganji,S. Soleimani,S. Asgharian,N. Sedaghatyzade and B. Mohammadi,Mathematical Methods in the Applied Sciences, 2011, 34 2209‐2217

The present note presents some errors in the aforementioned paper published in Mathematical Methods in the Applied Sciences. Two errors are found in the definition of the non‐dimensional parameters and correct results are presented for temperature profiles included in figure 10 of the previous paper. Copyright © 2014 John Wiley & Sons, Ltd.