Ricker Model Research Articles

Density dependence in a seasonal time series of the bamboo mosquito,Tripteroides bambusa(Diptera: Culicidae)

AbstractThe bamboo mosquito,Tripteroides bambusa(Yamada) (Diptera: Culicidae), is a mosquito species ubiquitous across forested landscapes in Japan. During 2014 we sampled adult mosquitoes from May to November using a sweep net in Nagasaki, Japan. We recorded and managed our field data using Open Data Kit, which eased the overall process of data management before performing their statistical analysis. Here, we analyse the resulting biweekly time series of the bamboo mosquito abundance using time-series statistical techniques. Specifically, we test for density dependence in the population dynamics fitting the Ricker model. Parameter estimates for the Ricker model suggest that the bamboo mosquito is under density dependence regulation and that its population dynamics is stable. Our data also suggest the bamboo mosquito increased its abundance when temperature was more variable at our study site. Further work is warranted to better understand the linkage between the observed density dependence in the adults and the larvae of this mosquito species.

A bifurcation theorem for evolutionary matrix models with multiple traits.

One fundamental question in biology is population extinction and persistence, i.e., stability/instability of the extinction equilibrium and of non-extinction equilibria. In the case of nonlinear matrix models for structured populations, a bifurcation theorem answers this question when the projection matrix is primitive by showing the existence of a continuum of positive equilibria that bifurcates from the extinction equilibrium as the inherent population growth rate passes through 1. This theorem also characterizes the stability properties of the bifurcating equilibria by relating them to the direction of bifurcation, which is forward (backward) if, near the bifurcation point, the positive equilibria exist for inherent growth rates greater (less) than 1. In this paper we consider an evolutionary game theoretic version of a general nonlinear matrix model that includes the dynamics of a vector of mean phenotypic traits subject to natural selection. We extend the fundamental bifurcation theorem to this evolutionary model. We apply the results to an evolutionary version of a Ricker model with an added Allee component. This application illustrates the theoretical results and, in addition, several other interesting dynamic phenomena, such as backward bifurcation induced strong Allee effects.

Preventing Noise-Induced Extinction in Discrete Population Models

A problem of the analysis and prevention of noise-induced extinction in nonlinear population models is considered. For the solution of this problem, we suggest a general approach based on the stochastic sensitivity analysis. To prevent the noise-induced extinction, we construct feedback regulators which provide a low stochastic sensitivity and keep the system close to the safe equilibrium regime. For the demonstration of this approach, we apply our mathematical technique to the conceptual but quite representative Ricker-type models. A variant of the Ricker model with delay is studied along with the classic widely used one-dimensional system.

An alternative stock-recruitment function for age-structured models

In this work I introduce a probabilistic stock-recruitment function, of the Cushing family, that stands as an alternative to the canonical formulas provided by Beverton-Holt and Ricker, among others. I embed this function in a mathematically tractable (dynamic linear) population model, which renders inference of abundance-at-age and unknown biological parameters (natural mortality, virgin stock's egg production rate, and steepness), as well as fisheries parameters (catchability and selectivity), easier than with canonical representations. To assist management, I provide formulas for exact and approximate reference points, associated with Maximum Sustainable Yield (MSY) and Maximum Excess Recruitment (MER). I also introduce a new summary statistic, called bottleneck abundance ratio, which requires no knowledge of steepness under the proposed stock-recruitment function. With simulated data and the concept of Pretty Good Yield, I generate bounds for MSY- and MER-based reference points and show that those based on the new function have greater resilience to uncertainty about steepness. As a case study, I apply a state-space model to the US Gulf menhaden fishery, 1964–2004. Results suggest higher than previously considered natural mortality and a discernible connection between parental stock abundance and recruitment, undetected with Beverton-Holt and Ricker models.

Dynamics of populations with delayed density dependent birth rate regulation

This study focuses on the Moran–Ricker model with time lag for the dynamics of limited homogeneous population. The reduction of required resources is caused by their consumption by the previous generation, which corresponds to delayed density dependence. The model shows multimodality. The population can demonstrate different types of dynamics (i.e., stable, periodic, or chaotic) at the same values of demographic parameters. The Moran–Ricker model with time lag can successfully describe the population dynamics of some insect species. The point estimations of population parameters are statistically significant. The obtained point estimates that correspond to real population dynamics are located in a quasi-periodic fluctuation area and adjoin other dynamic modes. A variation of the values of demographic parameters or random fluctuations of the current population size can lead to dynamic mode change. The investigation of the possible model dynamic modes near the found point estimation of parameters is necessary to identify the dynamic modes between which transition may occur.

Integrating population dynamics models and distance sampling data: a spatial hierarchical state-space approach.

Stochastic versions of Gompertz, Ricker, and various other dynamics models play a fundamental role in quantifying strength of density dependence and studying long-term dynamics of wildlife populations. These models are frequently estimated using time series of abundance estimates that are inevitably subject to observation error and missing data. This issue can be addressed with a state-space modeling framework that jointly estimates the observed data model and the underlying stochastic population dynamics (SPD) model. In cases where abundance data are from multiple locations with a smaller spatial resolution (e.g., from mark-recapture and distance sampling studies), models are conventionally fitted to spatially pooled estimates of yearly abundances. Here, we demonstrate that a spatial version of SPD models can be directly estimated from short time series of spatially referenced distance sampling data in a unified hierarchical state-space modeling framework that also allows for spatial variance (covariance) in population growth. We also show that a full range of likelihood based inference, including estimability diagnostics and model selection,is feasible in this class of models using a data cloning algorithm. We further show through simulation experiments that the hierarchical state-space framework introduced herein efficiently captures the underlying dynamical parameters and spatial abundance distribution. We apply our methodology by analyzing a time series of line-transect distance sampling data for fin whales (Balaenoptera physalus) off the U.S. west coast. Although there were only seven surveys conducted during the study time frame, 1991-2014, our analysis detected presence of strong density regulation and provided reliable estimates of fin whale densities. In summary, we show that the integrative framework developed herein allows ecologists to better infer key population characteristics such as presence of density regulation and spatial variability in a population's intrinsic growth potential.

The reverse effects of random perturbation on discrete systems for single and multiple population models

The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.

Performance of seismic arrays in the presence of weathering layer variations

Near-surface layer variations can degrade the desired response of seismic arrays which are typically used to attenuate horizontally traveling coherent noise and enhance vertically traveling signal. We investigate the effect of variations in the near-surface layer thickness on the performance of arrays by studying their impulse and wavelet responses. The models considered include the topographic variations and a channel in the base of weathering layer. The topographic variations include a dipping surface layer as well as a surface layer that follows a sine wave. The geological channel is assumed to be present under the entire receiver array as well as partially under a few receivers. We use Ricker wavelet and model plane wavefronts with incidence angles (90, 70, 45, 20, and 5 °) on a 12-element equally weighted array for the weathering layer models. We found that the array responses are more degraded for near-vertically traveling waves in all cases. The array responses are also found to be more degraded when channel variations are present underneath a few receivers as compared to the entire array length. We recommend designing a spatial filter or using single-sensor records after correcting for intra-array statics to preserve the reflection amplitudes in the presence of weathering layer variations.

Quantifying Recruitment Compensation in Florida Largemouth Bass, with Implications for Fisheries

AbstractFish populations that undergo heavy exploitation and those for which the act of fishing can influence individual brood success are at risk of recruitment effects due to angling. The angling of brood‐guarding male black bass Micropterus spp. has been shown to decrease brood success, although there is no evidence that a loss of individual broods has population‐level impacts. Therefore, some level of recruitment compensation may influence juvenile bass survival. We sought to measure recruitment compensation and the form of the stock–recruit relationship for a brood‐guarding species, the Florida Largemouth Bass M. salmoides floridanus (hereafter, Florida Bass). The study was conducted in four north‐central Florida lakes during 4 years (2010–2013). We quantified adult stock density by using mark–recapture electrofishing surveys. The estimated broods produced in each spawning season, the number of those broods that were successful, and the age‐1 recruit density were quantified via snorkel surveys. We evaluated three models for describing the effects of stock density or successful brood density on recruitment: a proportional (linear; i.e., no compensation) model, a Ricker (dome‐shaped) model, and a Beverton–Holt (asymptotic) model. Recruit density was better indicated by the number of successful broods produced than by spawning stock density. Model comparisons indicated that the density‐dependent models had the most support, whereas there was no apparent support for the proportional or density‐independent model. The Ricker model had the most empirical support overall (estimated parameters: a = 2.2, b = 0.009). Our results indicate that the number of successful broods would have to fall below about 5 broods/ha to generate direct declines in observed average recruitment of Florida Bass.Received August 5, 2015; accepted December 9, 2015 Published online April 14, 2016

A Mechanistic Stochastic Ricker Model: Analytical and Numerical Investigations

The Ricker model is one of the simplest and most widely-used ecological models displaying complex nonlinear dynamics. We study a discrete-time population model, which is derived from simple assumptions concerning individual organisms’ behavior, using the “site-based” approach, developed by Brännström, Broomhead, Johansson and Sumpter. In the large-population limit the model converges to the Ricker model, and can thus be considered a mechanistic version of the Ricker model, derived from basic ecological principles, and taking into account the demographic stochasticity inherent to finite populations. We employ several analytical and precise numerical methods to study the model, showing how each approach contributes to understanding the model’s dynamics. Expressing the model as a Markov chain, we employ the concept of quasi-stationary distributions, which are computed numerically, and used to examine the interaction between complex deterministic dynamics and demographic stochasticity, as well as to calculate mean times to extinction. A Gaussian Markov chain approximation is used to obtain quantitative asymptotic approximations for the size of fluctuations of the stochastic model’s time series around the deterministic trajectory, and for the correlations between successive fluctuations. Results of these approximations are compared to results obtained from quasi-stationary distributions and from direct simulations, and are shown to be in good agreement.

Extinction, periodicity and multistability in a Ricker model of stage-structured populations

We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (adult-juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the non-autonomous case yielding general conditions for extinction in the biological context. We also study the dynamics of an autonomous special case of the equation that generates multistable periodic and non-periodic orbits in the positive quadrant of the plane.

2-циклы уравнения Рикера с периодически изменяющимся мальтузианским параметром: устойчивость и мультистабильность

2-циклы уравнения Рикера с периодически изменяющимся мальтузианским параметром: устойчивость и мультистабильность

Population Dynamics of an Estuarine Forage Fish: Disaggregating Forces Driving Long‐Term Decline of Longfin Smelt in California's San Francisco Estuary

AbstractForage fish production has become a central concern of fisheries and ecosystem managers because populations of small fish are a critical energetic pathway between primary producers and predator populations. Management of forage fish often focuses on controlling exploitation rates, but it is also possible to manage productivity of these species in coastal ecosystems, particularly estuaries. Like several forage fish species that are native to the San Francisco Estuary (SFE) in California, the Longfin Smelt Spirinchus thaleichthys has experienced dramatic population declines over the past few decades. This population is not fished commercially or recreationally; trends in its relative abundance have been described statistically, but the mechanisms that drive population dynamics are still poorly understood. Our objective was to evaluate alternative conceptual models of Longfin Smelt population dynamics to better understand the forces that may constrain the species' productivity during different phases of its life cycle. We created contrasting variants of a generalizable population model (the Ricker model) and parameterized those variants using empirical data from a long‐term sampling program in the SFE. Predictions from alternative models were compared with empirical results from a second (independent) data series of relative abundance to identify the model variants that best captured the empirical trend. The results indicated that (1) freshwater flow had a positive association with recruits per spawner and (2) both recruits per spawner and spawners per recruit appeared to be density‐dependent life stage transitions. Juvenile survival may have declined to some extent, but we could not conclusively demonstrate this. By constraining the possible timing and location of mechanisms that modulate productivity at different life stages, the present results improve our understanding of production for a key native forage fish in the SFE.

Modeling transportation of efavirenz: inference on possibility of mixed modes of transportation and kinetic solubility.

Understanding drug transportation mechanisms in the human body is of paramount importance in modeling Pharmacokinetic-Pharmacodynamic relationships. This work gives a novel general model of efavirenz transportation projections based on concentrations simulated from patients on a dose of 600 mg. The work puts forward a proposition that transportation can wholly be modeled by concentration and time in a uniform volumetric space. Furthermore, movement entities are used to inform the state of “kinetic solubility” of a solution. There is use of Ricker's model, and forms of the Hill's equation in modeling transportation. Characterization on the movement rates of solution particle are suggested in relation to advection rate of solution particle. At turning points on the transportation rate of solution particle vs. concentration curve, a suggestion of possibly change of dominance in the mode of transportation and saturation is made. There are four movement rates postulated at primary micro-level transportation, that are attributed to convection, diffusion [passive transportation (EI)] and energy dependent system transportation (ED) in relation to advection. Furthermore, a new parameter is introduced which is defined as an advection rate constant of solution particle. It is postulated to be dependent on two rate constants of solution particle, that is a convection rate constant of solution particle and a saturable transportation rate constant of solution particle. At secondary micro-level transportation, the results show convection as sum of advection and saturable transportation. The kinetics of dissolution of efavirenz in the solution space is postulated. Relatively, a good level of kinetics of dissolution is projected in the concentration region 0 − 32.82 μg/ml.

Maternal age effects on Atlantic cod recruitment and implications for future population trajectories

Abstract Exploited fish populations frequently exhibit truncated age-structure. To address a basic question in fisheries science and conservation biology—how does age truncation affect population dynamics and productivity?—we explored the effect of age-structure on recruitment dynamics of ten stocks of Atlantic cod (Gadus morhua). Based on six alternative stock–recruitment relationships, we compared models that included and excluded maternal age-structure effects on recruitment. In all ten stocks, a recruitment model that included a maternal age-dependent effect was preferred over the standard Ricker model and in seven of the ten stocks, the preferred statistical model included a positive effect of either maternal age or mass on recruitment. Simulations comparing standard and maternal age dependent recruitment two decades into the future suggest that the inclusion of maternal age in recruitment models has little effect on projected biomasses. However, this similarity in biomass trajectory masked an increased sensitivity of populations with maternal age-dependent recruitment to stock age-structure. In particular, simulations with maternal age-dependent recruitment responded strongly to changes in fishing mortality on the oldest age classes, while simulations using standard recruitment models did not. Populations with maternal age-dependent recruitment can exhibit increased biomass catch even if fishing mortality on older individuals was reduced. Overall, simulations suggested that the influence of maternal age on population dynamics are more nuanced than suggested by previous research and indicate that careful consideration of the effects of age-structure on populations may lead to substantially different fisheries management reference points—particularly with respect to age-specific fishing mortality—than classical models. While these results suggest a link between maternal age and population productivity, future research requires the incorporation of biologically reasonable and empirically defensible mechanisms to clarify the effect of age on population dynamics.

Competitive exclusion and coexistence in an n-species Ricker model

We analyse a discrete-time Ricker competition model with n competing species and give sufficient conditions, which depend on the competition coefficients only, for one species to survive (not necessarily at an equilibrium) and to drive all the other species to extinction. Our results complement and extend similar existing results from the literature. For the model reduced to three species (), we also investigate various scenarios under which all species coexist, in the sense that each species is robustly uniformly persistent. We provide a few numerical simulations to illustrate that coexistence does not necessarily mean convergence to the interior equilibrium, and that the interior dynamics can be quite complex.

Growth rates and variances of unexploited wolf populations in dynamic equilibria

ABSTRACTSeveral states have begun harvesting gray wolves (Canis lupus), and these states and various European countries are closely monitoring their wolf populations. To provide appropriate perspective for determining unusual or extreme fluctuations in their managed wolf populations, we analyzed natural, long‐term, wolf‐population‐density trajectories totaling 130 years of data from 3 areas: Isle Royale National Park in Lake Superior, Michigan, USA; the east‐central Superior National Forest in northeastern Minnesota, USA; and Denali National Park, Alaska, USA. Ratios between minimum and maximum annual sizes for 2 mainland populations (n = 28 and 46 yr) varied from 2.5–2.8, whereas for Isle Royale (n = 56 yr), the ratio was 6.3. The interquartile range (25th percentile, 75th percentile) for annual growth rates, N t +1/N t , was (0.88, 1.14), (0.92, 1.11), and (0.86, 1.12) for Denali, Superior National Forest, and Isle Royale respectively. We fit a density‐independent model and a Ricker model to each time series, and in both cases we considered the potential for observation error. Mean growth rates from the density‐independent model were close to 0 for all 3 populations, with 95% credible intervals including 0. We view the estimated model parameters, including those describing annual variability or process variance, as providing useful summaries of the trajectories of these populations. The estimates of these natural wolf population parameters can serve as benchmarks for comparison with those of recovering wolf populations. Because our study populations were all from circumscribed areas, fluctuations in them represent fluctuations in densities (i.e., changes in numbers are not confounded by changes in occupied area as would be the case with populations expanding their range, as are wolf populations in many states). © 2014 The Wildlife Society.

Non-stationary recruitment dynamics of rainbow smelt: The influence of environmental variables and variation in size structure and length-at-maturation

Fish stock-recruitment dynamics may be difficult to elucidate because of nonstationary relationships resulting from shifting environmental conditions and fluctuations in important vital rates such as individual growth or maturation. The Great Lakes have experienced environmental stressors that may have changed population demographics and stock-recruitment relationships while causing the declines of several prey fish species, including rainbow smelt (Osmerus mordax). We investigated changes in the size and maturation of rainbow smelt in Lake Michigan and Lake Huron and recruitment dynamics of the Lake Michigan stock over the past four decades. Mean lengths and length-at-maturation of rainbow smelt generally declined over time in both lakes. To evaluate recruitment, we used both a Ricker model and a Kalman filter-random walk (KF-RW) model which incorporated nonstationarity in stock productivity by allowing the productivity term to vary over time. The KF-RW model explained nearly four times more variation in recruitment than the Ricker model, indicating the productivity of the Lake Michigan stock has increased. By accounting for this nonstationarity, we were able identify significant variations in stock productivity, evaluate its importance to rainbow smelt recruitment, and speculate on potential environmental causes for the shift. Our results suggest that investigating mechanisms driving nonstationary shifts in stock-recruit relationships can provide valuable insights into temporal variation in fish population dynamics.

A possible mechanism for the attainment of out-of-phase periodic dynamics in two chaotic subpopulations coupled at low dispersal rate.

Much research in metapopulation dynamics has concentrated on identifying factors that affect coherence in spatially structured systems. In this regard, conditions for the attainment of out-of-phase dynamics have received considerable attention, due to the stabilizing effect of asynchrony on global dynamics. At low to moderate rates of dispersal, two coupled subpopulations with intrinsically chaotic dynamics tend to go out-of-phase with one another and also become periodic in their dynamics. The onset of out-of-phase dynamics and periodicity typically coincide. Here, we propose a possible mechanism for the onset of out-of-phase dynamics, and also the stabilization of chaos to periodicity, in two coupled subpopulations with intrinsically chaotic dynamics. We suggest that the onset of out-of-phase dynamics is due to the propensity of chaotic subpopulations governed by a steep, single-humped one-dimensional population growth model to repeatedly reach low subpopulation sizes that are close to a value Nt = A (A ≠ equilibrium population size, K) for which Nt( + 1) = K. Subpopulations with very similar low sizes, but on opposite sides of A, will become out-of-phase in the next generation, as they will end up at sizes on opposite sides of K, resulting in positive growth for one subpopulation and negative growth for the other. The key to the stabilization of out-of-phase periodic dynamics in this mechanism is the net effect of dispersal placing upper and lower bounds to subpopulation size in the two coupled subpopulations, once they have become out-of-phase. We tested various components of this proposed mechanism by simulations using the Ricker model, and the results of the simulations are consistent with predictions from the hypothesized mechanism. Similar results were also obtained using the logistic and Hassell models, and with the Ricker model incorporating the possibility of extinction, suggesting that the proposed mechanism could be key to the attainment and maintenance of out-of-phase periodicity in two-patch metapopulations where each patch has local dynamics governed by a single-humped population growth model.

Dynamics of larch bud moth populations: Application of Moran – Ricker models with time lag

Modifications of Moran–Ricker model with time lags are applied for fitting of larch bud moth (Zeiraphera diniana Gn.) time series. Model parameters were estimated, and deviations between model trajectories and empirical time series were analyzed with various statistical tests. It was shown that some of considered models allowed obtaining rather good fitting. For estimated parameters asymptotic stable dynamic regimes were found: it is 9-year cycle (for model with time lag in four years), it is 18-year cycle (with close values of cycle coordinates for model with time lag in one year), or regime with complicated dynamics (for model with time lag in three years). Obtained results correspond to biological imagination about fluctuations of larch bud moth populations.