Cats Are Not Fish: A Ricker Model Fails to Account for Key Aspects of Trap-Neuter-Return Programs.

In a frequently cited 2005 paper, a Ricker model was used to assess the effectiveness of trap-neuter-return (TNR) programs for managing free-roaming domestic cat populations. The model (which was originally developed for application in the management of fisheries) used data obtained from two countywide programs, and the results indicated that any population reductions, if they existed, were at best modest. In the present study, we applied the same analysis methods to data from two long-term (i.e., >20 years) TNR programs for which significant population reductions have been documented. Our results revealed that the model cannot account for some key aspects of typical TNR programs, and the wild population swings it predicts do not correspond to the relative stability of free-roaming cat populations. A Ricker model is therefore inappropriate for use in assessing the effectiveness of TNR programs. A more recently developed, stochastic model, which accounts for the movement of cats in and out of a given area, is better suited for predicting the sterilization effort necessary to reduce free-roaming cat numbers through TNR programs.

Using the intrinsic growth rate of the mosquito population improves spatio-temporal dengue risk estimation.

Understanding geographic population dynamics of mosquitoes is an essential requirement for estimating the risk of mosquito-borne disease transmission and geographically targeted interventions. However, the use of population dynamics measures, such as the intrinsic growth rate, as predictors in spatio-temporal point processes has not been investigated before. In this work we compared the predictive accuracy of four spatio-temporal log-Gaussian Cox models: (i) With no predictors; (ii) mosquito abundance as predictor; (iii) intrinsic growth rate as predictor; (iv) intrinsic growth rate and mosquito abundance as predictors. This analysis is based on Aedes aegypti mosquito surveillance and human dengue data obtained from the urban area of Caratinga, Brazil. We used a statistical Moran Curve approach to estimate the intrinsic growth rate and a zero inflated Poisson kriging model for estimating mosquito abundance at locations of dengue cases. The incidence of dengue cases was positively associated with mosquito intrinsic growth rate and this model outperformed, in terms of predictive accuracy, the abundance and the null models. The latter includes only the spatio-temporal random effect but no predictors. In the light of these results we suggest that the intrinsic growth rate should be investigated further as a potential tool for predicting the risk of dengue transmission and targeting health interventions for vector-borne diseases.

Empirical orthogonal function regression: Linking population biology to spatial varying environmental conditions using climate projections.

Ecologists and oceanographers inform population and ecosystem management by identifying the physical drivers of ecological dynamics. However, different research communities use different analytical tools where, for example, physical oceanographers often apply rank-reduction techniques (a.k.a. empirical orthogonal functions [EOF]) to identify indicators that represent dominant modes of physical variability, whereas population ecologists use dynamical models that incorporate physical indicators as covariates. Simultaneously modeling physical and biological processes would have several benefits, including improved communication across sub-fields; more efficient use of limited data; and the ability to compare importance of physical and biological drivers for population dynamics. Here, we develop a new statistical technique, EOF regression, which jointly models population-scale dynamics and spatially distributed physical dynamics. EOF regression is fitted using maximum-likelihood techniques and applies a generalized EOF analysis to environmental measurements, estimates one or more time series representing modes of environmental variability, and simultaneously estimates the association of this time series with biological measurements. By doing so, it identifies a spatial map of environmental conditions that are best correlated with annual variability in the biological process. We demonstrate this method using a linear (Ricker) model for early-life survival ("recruitment") of three groundfish species in the eastern Bering Sea from 1982 to 2016, combined with measurements and end-of-century projections for bottom and sea surface temperature. Results suggest that (a) we can forecast biological dynamics while applying delta-correction and statistical downscaling to calibrate measurements and projected physical variables, (b) physical drivers are statistically significant for Pacific cod and walleye pollock recruitment, (c) separately analyzing physical and biological variables fails to identify the significant association for walleye pollock, and (d) cod and pollock will likely have reduced recruitment given forecasted temperatures over future decades.

Using mathematical models to describe aerial dispersal and silk ball formation of peanut red spider mite, Tetranychus ogmophallos (Acari: Tetranychidae).

Peanut red spider mite, Tetranychus ogmophallos, exhibits a peculiar dispersal behavior using silk balls, which involves clustering of mites and spinning of webs at the top of plants. Such a dispersal mechanism has not been studied for this species yet. Therefore, this study aimed at using mathematical models to describe aerial dispersal and silk ball formation of peanut red spider mite on peanut plants. The influence of wind speed, generated by a wind tunnel, on the dispersal of mites was studied in two experiments, one with 500 mites per plant and one with 1000 mites per plant, and six wind speeds (5, 10, 15, 20, 25, and 30 km h-1) for each mite density. The proportion of displaced mites and the distance they were blown were measured. Another series of experiments considered the formation of silk balls to assess how fast balls were formed as a function of time and the number of mites present on a peanut plant. Data from the wind tunnel experiments were analyzed by logistic regression and multiple regression to assess the proportion of displaced mites and the distance moved, respectively, as functions of wind speed and the initial density of mites on the donor plant. The distribution of dispersal distances from the donor plant was fitted by a mathematical model proposed by Ricker (J Fish Res Board Can 11:559-623, 1954). The number of mites moving upwards on a plant to be involved in silk ball formation was modeled as a function of time based on the initial number of spider mites and their estimated birth, death and movement rates per capita. Logistic regression was used to analyze the presence of balls as a function of time elapsed since a plant was infested with spider mites. Finally, non-linear regression was applied to link ball size to the total number of mites occupying the ball. The data analyses revealed that wind speed had a significant positive effect on take-off probability and distance moved by individual mites, whereas mite density had little influence. Ricker's model adequately described the distribution of dispersal distances. The models describing silk ball formation also described data very well. Ball size was found to increase almost linearly with the number of mites found in the ball. We expect that the knowledge provided by the present study will help to develop efficient management strategies against T. ogmophallos in peanut crops as dispersal seems to be a key factor in the species' capability to become a serious pest.

Age structured discrete-time disease models with demographic population cycles.

We use juvenile-adult discrete-time infectious disease models with intrinsically generated demographic population cycles to study the effects of age structure on the persistence or extinction of disease and the basic reproduction number, [Formula: see text]. Our juvenile-adult Susceptible-Infectious-Recovered (SIR) and Infectious-Salmon Anemia-Virus (ISA[Formula: see text] models share a common disease-free system that exhibits equilibrium dynamics for the Beverton-Holt recruitment function. However, when the recruitment function is the Ricker model, a juvenile-adult disease-free system exhibits a range of dynamic behaviours from stable equilibria to deterministic period k population cycles to Neimark-Sacker bifurcations and deterministic chaos. For these two models, we use an extension of the next generation matrix approach for calculating [Formula: see text] to account for populations with locally asymptotically stable period k cycles in the juvenile-adult disease-free system. When [Formula: see text] and the juvenile-adult demographic system (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove that the juvenile-adult disease goes extinct whenever [Formula: see text]. Under the same period k juvenile-adult demographic assumption but with [Formula: see text], we prove that the juvenile-adult disease-free period k population cycle is unstable and the disease persists. When [Formula: see text], our simulations show that the juvenile-adult disease-free period k cycle dynamics drives the juvenile-adult SIR disease dynamics, but not the juvenile-adult ISAv disease dynamics.

Hierarchical multi-population viability analysis.

Population viability analysis (PVA) uses concepts from theoretical ecology to provide a powerful tool for quantitative estimates of population dynamics and extinction risks. However, conventional statistical PVA requires long-term data from every population of interest, whereas many species of concern exist in multiple isolated populations that are only monitored occasionally. We present a hierarchical multi-population viability analysis model that increases inference power from sparse data by sharing information among populations to assess extinction risks while accounting for incomplete detection and sampling biases with explicit observation and sampling sub-models. We present a case study in which we customized this model for historical population monitoring data (1985-2015) from federally threatened Lahontan cutthroat trout populations in the Great Basin, USA. Data were counts of fish captured during backpack electrofishing surveys from locations associated with 155 isolated populations. Some surveys (25%) included multi-pass removal sampling, which provided valuable information about capture efficiency. GIS and remote sensing were used to estimate August stream temperatures, peak flows, and riparian vegetation condition in each population each year. Field data were used to derive an annual index of nonnative trout densities. Results indicated that population growth rates were higher in colder streams and that nonnative trout reduced carrying capacities of native trout. Extinction risks increased with more environmental stochasticity and were also related to population extent, water temperatures, and nonnative densities. We developed a graphical user interface to interact with the fitted model results and to simulate future habitat scenarios and management actions to assess their influence on extinction risks in each population. Hierarchical multi-population viability analysis bridges the gap between site-level field observations and population-level processes, making effective use of existing datasets to support management decisions with robust estimates of population dynamics, extinction risks, and uncertainties.

Stabilization of Structured Populations via Vector Target-Oriented Control.

In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a one-dimensional setting. Here, by introducing target-oriented control for discrete dynamical systems, we prove the possibility to stabilize a chosen state for a wide range of structured population models. The results are illustrated with introducing a control in the celebrated LPA model describing a flour beetle dynamics. Moreover, we show that the new control allows to stabilize periodic solutions for higher-order difference equations, such as the delayed Ricker model, for which previous target-oriented methods were not designed.

How environmental noise can contract and destroy a persistence zone in population models with Allee effect.

A problem of the analysis of the noise-induced extinction in population models with Allee effect is considered. To clarify mechanisms of the extinction, we suggest a new technique combining an analysis of the geometry of attractors and their stochastic sensitivity. For the conceptual one-dimensional discrete Ricker-type model, on the base of the bifurcation analysis, deterministic persistence zones are constructed in the space of initial states and biological parameters. It is shown that the random environmental noise can contract, and even destroy these persistence zones. A parametric analysis of the probabilistic mechanism of the noise-induced extinction in regular and chaotic zones is carried out with the help of the unified approach based on the sensitivity functions technique and confidence domains method.

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.

An explicit solution for calculating optimum spawning stock size from Ricker's stock recruitment model.

Stock-recruitment models have been used for decades in fisheries management as a means of formalizing the expected number of offspring that recruit to a fishery based on the number of parents. In particular, Ricker's stock recruitment model is widely used due to its flexibility and ease with which the parameters can be estimated. After model fitting, the spawning stock size that produces the maximum sustainable yield (S MSY) to a fishery, and the harvest corresponding to it (U MSY), are two of the most common biological reference points of interest to fisheries managers. However, to date there has been no explicit solution for either reference point because of the transcendental nature of the equation needed to solve for them. Therefore, numerical or statistical approximations have been used for more than 30 years. Here I provide explicit formulae for calculating both S MSY and U MSY in terms of the productivity and density-dependent parameters of Ricker's model.

Population dynamics of Armigeres subalbatus (Diptera: Culicidae) across a temperate altitudinal gradient.

Understanding the impacts of weather fluctuations, and environmental gradients, on the abundance of vectors is fundamental to grasp the dynamic nature of the entomological risk for disease transmission. The mosquito Armigeres subalbatus (Coquillet) is a common vector of filariasis. Nevertheless, its population dynamics have been relatively poorly studied. Here, we present results from a season long study where we studied spatio-temporal abundance patterns of Ar. subalbatus across the altitudinal gradient of Mt. Konpira in Nagasaki, Japan. Spatially, we found that abundance of adult Ar. subalbatus decreased with altitude and increased in areas where the ground was rich in leaf litter. Similarly, adult activity was observed only when relative humidity was over 65%. Temporally, we found that peaks in abundance followed large rainfall events. Nevertheless, this mosquito was under significant density dependence regulation. Our results suggest that Ar. subalbatus population peaks following large rainfall events could reflect the recruitment of individuals that were dormant as dry eggs. We did not find a clear signal of temperature on abundance changes of this mosquito, but only on its phenology. Since ground cover seemed more critical than temperature to its spatial distribution, we propose that this mosquito might have some degree of autonomy to changes in temperature.

A comparison of six methods for stabilizing population dynamics.

Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very different concepts of stability, which makes it difficult to compare their relative efficiencies. Moreover, since the dynamics of populations are dependent on the life-history of the species and its environment, it is conceivable that the stabilizing effects of control methods would also be affected by such factors, a complication that has typically not been investigated. In this study, we compare six different control methods with respect to their efficiency at inducing a common level of enhancement (defined as 50% increase) for two kinds of stability (constancy and persistence) under four different life-history/environment combinations. Since these methods have been analytically studied elsewhere, we concentrate on an intuitive understanding of realistic simulations incorporating noise, extinction probability and lattice effect. We show that for these six methods, even when the magnitude of stabilization attained is the same, other aspects of the dynamics like population size distribution can be very different. Consequently, correlated aspects of stability, like the amount of persistence for a given degree of constancy stability (and vice versa) or the corresponding effective population size (a measure of resistance to genetic drift) vary widely among the methods. Moreover, the number of organisms needed to be added or removed to attain similar levels of stabilization also varies for these methods, a fact that has economic implications. Finally, we compare the relative efficiencies of these methods through a composite index of various stability related measures. Our results suggest that Lower Limiter Control (LLC) seems to be the optimal method under most conditions, with the recently proposed Adaptive Limiter Control (ALC) being a close second.

Effects of symmetric and asymmetric dispersal on the dynamics of heterogeneous metapopulations: two-patch systems revisited.

Although the effects of dispersal on the dynamics of two-patch metapopulations are well studied, potential interactions between local dynamics and asymmetric dispersal remain unexplored. We examined the dynamics of two Ricker models coupled by symmetric or asymmetric constant-fraction dispersal at different rates. Unlike previous studies, we extensively sampled the r1-r2 space and found that stability of the coupled system was markedly affected by interactions between dispersal (in terms of strength and asymmetry) and local dynamics. When both subpopulations were intrinsically chaotic, increased symmetry in the exchange of individuals had a greater stabilizing impact on the dynamics of the system. When one subpopulation showed considerably more unstable dynamics than the other, higher asymmetry in the exchange of individuals had a stabilizing or destabilizing effect on the dynamics depending on whether the net dispersal bias was from the relatively stable to the relatively unstable subpopulation, or vice versa. The sensitivity of chaotic dynamics to stabilization due to dispersal varied with r-value in the chaotic subpopulation. Under unidirectional or bidirectional symmetric dispersal, when one subpopulation was intrinsically chaotic and the other had stable dynamics, the stabilization of chaotic subpopulations with r~3.3-4.0 occurred at the lowest dispersal rates, followed by chaotic subpopulations with r~2.7-2.95 and, finally, chaotic subpopulations with r~2.95-3.3. The mechanism for this pattern is not known but might be related to the range and number of different attainable population sizes possible in different r-value zones.

Time-lag in extinction dynamics in experimental populations: evidence for a genetic Allee effect?

1. Propagule pressure, i.e. the number of individuals introduced, is thought to be a major predictor of the establishment success of introduced populations in the field. Its influence in laboratory experimental systems has however been questioned. In fact, other factors involved in long-term population persistence, like habitat size, were usually found to explain most of the dynamics of experimental populations. 2. To better understand the respective influence of short- and long-term factors and their potential interaction on extinction dynamics in experimental systems, we investigated the influence of propagule pressure, habitat size and genetic background on the early dynamics of laboratory-based populations of a hymenopteran parasitoid. 3. The amount of demographic variance differed between establishment and persistence phase and was influenced by habitat size and genetic background (geographic strain), but independent of propagule pressure. In contrast, the probability of extinction within five generations depended on the genetic background and on the interaction between propagule pressure and habitat size. Vulnerability to extinction in small size habitats was increased when populations were founded with a small number of individuals, but this effect was delayed until the third to fifth generations. 4. These results indicate that demographic stochasticity is influential during population establishment, but is not affected by the genetic variability of propagules. On the other hand, extinction might be influenced by a genetic Allee effect triggered by the combination of low propagule pressure and genetic drift. Finally, we documented consistent differences between genetic backgrounds in both deterministic and stochastic population dynamics patterns, with major consequences on extinction risk and ultimately population establishment.