Periodic dynamics in a two-stage Allee effect model are driven by tension between stage equilibria

Single species difference population models can show complex dynamics such as periodicity and chaos under certain circumstances, but usually only when rates of intrinsic population growth or other life history parameter are unrealistically high. Single species models with Allee effects (positive density dependence at low density) have also been shown to exhibit complex dynamics when combined with over-compensatory density dependence or a narrow fertility window. Here we present a simple two-stage model with Allee effects which shows large amplitude periodic fluctuations for some initial conditions, without these requirements. Periodicity arises out of a tension between the critical equilibrium of each stage, i.e. when the initial population vector is such that the adult stage is above the critical value, while the juvenile stage is below the critical value. Within this area of parameter space, the range of initial conditions giving rise to periodic dynamics is driven mainly by adult mortality rates. Periodic dynamics become more important as adult mortality increases up to a certain point, after which periodic dynamics are replaced by extinction. This model has more realistic life history parameter values than most 'chaotic' models. Conditions for periodic dynamics might arise in some marine species which are exploited (high adult mortality) leading to recruitment limitation (low juvenile density) and might be an additional source of extinction risk.     

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R₀=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R₀) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R₀>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).     

Losing your edge: climate change and the conservation value of range‐edge populations

Populations occurring at species' range edges can be locally adapted to unique environmental conditions. From a species' perspective, range‐edge environments generally have higher severity and frequency of extreme climatic events relative to the range core. Under future climates, extreme climatic events are predicted to become increasingly important in defining species' distributions. Therefore, range‐edge genotypes that are better adapted to extreme climates relative to core populations may be essential to species' persistence during periods of rapid climate change. We use relatively simple conceptual models to highlight the importance of locally adapted range‐edge populations (leading and trailing edges) for determining the ability of species to persist under future climates. Using trees as an example, we show how locally adapted populations at species' range edges may expand under future climate change and become more common relative to range‐core populations. We also highlight how large‐scale habitat destruction occurring in some geographic areas where many species range edge converge, such as biome boundaries and ecotones (e.g., the arc of deforestation along the rainforest‐cerrado ecotone in the southern Amazonia), can have major implications for global biodiversity. As climate changes, range‐edge populations will play key roles in helping species to maintain or expand their geographic distributions. The loss of these locally adapted range‐edge populations through anthropogenic disturbance is therefore hypothesized to reduce the ability of species to persist in the face of rapid future climate change.     

Allee effect and self-fertilization in hermaphrodites: reproductive assurance in demographically stable populations

The fact that selfing increases seed set (reproductive assurance) has often been put forward as an important selective force for the evolution of selfing. However, the role of reproductive assurance in hermaphroditic populations is far from being clear because of a lack of theoretical work. Here, I propose a theoretical model that analyzes self-fertilization in the presence of reproductive assurance. Because reproductive assurance directly influences the per capita growth rate, I developed an explicit demographic model for partial selfers in the presence of reproductive assurance, specifically when outcrossing is limited by the possibility of pollen transfer (Allee effect). Mating system parameters are derived as a function of the underlying demographical parameters. The functional link between population demography and mating system parameters (reproductive assurance, selfing rate) can be characterized. The demographic model permits the analysis of the evolution of self-fertilization in stable populations when reproductive assurance occurs. The model reveals some counterintuitive results such as the fact that increasing the fraction of selfed ovules can, in certain circumstances, increase the fraction of outcrossed ovules. Moreover, I demonstrate that reproductive assurance per se cannot account for the evolution of stable mixed selfing rates. Also, the model reveals that the extinction of outcrossing populations depends on small changes in population density (ecological perturbations), while the transition from outcrossing to selfing can, in certain cases, lead the population to extinction (evolutionary suicide). More generally, this paper highlights the fact that self-fertilization affects both the dynamics of individuals and the dynamics of selfing genes in hermaphroditic populations.     

Pushed beyond the brink: Allee effects,environmental stochasticity,and extinction

To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that persistence requires that the geometric mean of fitness at low densities is greater than one. When this geometric mean is less than one, asymptotic extinction occurs with high probability for low initial population densities. Additionally, if the population only experiences positive density-dependent feedbacks, conditional persistence occurs provided the geometric mean of fitness at high population densities is greater than one. However, if the population experiences both positive and negative density-dependent feedbacks, conditional persistence only occurs if environmental fluctuations are sufficiently small. We illustrate counter-intuitively that environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and can cause asymptotic extinction of populations experiencing intermediate predation rates despite conditional persistence occurring at higher predation rates.     

Allee effect in larval resource exploitation in Drosophila: an interaction among density of adults, larvae, and micro-organisms

Abstract 1. Aggregation pheromones can evolve when individuals benefit from clustering. Such a situation can arise with an Allee effect, i.e. a positive relationship between individual fitness and density of conspecifics. Aggregation pheromone in Drosophila induces aggregated oviposition. The aim of the work reported here was to identify an Allee effect in the larval resource exploitation by Drosophila melanogaster, which could explain the evolution of aggregation pheromone in this species. 2. It is hypothesised that an Allee effect in D. melanogaster larvae arises from an increased efficiency of a group of larvae to temper fungal growth on their feeding substrate. To test this hypothesis, standard apple substrates were infested with specified numbers of larvae, and their survival and development were monitored. A potential beneficial effect of the presence of adult flies was also investigated by incubating a varying number of adults on the substrate before introducing the larvae. Adults inoculate substrates with yeast, on which the larvae feed. 3. Fungal growth was related negatively to larval survival and the size of the emerging flies. Although the fungal growth on the substrate was largely reduced at increased larval densities, the measurements of fitness components indicated no Allee effect between larval densities and larval fitness, but rather indicated larval competition. 4. In contrast, increased adult densities on the substrates prior to larval development yielded higher survival of the larvae, larger emerging flies, and also reduced fungal growth on the substrates. Hence, adults enhanced the quality of the larval substrate and significant benefits of aggregated oviposition in fruit flies were shown. Experiments with synthetic pheromone indicated that the aggregation pheromone itself did not contribute directly to the quality of the larval resource. 5. The interaction among adults, micro‐organisms, and larval growth is discussed in relation to the consequences for total fitness.     

Phenological observations and trapping tactics for the granulate ambrosia beetle Xylosandrus crassiusculus (Coleoptera: Curculionidae,Scolytinae) in New Zealand

1. The granulate ambrosia beetle (GAB) Xylosandrus crassiusculus, was first formally detected in New Zealand in 2019. Since then, GAB has subsequently been found infesting numerous tree species in the Auckland region.
2. Flight intercept traps baited with ethanol lures were deployed from October 2019 to May 2021 at three sites in the Auckland region to ascertain the phenology of GAB in New Zealand. Two distinct peak flight periods were identified in early and late summer, while a smaller and inconsistent third peak was detected in early autumn. Logistical analysis of GAB captures in the ethanol-lured traps and degree-day (DD) accumulation indicated that 90% of flight activity is completed by 800 DD.
3. To assess monitoring tactics, flight intercept traps were baited with three different ethanol lures with varying release rates or ethanol-soaked or non-soaked wood bolts from three species of trees. A lure releasing 2 g ethanol per day was most effective at capturing GAB. Ethanol-soaked bolts were less effective than the lures.
4. Xylosandrus crassiusculus represents a significant risk for shrubs and trees native to New Zealand, as well as commercial horticultural and forestry trees. We recommend using ethanol-lured panel traps for monitoring purposes.

     

Temporal dynamics influenced by global change: bee community phenology in urban,agricultural, and natural landscapes

Urbanization and agricultural intensification of landscapes are important drivers of global change, which in turn have direct impacts on local ecological communities leading to shifts in species distributions and interactions. Here, we illustrate how human‐altered landscapes, with novel ornamental and crop plant communities, result not only in changes to local community diversity of floral‐dependent species, but also in shifts in seasonal abundance of bee pollinators. Three years of data on the spatio‐temporal distributions of 91 bee species show that seasonal patterns of abundance and species richness in human‐altered landscapes varied significantly less compared to natural habitats in which floral resources are relatively scarce in the dry summer months. These findings demonstrate that anthropogenic environmental changes in urban and agricultural systems, here mediated through changes in plant resources and water inputs, can alter the temporal dynamics of pollinators that depend on them. Changes in phenology of interactions can be an important, though frequently overlooked, mechanism of global change.     

Delayed density dependence and oscillatory population dynamics in overlapping-generation systems of a seed beetle Callosobruchus chinensis: matrix population model

Long-term experimental systems with overlapping generations using a seed beetle, Callosobruchus chinensis, were maintained by providing 5 g of azuki beans (Vigna angularis) in two different renewal intervals: either 7 days or 10 days. The 7-day-renewal system (system 1) showed oscillatory dynamics with a constant periodic cycle of ca. 7 weeks. More stable population dynamics were seen in the 10-day-interval system (system 2). Short-term experiments showed that survivorship of adults increased with higher adult density, and that the survival rate of adults up to the age of 7 days was much higher than up to 10 days of age. In addition, the per capita production of hatched eggs by females which had survived for 7 days increased with increasing density experienced by the females. Females aged 10 days rarely laid eggs which hatched. We constructed a matrix population model based on either 1 week for system 1 or 10 days for system 2. The model included five stages in system 1: the hatched egg, the final instar larva, the pupa, the young adult and the old adult. Four stages were incorporated in the model for system 2: the young instar larva, the pupa, the young adult, and the old adult. Logistic-difference equations were applied to formulate both overcompensatory density dependence in the hatched-egg production by adults and undercompensatory response in the larval development up to the pupa. The survivorship of young adults to the old stage and the per capita hatched-egg productivity of the old females followed a linear regression against the young adult density. Inside-bean processes were adjusted to be equivalent in the two models, irrespective of the resource renewal intervals. The model predicted that system 1 would oscillate for a long time but that system 2 would rapidly converge to the equilibrium point. Multiplicative effects of both the delayed density dependence through interstage restraint effects and the overcompensatory density dependence in hatched-egg production generated various dynamic patterns ranging from a quickly disappearing damped oscillation to stable limit cycles in system 1. The relationship between resource renewal cycles and delayed density dependence was discussed based on these simulations.     

Genetic differences in the elevational limits of native and introduced Lactuca serriola populations

Aim Differences in phenological timing might explain why populations of the annual Lactuca serriola reach higher elevational limits in a part of its introduced range than in its native range. I investigated (1) whether this difference in elevational limits has a genetic basis, (2) the importance of clinal genetic differentiation and phenotypic plasticity in phenology as responses to elevation in L. serriola, and whether these responses differ between regions, and (3) whether the realized temperature niche of L. serriola differs between the two regions. Location Plant material was collected in Canton Valais, Switzerland (native range) and the Wallowa Mountains, Oregon, USA (introduced range). The field experiment was conducted in Canton Grisons, Switzerland. Methods Plants from 20 populations collected along elevational gradients were grown in eight common gardens established at 200‐m elevational intervals (600–2000 m a.s.l.). The timing of phenological transitions was monitored and analysed with mixed‐effects models to determine differences in (1) elevational limits, and (2) clinal genetic differentiation and phenotypic plasticity as responses to elevation for plants from each region. The limits of the species along five temperature gradients were derived from generalized linear models using published occurrence data to quantify regional differences in the realized temperature niche. Results The limit of seed set (1400 m a.s.l.) was the same for plants of both regions. However, the limit of flowering, probably a better reflection of elevational limits in this study, was 400 m higher for plants from the introduced region due to their faster development. Native populations showed clines in development time with elevation consistent with expectations. However, these were weaker in introduced populations, the responses of which were rather characterized by phenotypic plasticity. Thus, although introduced populations grow at considerably cooler sites than in the native region, this is unlikely to have resulted from direct selection for tolerance of high‐elevation conditions. Main conclusions This study supports a genetic basis for differences in the elevational limits of L. serriola populations between two parts of its native and introduced range. Although it is not yet clear whether these differences evolved in the introduced range, these findings highlight the potential of alien species for gaining insights into niche evolution.     

Synchrony, scale and temporal dynamics of rock partridge (Alectoris graeca saxatilis) populations in the Dolomites

1. Harvesting records of rock partridge ( Alectoris graeca saxatilis ) were examined first to identify the presence of cycles in a species with a southern European distribution and then to examine synchrony between populations at a range of scales.
2. Hunting records from 1965 to 1994 were obtained from 210 hunting areas and analysed at three spatial scales: subpopulation, population and metapopulation. Rock partridge exhibited cyclic fluctuations in about 40% of the time series with a period of 4–7 years. The results did not change with spatial scale. The density-dependent structure of the populations showed that most populations exhibited damped oscillations.
3. The proportion of populations that were in synchrony increased with scale from the population to metapopulation level. There was no decline in synchrony with distance but a large variation between populations irrespective of distance.
4. The populations clustered into dry and wet habitats, with those in the dry habitat being more cyclic. We suggest the lack of spatial synchrony with distance but greater synchrony within habitats may reflect the influence of stochastic events operating on populations with different density dependence structures.     

Uncovering the tracks of a recent and rapid invasion: the case of the fruit fly pest Bactrocera invadens (Diptera: Tephritidae) in Africa

Phytophagous insects of the genus Bactrocera are among the most economically important invasive fruit fly pests. In 2003, an unknown Bactrocera species was found in Kenya. First identified as an ‘aberrant form’ of the Asian B. dorsalis complex, it was later recognized as a new species, Bactrocera invadens. Within 2 years of its discovery, the species was recorded in several African countries, becoming an important quarantine pest. As this invasive fly was discovered only recently, no data are available on its invasion pattern in Africa. This pilot study attempts to infer from genetic data the dynamic aspects of the African invasion of this pest. Using microsatellite markers, we evaluated the level of genetic diversity and the extent of common ancestry among several African populations collected across the invaded areas. A sample from the Asian Sri Lankan population was analysed to confirm the Asian origin of this pest. Genetic data cast no doubt that Sri Lanka belongs to the native range, but only a small percentage of its genotypes can be found in Africa. African populations display relatively high levels of genetic diversity associated with limited geographical structure and no genetic footprints of bottlenecks. These features are indicative of processes of rapid population growth and expansion with possible multiple introductions. In the span of relatively few years, the African invasion registered the presence of at least two uncorrelated outbreaks, both starting from the East. The results of the analyses support that invasion started in East Africa, where B. invadens was initially isolated.     

Pollination processes and the Allee effect in highly fragmented populations: consequences for the mating system in urban environments

The urban environment was used to study the plant reproductive system in small fragmented populations as well as the potential adaptations of plants to urban conditions. We examined the effect of density on the pollination process and on reproduction in urban populations of the allogamous species Crepis sancta. The habitat is composed of small uncultivated square patches (c. 2 m2) regularly spaced along the pavement in streets of the city of Montpellier, France. Pollinator behaviour (the presence of pollinators, the number of flowers visited and the duration of each visit) and seed set as a function of the number of plants in patches and selfing rates, determined using progeny array analysis, were studied. The propensity for the urban populations to produce seeds by self-fertilization in insect-proof glasshouse was also analysed. We found strong evidence of reduced pollinator activities at low densities, resulting in reduced pollination and a reduction in seed set from 80 to 20% of ovules fertilized (the Allee effect). Progeny array analysis revealed a slight increase (marginally significant) in selfing rates in urban populations compared with large populations. In spite of lower pollinator activity, urban populations did not show a greater ability to self-fertilize compared with rural populations from the nearby countryside.     

Isolation and characterization of microsatellite loci in the avocado thrips Scirtothrips perseae (Thysanoptera: Thripidae)

The recent invasion of California by avocado thrips, Scirtothrips perseae, has had a serious economic impact on the Californian avocado industry. Here we report the isolation and characterization of six microsatellite loci for S. perseae, four of which were highly polymorphic (number of observed alleles ranged from three to 13 and expected heterozygosity from 0.31 to 0.87). These markers will be used to investigate the invasion history and route of entry into California of S. perseae. Three of the six loci successfully amplified in other Scirtothrips and Neohydatothrips species.