Ancient DNA reveals a southern presence of the Northeast Arctic cod during the Holocene

Climate change has been implicated in an increased number of distributional shifts of marine species during the last century. Nonetheless, it is unclear whether earlier climatic fluctuations had similar impacts. We use ancient DNA to investigate the long-term spawning distribution of the Northeast Arctic cod (skrei) which performs yearly migrations from the Barents Sea towards spawning grounds along the Norwegian coast. The distribution of these spawning grounds has shifted northwards during the last century, which is thought to be associated with food availability and warming temperatures. We genetically identify skrei specimens from Ruskeneset in west Norway, an archaeological site located south of their current spawning range. Remarkably, ¹⁴C analyses date these specimens to the late Holocene, when temperatures were warmer than present-day conditions. Our results either suggest that temperature is not the only driver influencing the spawning distribution of Atlantic cod, or could be indicative of uncertainty in palaeoclimate reconstructions in this region. Regardless, our findings highlight the utility of aDNA to reconstruct the historical distribution of economically important fish populations and reveal the complexity of long-term ecological interactions in the marine environment.     

Evolutionarily stable transition rates in a stage-structured model. An application to the analysis of size distributions of badges of social status

This paper deals with the adaptive dynamics associated to a hierarchical non-linear discrete population model with a general transition matrix. In the model, individuals are categorized into n dominance classes, newborns lie in the subordinate class, and it is considered as evolutionary trait a vector eta of probabilities of transition among classes. For this trait, we obtain the evolutionary singular strategy and prove its neutral evolutionary stability. Finally, we obtain conditions for the invading potential of such a strategy, which is sufficient for the convergence stability of the latter. With the help of the previous results, we provide an explanation for the bimodal distribution of badges of status observed in the Siskin (Carduelis spinus). In the Siskin, as in several bird species, patches of pigmented plumage signal the dominance status of the bearer to opponents, and central to the discussion on the evolution of status signalling is the understanding of which should be the frequency distribution of badge sizes. Though some simple verbal models predicted a bimodal distribution, up to now most species display normal distributions and bimodality has only been described for the Siskin. In this paper, we give conditions leading to one of these two distributions in terms of the survival, fecundity and aggression rates in each dominance class.     

Simplifying a physiologically structured population model to a stage-structured biomass model

We formulate and analyze an archetypal consumer-resource model in terms of ordinary differential equations that consistently translates individual life history processes, in particular food-dependent growth in body size and stage-specific differences between juveniles and adults in resource use and mortality, to the population level. This stage-structured model is derived as an approximation to a physiologically structured population model, which accounts for a complete size-distribution of the consumer population and which is based on assumptions about the energy budget and size-dependent life history of individual consumers. The approximation ensures that under equilibrium conditions predictions of both models are completely identical. In addition we find that under non-equilibrium conditions the stage-structured model gives rise to dynamics that closely approximate the dynamics exhibited by the size-structured model, as long as adult consumers are superior foragers than juveniles with a higher mass-specific ingestion rate. When the mass-specific intake rate of juvenile consumers is higher, the size-structured model exhibits single-generation cycles, in which a single cohort of consumers dominates population dynamics throughout its life time and the population composition varies over time between a dominance by juveniles and adults, respectively. The stage-structured model does not capture these dynamics because it incorporates a distributed time delay between the birth and maturation of an individual organism in contrast to the size-structured model, in which maturation is a discrete event in individual life history. We investigate model dynamics with both semi-chemostat and logistic resource growth.     

Approximation of a physiologically structured population model with seasonal reproduction by a stage-structured biomass model

Seasonal reproduction causes, due to the periodic inflow of young small individuals in the population, seasonal fluctuations in population size distributions. Seasonal reproduction furthermore implies that the energetic body condition of reproducing individuals varies over time. Through these mechanisms, seasonal reproduction likely affects population and community dynamics. While seasonal reproduction is often incorporated in population models using discrete time equations, these are not suitable for size-structured populations in which individuals grow continuously between reproductive events. Size-structured population models that consider seasonal reproduction, an explicit growing season and individual-level energetic processes exist in the form of physiologically structured population models. However, modeling large species ensembles with these models is virtually impossible. In this study, we therefore develop a simpler model framework by approximating a cohort-based size-structured population model with seasonal reproduction to a stage-structured biomass model of four ODEs. The model translates individual-level assumptions about food ingestion, bioenergetics, growth, investment in reproduction, storage of reproductive energy, and seasonal reproduction in stage-based processes at the population level. Numerical analysis of the two models shows similar values for the average biomass of juveniles, adults, and resource unless large-amplitude cycles with a single cohort dominating the population occur. The model framework can be extended by adding species or multiple juvenile and/or adult stages. This opens up possibilities to investigate population dynamics of interacting species while incorporating ontogenetic development and complex life histories in combination with seasonal reproduction.     

Long‐term change in a behavioural trait: truncated spawning distribution and demography in Northeast Arctic cod

Harvesting may be a potent driver of demographic change and contemporary evolution, which both may have great impacts on animal populations. Research has focused on changes in phenotypic traits that are easily quantifiable and for which time series exist, such as size, age, sex, or gonad size, whereas potential changes in behavioural traits have been under‐studied. Here, we analyse potential drivers of long‐term changes in a behavioural trait for the Northeast Arctic stock of Atlantic cod Gadus morhua, namely choice of spawning location. For 104 years (1866–1969), commercial catches were recorded annually and reported by county along the Norwegian coast. During this time period, spawning ground distribution has fluctuated with a trend towards more northerly spawning. Spawning location is analysed against a suite of explanatory factors including climate, fishing pressure, density dependence, and demography. We find that demography (age or age at maturation) had the highest explanatory power for variation in spawning location, while climate had a limited effect below statistical significance. As to potential mechanisms, some effects of climate may act through demography, and explanatory variables for demography may also have absorbed direct evolutionary change in migration distance for which proxies were unavailable. Despite these caveats, we argue that fishing mortality, either through demographic or evolutionary change, has served as an effective driver for changing spawning locations in cod, and that additional explanatory factors related to climate add no significant information.     

Qualitative behavior of stage-structured populations: application to structural validation

 The transient behavior of a class of nonlinear differential systems representing stage-structured populations is studied. The qualitative dynamics are described in terms of succession of extrema for the state variables, or for the integrated difference between two trajectories. The rules giving the possibilities of extrema are derived, they characterize the classical stage-structured models. These rules can be compared with experiments to validate the structure of the model. An explanation for the disagreement of this transition scheme with some experiments could be an unexpected interaction with another variable. A new model taking the interaction into account thus engenders new transition rules, which are to be compared with experiments. These results are illustrated with experiments on copepods, showing how the qualitative experimental features can help the construction and the validation of the models. Received: 13 May 1996 / Revised version: 20 March 1998     

An epidemiological model with a delay and a nonlinear incidence rate

An epidemiological model with both a time delay in the removed class and a nonlinear incidence rate is analysed to determine the equilibria and their stability. This model is for diseases where individuals are first susceptible, then infected, then removed with temporary immunity and then susceptible again when they lose their immunity. There are multiple equilibria for some parameter values, and, for certain of these, periodic solutions arise by Hopf bifurcation from the large nontrivial equilibrium state.Research supported in parts by Centers for Disease Control Contract 200-87-0515Research supported in part by NSERC A-8965     

An age-dependent epidemic model with application to measles

A combined epidemic-demographic model is developed which models the spread of an infectious disease throughout a population of constant size. The model allows for births, deaths, temporary or permanent immunity, and immunization. The relationship of this model to previously studied epidemic and demographic models is illustrated. An advantage of this model is that all epidemic and demographic parameters may be estimated. The stability of the equilibrium point corresponding to the elimination of the disease is studied and a threshold value is found which indicates whether the disease will die out or remain endemic in the population. The application of the model to measles indicates that immunization levels needed to reduce the incidence to near zero may not be as high as previously predicted.     

Laboratory rearing of wild Arctic cod Boreogadus saida from egg to adulthood

The techniques and protocols used to successfully capture, transport and breed Arctic cod Boreogadus saida, as well as to rear their larvae through to adulthood are summarized. Breeding B. saida will increase the opportunity to study this fish species, which is a critical part of the Arctic food web.     

A Bayesian estimation approach for the mortality in a stage-structured demographic model

Journal of Mathematical Biology - Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be...     

Sexual cannibalism in the fishing spider and a model for the evolution of sexual cannibalism based on genetic constraints

Several hypotheses have been proposed for the evolution of sexual cannibalism by females. Newman and Elgar (1991) suggested that sexual cannibalism prior to mating by virgin female spiders may have evolved as a result of female foraging considerations. According to this model, an adult female's decision to mate or cannibalize a courting male should be based on an assessment of the male's value as a meal versus his value as a mate. The current study provides an empirical test of the assumptions and predictions of this model in the sexually cannibalistic fishing spider. Adult females were subjected to different food treatments, and exposed to adult males in the laboratory. However, only one of the assumptions of the model and none of its five predictions were upheld. We failed to find any effects of female foraging, female mating status, female size, male size or time of the season on females' behaviour towards courting males. Females behaved stereotypically, and many females were left unmated despite numerous mating opportunities. We also demonstrate costs of sexual cannibalism in a natural population. We propose that the act of sexual cannibalism in the fishing spider is non-adaptive, and develop a model for the evolution of premating sexual cannibalism in spiders based on genetic constraints. According to this hypothesis, sexual cannibalism by adult females may have evolved as an indirect result of selection for high and non-discriminate aggression during previous ontogenetic stages. Genetic covariance between different components of aggressive behaviour may constrain the degree to which (1) juvenile and adult aggression and/or (2) aggression towards conspecifics and heterospecifics can vary independently. We briefly review the support for our model, and suggest several critical tests that may be used to assess the assumptions and predictions of the model.     

The stage-structured epidemic: linking disease and demography with a multi-state matrix approach model

Stage-structured epidemic models provide a way to connect the interacting processes of infection and demography. Reproduction and development can replenish the pool of susceptible hosts, and demographic structure leads to heterogeneous transmission and disease risk. Epidemics, in turn, can increase mortality or reduce fertility of the host population. Here we present a framework that integrates both demography and epidemiology in models for stage-structured epidemics. We use the vec-permutation matrix approach to classify individuals jointly by their demographic stage and infection status. We describe demographic and epidemic processes as alternating in time with a periodic matrix model. The application of matrix calculus to this framework allows for the calculation of R₀{mathcal{R}_0} and sensitivity analysis.     

Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations

Populations fluctuate because of their internal dynamics, which can be nonlinear and stochastic, and in response to environmental variation. Theory predicts how the colour of environmental stochasticity affects population means, variances and correlations with the environment over time. The theory has not been tested for cycling populations, commonly observed in field systems. We applied noise of different colours to cycling laboratory beetle populations, holding other statistical properties of the noise fixed. Theory was largely validated, but failed to predict observations in sufficient detail. The main period of population cycling was shifted up to 33% by the colour of environmental stochasticity. Noise colour affected population means, variances and dominant periodicities differently for populations that cycled in different ways without noise. Our results show that changes in the colour of climatic variability, partly caused by humans, may affect the main periodicity of cycling populations, possibly impacting industry, pest management and conservation.     

A snapshot of cannibalism in 0-group Atlantic cod (Gadus morhua) in a marine pond

Cannibalism in 0-group Atlantic cod ( Gadus morhua ) was investigated in a semi-natural marine pond using stomach content analysis. About 6000 individuals were eradicated by rotenone treatment of the pond in November 1991. Total lengths of cod ranged from 7.4–28.8 cm with a median of 10.4 cm. The proportion of cannibalistic cod in the population was estimated at 1.3%. Cannibalism accounted for a daily loss of 1.1% of the population. The frequency of cod with ≥ 2 cod prey per stomach was higher in the population compared with a Poisson model. Predator-prey length ratios ranged between 1.6 and 3.2 when estimated from otolith-length relationships. Chesson's 1983 α-index indicated that cannibalistic cod had a positive selectivity for conspecifics < 9.0 cm in total length.     

Bayesian analysis for nonlinear regression model under skewed errors,with application in growth curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew‐t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.     

Coexistence of competitive species with a stage-structured life cycle

Ecological theory provides explanations for exclusion or coexistence of competing species. Most theoretical works on competition dynamics that have shaped current perspectives on coexistence assume a simple life cycle. This simplification, however, may omit important realities. We present a simple two-stage structured competition model to investigate the effects of life-history characteristics on coexistence. The achievement and the stability of coexistence depend not only on competition coefficients but also on a set of life-history parameters that reflect the viability of an individual, namely, adult death rate, maturation rate, and birth rate. High individual viability is necessary for a species to persist, but it does not necessarily facilitate coexistence. Intense competition at the juvenile or adult stage may require higher or lower viability, respectively, for stable coexistence to be possible. The stability mechanism can be explained by the refuge effect of the less competitive stage, and the birth performance, which preserves the less competitive stage as a refuge. Coexistence might readily collapse if the life-history characteristics, which together constitute individual viability, change, even though two species have an inherent competitive relation conducive to stable coexistence.     

Bifurcation analysis of a nonlinear field model of regeneration

The analysis of bifurcating solutions in the Totafurno and Trainor [23] model of supernumerary limb production in salamanders is re-examined using the symmetry analysis developed by Totafurno [22]. In particular, we show analytically that the appearance of field solutions possessing 2 and 4 singularities (the 2- and 4-centered solutions, respectively) also correspond to true bifurcations with reduced symmetries, just as had been previously found for a solution to the field equations not possessing such singularities (the twist solution). While the results have significance primarily for the biological problem, this work serves as an instructive example of the application of symmetry groups to the bifurcation analysis of nonlinear field equations arising from a variational principle. The relationship between the solutions of the nonlinear equations and the corresponding linear equations is discussed.Supported by the National Sciences and Engineering Research Council and the Medical Research Council of CanadaTo whom correspondence should be sent