Variation in Avian Predation Pressure as a Driver for the Diversification of Periodical Cicada Broods.

AbstractPeriodical cicadas live 13 or 17 years underground as nymphs, then emerge in synchrony as adults to reproduce. Developmentally synchronized populations called broods rarely coexist, with one dominant brood locally excluding those that emerge in off years. Twelve modern 17-year cicada broods are believed to have descended from only three ancestral broods following the last glaciation. The mechanisms by which these daughter broods overcame exclusion by the ancestral brood to synchronously emerge in a different year, however, are elusive. Here, we demonstrate that temporal variation in the population density of generalist predators can allow intermittent opportunities for new broods to invade, even though a single brood remains dominant most of the time. We show that this mechanism is consistent, in terms of the type and frequency of brood replacements, with the distribution of periodical cicada broods throughout North America today. Although we investigate one particularly charismatic case study, the mechanisms involved (competitive exclusion, Allee effects, trait variation, predation, and temporal variability) are ubiquitous and could contribute to patterns of species diversity in a range of systems.

The role of Allee effects for Gaussian and Lévy dispersals in an environmental niche.

In the study of biological populations, the Allee effect detects a critical density below which the population is severely endangered and at risk of extinction. This effect supersedes the classical logistic model, in which low densities are favorable due to lack of competition, and includes situations related to deficit of genetic pools, inbreeding depression, mate limitations, unavailability of collaborative strategies due to lack of conspecifics, etc. The goal of this paper is to provide a detailed mathematical analysis of the Allee effect. After recalling the ordinary differential equation related to the Allee effect, we will consider the situation of a diffusive population. The dispersal of this population is quite general and can include the classical Brownian motion, as well as a Lévy flight pattern, and also a "mixed" situation in which some individuals perform classical random walks and others adopt Lévy flights (which is also a case observed in nature). We study the existence and nonexistence of stationary solutions, which are an indication of the survival chance of a population at the equilibrium. We also analyze the associated evolution problem, in view of monotonicity in time of the total population, energy consideration, and long-time asymptotics. Furthermore, we also consider the case of an "inverse" Allee effect, in which low density populations may access additional benefits.

Spread and persistence for integro-difference equations with shifting habitat and strong Allee effect.

We study an integro-difference equation model that describes the spatial dynamics of a species with a strong Allee effect in a shifting habitat. We examine the case of a shifting semi-infinite bad habitat connected to a semi-infinite good habitat. In this case we rigorously establish species persistence (non-persistence) if the habitat shift speed is less (greater) than the asymptotic spreading speed of the species in the good habitat. We also examine the case of a finite shifting patch of hospitable habitat, and find that the habitat shift speed must be less than the asymptotic spreading speed associated with the habitat and there is a critical patch size for species persistence. Spreading speeds and traveling waves are established to address species persistence. Our numerical simulations demonstrate the theoretical results and show the dependence of the critical patch size on the shift speed.

Allee effects introduced by density dependent phenology.

We consider a hybrid model of an annual species with the timing of a stage transition governed by density dependent phenology. We show that the model can produce a strong Allee effect as well as overcompensation. The density dependent probability distribution that describes how population emergence is spread over time plays an important role in determining population dynamics. Our extensive numerical simulations with a density dependent gamma distribution indicate very rich population dynamics, from stable/unstable equilibria, limit cycles, to chaos.

Modelling mosquito population suppression based on competition system with strong and weak Allee effect.

Mosquito-borne diseases are threatening half of the world's population. To prevent the spread of malaria, dengue fever, or other mosquito-borne diseases, a new disease control strategy is to reduce or eradicate the wild mosquito population by releasing sterile mosquitoes. To study the effects of sterile insect technique on mosquito populations, we developed a mathematical model of constant release of sterile Aedes aegypti mosquitoes with strong and weak Allee effect and considered interspecific competition with Anopheles mosquitoes. We calculated multiple release thresholds and investigated the dynamical behavior of this model. In order to get closer to reality, an impulsive differential equation model was also introduced to study mosquito suppression dynamics under the strategy of releasing $ c $ sterile male mosquitoes at each interval time $ T $. Finally, the relationship between the releasing amount or the waiting period and the number of days required to suppress mosquitoes was illustrated by numerical simulations.

Demographic effects of aggregation in the presence of a component Allee effect.

The component Allee effect (AE) is the positive correlation between an organism's fitness component and population density. Depending on the population spatial structure, which determines the interactions between organisms, a component AE might lead to positive density dependence in the population per-capita growth rate and establish a demographic AE. However, existing spatial models impose a fixed population spatial structure, which limits the understanding of how a component AE and spatial dynamics jointly determine the existence of demographic AEs. We introduce a spatially explicit theoretical framework where spatial structure and population dynamics are emergent properties of the individual-level demographic and movement rates. This framework predicts various spatial patterns depending on its specific parametrization, including evenly spaced aggregates of organisms, which determine the demographic-level by-products of the component AE. We find that aggregation increases population abundance and allows population survival in harsher environments and at lower global population densities when compared with uniformly distributed organisms. Moreover, aggregation can prevent the component AE from manifesting at the population level or restrict it to the level of each independent aggregate. These results provide a mechanistic understanding of how component AEs might operate for different spatial structures and manifest at larger scales.

Dynamical analysis of a discrete two-patch model with the Allee effect and nonlinear dispersal.

The dynamic behavior of a discrete-time two-patch model with the Allee effect and nonlinear dispersal is studied in this paper. The model consists of two patches connected by the dispersal of individuals. Each patch has its own carrying capacity and intraspecific competition, and the growth rate of one patch exhibits the Allee effect. The existence and stability of the fixed points for the model are explored. Then, utilizing the central manifold theorem and bifurcation theory, fold and flip bifurcations are investigated. Finally, numerical simulations are conducted to explore how the Allee effect and nonlinear dispersal affect the dynamics of the system.

Ulam type stability for von Bertalanffy growth model with Allee effect.

In many studies dealing with mathematical models, the subject is examining the fitting between actual data and the solution of the mathematical model by applying statistical processing. However, if there is a solution that fluctuates greatly due to a small perturbation, it is expected that there will be a large difference between the actual phenomenon and the solution of the mathematical model, even in a short time span. In this study, we address this concern by considering Ulam stability, which is a concept that guarantees that a solution to an unperturbed equation exists near the solution to an equation with bounded perturbations. Although it is known that Ulam stability is guaranteed for the standard von Bertalanffy growth model, it remains unsolved for a model containing the Allee effect. This paper investigates the Ulam stability of a von Bertalanffy growth model with the Allee effect. In a sense, we obtain results that correspond to conditions of the Allee effect being very small or very large. In particular, a more preferable Ulam constant than the existing result for the standard von Bertalanffy growth model, is obtained as the Allee effect approaches zero. In other words, this paper even improves the proof of the result in the absence of the Allee effect. By guaranteeing the Ulam stability of the von Bertalanffy growth model with Allee effect, the stability of the model itself is guaranteed, and, even if a small perturbation is added, it becomes clear that even a small perturbation does not have a large effect on the solutions. Several examples and numerical simulations are presented to illustrate the obtained results.

Dynamics of a modified Leslie-Gower predator-prey model with double Allee effects.

In this paper, we investigate the dynamic behavior of a modified Leslie-Gower predator-prey model with the Allee effect on both prey and predator. It is shown that the model has at most two positive equilibria, where one is always a hyperbolic saddle and the other is a weak focus with multiplicity of at least three by concrete example. In addition, we analyze the bifurcations of the system, including saddle-node bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. The results show that the model has a cusp of codimension three and undergoes a Bogdanov-Takens bifurcation of codimension two. The system undergoes a degenerate Hopf bifurcation and has two limit cycles (the inner one is stable and the outer one is unstable). These enrich the dynamics of the modified Leslie-Gower predator-prey model with the double Allee effects.

Dynamics and control of a plant-herbivore model incorporating Allee's effect.

This research focuses on the interaction between the grape borer and grapevine using a discrete-time plant-herbivore model with Allee's effect. We specifically investigate a model that incorporates a strong predator functional response to better understand the system's qualitative behavior at positive equilibrium points. In the present study, we explore the topological classifications at fixed points, stability analysis, Neimark-Sacker, Transcritical bifurcation and State feedback control in the two-dimensional discrete-time plant-herbivore model. It is proved that for all involved parameters ς1,ϱ1,γ1 and ϒ1, discrete-time plant-herbivore model has boundary and interior fixed points: c1=(0,0), c2=(ς1-1ϱ1,0) and c3=(ϒ1(1-γ1)2γ1-1,γ1(2ς1+ϱ1ϒ1-2)-ϱ1ϒ1+1-ς12γ1-1) respectively. Then by linear stability theory, local dynamics with different topological classifications are investigated at fixed points: c1=(0,0), c2=(ς1-1ϱ1,0) and c3=(ϒ1(1-γ1)2γ1-1,γ1(2ς1+ϱ1ϒ1-2)-ϱ1ϒ1+1-ς12γ1-1). Our investigation uncovers that the boundary equilibrium c2=(ς1-1ϱ1,0) experiences a transcritical bifurcation, whereas the unique positive steady-state c3=(ϒ1(1-γ1)2γ1-1,γ1(2ς1+ϱ1ϒ1-2)-ϱ1ϒ1+1-ς12γ1-1) of the discrete-time plant-herbivore model undergoes a Neimark-Sacker bifurcation. To address the periodic fluctuations in grapevine population density and other unpredictable behaviors observed in the model, we propose implementing state feedback chaos control. To support our theoretical findings, we provide comprehensive numerical simulations, phase portraits, dynamics diagrams, and a graph of the maximum Lyapunov exponent. These visual representations enhance the clarity of our research outcomes and further validate the effectiveness of the chaos control approach.

Boric acid toxic sugar bait suppresses male Aedes aegypti (Diptera: Culicidae): wing beat frequency and amplitude, flight activity, fecundity, insemination, and mate-finding Allee effect.

BACKGROUND: Controlling the spread of arboviral diseases remains a considerable challenge due to the rapid development of insecticide resistance in Aedes mosquitoes. This study evaluated the effects of boric acid-containing toxic sugar bait (TSB) on field populations of resistant Aedes aegypti mosquitoes. In addition, this study examined the flight activity and wing beat frequency and amplitude of males and the flight activity, fecundity, and insemination of females after pairing with males exposed to TSB. The population dynamics of Aedes mosquitoes under imbalanced sex ratios were examined to simulate realistic field conditions for male suppression under the effect of TSB. RESULTS: The mortality of male mosquitoes was consistently high within 24 h after exposure. By contrast, the mortality of female mosquitoes was inconsistent, with over 70% mortality observed at 168 h. The flight activity and wing beat amplitude of treated males were significantly lower than those of controls, but no significant difference in wing beat frequency was detected. The fecundity and insemination of treated female mosquitoes were lower than those of controls. A simulation study indicated that considerably low male population densities led to mating failures, triggering a mate-finding Allee effect and resulting in persistently low population levels. CONCLUSION: Boric acid-containing TSB could effectively complement current chemical intervention approaches to control resistant mosquito populations. TSB is effective in reducing field male populations and impairing male flight activity and female-seeking behavior, resulting in decreased fecundity and insemination. Male suppression due to TSB potentially results in a small mosquito population. © 2024 Society of Chemical Industry.

Sustainable management of predatory fish affected by an Allee effect through marine protected areas and taxation.

Ecological balance and stable economic development are crucial for the fishery. This study proposes a predator-prey system for marine communities, where the growth of predators follows the Allee effect and takes into account the rapid fluctuations in resource prices caused by supply and demand. The system predicts the existence of catastrophic equilibrium, which may lead to the extinction of prey, consequently leading to the extinction of predators, but fishing efforts remain high. Marine protected areas are established near fishing areas to avoid such situations. Fish migrate rapidly between these two areas and are only harvested in the nonprotected areas. A three-dimensional simplified model is derived by applying variable aggregation to describe the variation of global variables on a slow time scale. To seek conditions to avoid species extinction and maintain sustainable fishing activities, the existence of positive equilibrium points and their local stability are explored based on the simplified model. Moreover, the long-term impact of establishing marine protected areas and levying taxes based on unit catch on fishery dynamics is studied, and the optimal tax policy is obtained by applying Pontryagin's maximum principle. The theoretical analysis and numerical examples of this study demonstrate the comprehensive effectiveness of increasing the proportion of marine protected areas and controlling taxes on the sustainable development of fishery.

Viability of the vaquita, Phocoena sinus (Cetacea: Phocoenidae) population, threatened by poaching of Totoaba macdonaldi (Perciformes: Sciaenidae) / Viabilidad de la población de vaquita marina, Phocoena sinus (Cetacea: Phocoenidae), amenazada por la pesca ilegal de Totoaba macdonaldi (Perciformes: Sciaenidae)

Abstract Introduction: Despite extensive science-based conservation policy recommendations, with fewer than 20 individuals remaining, the vaquita (Phocoena sinus) -endemic to the Gulf of California- is the world's most endangered marine mammal due to incidental catch in fishing nets and whether it can recover is unclear. Objective: Assess expectations for vaquita over the next two decades. Methods: We identified factors affecting the vaquita, constructed life tables, derived demographic parameters for different scenarios and conducted a population viability analysis using stochastic age-structured matrix Leslie models. Results: Analytical results indicate that the vaquita net growth rate is particularly sensitive to juvenile survival. We find that intensive, ongoing bycatch in gillnets used to poach totoaba (Totoaba macdonaldi) over the past decade brought the vaquita population to its current critically low size. Currently this seems to be exacerbated by demographic stochasticity and a potential Allee effect. Conclusions: If totoaba poaching is eliminated immediately, demographically, vaquita can recover; its long-term survival will depend on its uncertain genetic status, although a recent study found encouraging results in this regard.

Resumen Introducción: Pese a las acciones de conservación basadas en la ciencia y las políticas recomendadas, con menos de 20 individuos sobrevivientes, la vaquita (Phocoena sinus) -endémica del Golfo de California- es el mamífero marino más amenazado del mundo debido a su muerte incidental en redes de pesca; una pregunta relevante es si su población se puede recuperar. Objetivo: Evaluar las expectativas para la vaquita marina durante los próximos 20 años. Métodos: Identificamos los factores que afectan a la vaquita marina, construimos tablas de vida, derivamos parámetros demográficos para diferentes escenarios y realizamos un análisis de viabilidad poblacional utilizando matrices estocásticas de Leslie, estructuradas por edad. Resultados: La tasa de crecimiento neto de la vaquita es muy sensible a la supervivencia de los juveniles. Encontramos que la captura incidental intensiva y continua en redes de enmalle para la pesca furtiva de totoaba (Totoaba macdonaldi) durante la última década llevó a la población de vaquitas a su actual estado crítico. Esto parece agravarse por la estocasticidad demográfica y un potencial efecto Allee. Conclusiones: Si la pesca furtiva de totoaba se elimina de inmediato, demográficamente la vaquita puede recuperarse; su supervivencia a largo plazo dependerá de su incierto estatus genético, aunque los resultados de un estudio reciente son alentadores en este sentido.

Is the Queen conch Strombus gigas (Mesogastropoda: Strombidae) a species with Allee effect? / Es el caracol marino Strombus gigas (Mesogastropoda: Strombidae) una especie con efecto Allee?

The marine park of Xel-Há has a population of Strombus gigas which breeds in the area. We determined the relationship between reproductive activity, conch density and environmental parameters. Samples were collected from February to December 2012, using the transect method, at four sites of Marine Park Xel-Ha, Quintana Roo, Mexico. Sediment samples were analyzed and classified using Folk & Ward’s method. Temperature, salinity and dissolved oxygen were also recorded. Density had a small correlation with sediment (Pearson r=0.29 with very coarse and r=0.26 with coarse sand), while mating and spawning had a correlation of r=0.54 and 0.62 with medium sand, respectively. Density was high in the four sites and was not associated with mating and spawning (r=0.08 and 0.03, respectively). For reproduction, S. gigas requires specific substrate conditions (sandy effect) and not just a density of 56 Conch Ha-1 (Allee effect).

El parque marino de Xel -Há tiene una población de Strombus gigas que se cría en la zona. Determinamos la relación entre la actividad reproductiva, la densidad de la concha de S. gigas y los parámetros ambientales. Las muestras fueron recolectadas de febrero a diciembre de 2012, utilizando el método de transecto, en cuatro sitios del Parque Marino de Xel -Ha, Quintana Roo, México. Fueron analizados y clasificados utilizando la metodología de Folk & Ward. También se registraron temperaturas, salinidad y oxígeno disuelto. La densidad de concha mostró una baja correlación en la categoría de sedimentos (r = 0.29 , con muy gruesos y r = 0.26 con arena gruesa ), mientras que el apareamiento y desove con arena media mostraron una correlación de r = 0.54 y 0.62, respectivamente. Las densidades en cuatro sitios fueron altas y no se asociaron con el número de apareamientos y desove (r = 0.08 y 0.03, respectivamente). Para la reproducción, S. gigas requiere condiciones específicas de sustrato (efecto arenoso) y no sólo una densidad de 56 Conch Ha-1 (efecto Allee ).

Declining densities and reproductive activities of the queen conch Strombus gigas (Mesogastropoda: Strombidae) in Banco Chinchorro, Eastern Caribbean, Mexico / Disminución de la densidad y actividades reproductivas de la concha reina Strombus gigas (Mesogastropoda: Strombidae) en el Banco Chinchorro, Caribe Oriental

Queen conch is a gastropod inhabiting the Caribbean Sea, it represents the second largest fishery after the spiny lobster, but it has been extensively captured in the area. In order to know its population status in Chinchorro Bank, we determined conch density changes and its effects on reproductive activities, between July and November 2009. For this, data on conch density, morphology and reproductive activities were obtained from 15 sites within three fishing zones, and compared with previously collected data (1990, 1992, 1994, and 1997). Data showed that adult density decreased with time, from 10 700ind./ha in 1990, to 198ind./h in 2009. Neither egg masses nor spawns were found and mating was only observed once in July 2009. In July, adult (lip>4mm) density in the Southern zone was 23ind./ha whereas in the Northern zone and Central zone densities were 15 and 9ind./ha respectively. In November, density was somewhat higher: Southern zone 96ind./ha; Central zone 39ind./ha and Northern zone had 38ind./ha. In July, mean shell length was 170.80±46.28mm, with a higher median abundance at 180-189mm. In November, higher frequency was 187.63±45.14mm, maximum at 210-219mm interval. For the last 10 years period, mean adult conch densities have diminished in each zone, which might be the main cause of decreased reproductive activities of the conch at Banco Chinchorro. It is therefore an immediate need to analyse the management plan for this species in this Reserve and perhaps to promote a re-population of queen conch and culture activities. Rev. Biol. Trop. 61 (4): 1671-1679. Epub 2013 December 01.

El caracol Rosado es un gasterópodo que habita en el Caribe, y representa la segunda pesquería después de la langosta espinosa, sin embargo, el caracol ha sido pescado a niveles de casi extinción. Para conocer el estatus de la población se analizaron los cambios de densidad del caracol rosado en Banco Chinchorro y su efecto en las actividades reproductivas entre julio y noviembre 2009. Se recolectaron datos de densidad y morfología en tres zonas de pesca en 15 localidades; y se compararon con datos recolectados previamente en los mismos sitios (1990, 1992, 1994, y 1997). Los datos mostraron que la densidad de adultos ha decrecido con el tiempo de 10 700 (ind./ha) en 1990 a 198 (ind./ha). Las actividades reproductivas o productos se registraron, no se encontraron ni masas de huevo ni desoves, y únicamente se observó una copulación en julio. Considerando únicamente a los adultos (labio>4mm), en julio 2009, la densidad fue de 23ind./ha, mientras que en la zona norte y centro las densidades fueron 15 and 9 (ind./ha). En noviembre 2009, la densidad fue ligeramente más alta: zona sur 96 (ind./ha); zona Centro 39 (ind./ha) y zona Norte 38 (ind./ha). En julio (2009) la longitud de concha promedio fue de 170.80±46.28mm, con una mayor abundancia en las tallas 180-189mm. En noviembre (2009) la frecuencia más alta ocurrió en las talla promedio 187.63±45.14mm, con un intervalo de 210-219mm de longitud de concha. En los últimos 10 años, la densidad de los caracoles adultos ha disminuido en cada una de las zonas de pesca, lo cual podría ser la causa de la disminución de las actividades reproductivas del caracol rosado en Banco Chinchorro.

Densidad, estructura de tallas y actividad reproductiva del caracol rosado Eustrombus gigas (Mesogastropoda: Strombidae) en Banco Chinchorro, México / Density, size structure and reproductive activity of the pink conch Eustrombus gigas (Mesogastropoda: Strombidae) in Banco Chinchorro, Mexico

The pink conch Eustrombus gigas is an important fisheries resource. At the regional level in the Caribbean, over-exploitation and habitat destruction have caused a decrease in the abundance of this resource. In order to provide necessary information for the species management in Mexico, this work aimed to analyze the total density, adult density, size structure and reproductive behavior of pink conch population at Banco Chinchorro during 2009-2010. Data from three seasons were obtained (rainy, dry and cold fronts periods) in three areas: Norte (North), Centro (Center) and Sur (South). The organisms were separated into two groups: (a) the criteria based upon legal harvest in Mexico: legal size conchs (siphonal length≥200mm) and illegal size conchs (siphonal length<200mm), and (b) the criteria based upon sexual maturity using the 15mm lip thickness standard: lip<15mm as juvenile conch and lip≥15mm as adult conch. Copulation, spawning, egg masses and aggregations were evaluated as reproductive evidences. The highest total density was observed during the dry season with 384ind./ha, and the lowest during the rainy season with 127ind./ha. The highest density was reported at Sur (385ind./ha) and the lowest at Norte (198ind./ha). The highest adult density was observed during the rainy season (8.33ind./ha), and the lowest occurred in the dry season (6.11ind./ha). Adult density values were 5.55, 7.05 and 8.33ind./ha for Centro, Sur and Norte areas, respectively. Adult densities were lower than the threshold needed for reproduction, and 42% of the population may be vulnerable to fishing, as they had the minimum size for catch (Lsi 200mm). Furthermore, only 2.2% of the population reached a Gl>15mm as sexual maturity indicator. During the study period, only six evidences of reproductive activity were observed. The smaller densities reported at Banco Chinchorro may cause reproduction events to be almost absent which in turn is sufficient ...

Eustrombus gigas es uno de los recursos pesqueros costeros más valiosos en la región del Caribe y constituye un molusco con un elevado valor estético y ecológico. En esta investigación se evalúa su densidad total, densidad de adultos, la estructura de tallas y frecuencia de evidencias reproductivas en Banco Chinchorro, México, periodo 2009-2010; durante tres períodos (de lluvias, seca y de frentes fríos) en tres zonas: Norte, Centro y Sur. La densidad total para el área de estudio varió de 127ind./ha en lluvias a 384ind./ha en seca, la menor densidad se presentó en la zona Norte del Banco (198ind./ha) y la mayor en la zona Sur (385ind./ha). La densidad de caracoles adultos fue baja (6.11ind./ha en seca y 8.33ind./ha en lluvias y 5.55, 7.05 y 8.33ind./ha para las zonas Centro, Sur y Norte, respectivamente). Las densidades de adultos estuvieron por debajo del umbral mínimo necesario para mantener la reproducción. El 42% de la población es vulnerable a la pesca (Lsi≥200mm); sin embargo, solo 2.2% de la población alcanza un Gl>15mm. Solo se observaron seis evidencias de reproducción durante el período de estudio, lo que señala la presencia del efecto Allee en la población y la urgente necesidad del cierre de su pesquería. Se proponen tres puntos importantes para el manejo de la especie: cierre de la pesca, monitoreo de la población y la implementación refugios pesqueros.