Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Allee effects and population spread in patchy landscapes

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Big bang bifurcations in von Bertalanffy’s dynamics with strong and weak Allee effects

The main purpose of this work was to study population dynamic discrete models in which the growth of the population is described by generalized von Bertalanffy's functions, with an adjustment or correction factor of polynomial type. The consideration of this correction factor is made with the aim to introduce the Allee effect. To the class of generalized von Bertalanffy's functions is identified and characterized subclasses of strong and weak Allee's functions and functions with no Allee effect. This classification is founded on the concepts of strong and weak Allee's effects to population growth rates associated. A complete description of the dynamic behavior is given, where we provide necessary conditions for the occurrence of unconditional and essential extinction types. The bifurcation structures of the parameter plane are analyzed regarding the evolution of the Allee limit with the aim to understand how the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, is realized. To generalized von Bertalanffy's functions with strong and weak Allee effects is identified an Allee's effect region, to which is associated the concepts of chaotic semistability curve and Allee's bifurcation point. We verified that under some sufficient conditions, generalized von Bertalanffy's functions have a particular bifurcation structure: the big bang bifurcations of the so-called box-within-a-box type. To this family of maps, the Allee bifurcation points and the big bang bifurcation points are characterized by the symmetric of Allee's limit and by a null intrinsic growth rate. The present paper is also a significant contribution in the framework of the big bang bifurcation analysis for continuous 1D maps and unveil their relationship with the explosion birth and the extinction phenomena.

Manipulating sex ratio to increase population growth: the example of the Lesser Kestrel

Small or decreasing populations call for emergency actions like, for example, captive breeding programs. Such programs aim at rapidly increasing population sizes in order to reduce the loss of genetic variability and to avoid possible Allee effects. The Lesser Kestrel Falco naumanni is one of the species that is currently supported in several captive breeding programs at various locations. Here, we model the demographic and genetic consequences of potential management strategies that are based on offspring sex ratio manipulation. Increased population growth could be achieved by manipulating female conditions and/or male attractiveness in the captive breeders and consequently shifting the offspring sex ratio towards more female offspring, which are then used for reintroduction. Fragmenting populations into wild-breeding and captive-breeding demes and manipulating population sex ratio both immediately increase the inbreeding coefficient in the next generation (i.e. decrease N-e) but may, in the long term, reduce the loss of genetic variability if population growth is restricted by the number of females. We use the Lesser Kestrel and the wealth of information that is available on this species to predict the long-term consequences of various kinds of sex-ratio manipulation. We find that, in our example and possibly in many other cases, a sex-ratio manipulation that seems realistic could have a beneficial effect on the captive breeding program. However, the possible long-term costs and benefits of such measures need to be carefully optimized.

A matter of time: delayed mate encounter postpones mating window initiation and reduces the strength of female choosiness

Reproductive success is determined by the presence and timing of encounter of mates. The latter depends on species-specific reproductive characteristics (e.g. initiation/duration of the mating window), season, and reproductive strategies (e.g. intensity of choosiness) that may potentially mitigate constraints imposed by mating windows. Despite their potentially crucial role for fitness and population dynamics, limited evidence exists about mating window initiation, duration and reproductive strategies. Here, we experimentally tested the mechanisms of initiation and the duration of the common lizard's Zootoca vivipara mating window, by manipulating the timing of mate encounter and analyzing its effect on (re-)mating probability. We furthermore tested treatment effects on female reproductive strategies, by measuring female choosiness. The timing of mate encounter and season did not significantly affect mating probability. However, a longer delay until mate encounter reduced female choosiness. Re-mating probability decreased with re-mating delay and was independent of mating delay. This indicates that mating window initiation depends on mate encounter, that its duration is fixed, and that plastic reproductive strategies exist. These findings contrast with previous beliefs and shows that mating windows per se may not necessarily constrain reproductive success, which is congruent with rapid range expansion and absence of positive density-effects on reproductive success (Allee effects). In summary, our results show that predicting the effect of mating windows on reproduction is complex and that experimental evidence is essential for evaluating their effect on reproduction and reproductive strategies, both being important determinants of population dynamics and the colonization of new habitats.

The future of coral reefs

Coral reefs, with their millions of species, have changed profoundly because of the effects of people, and will continue to do so for the foreseeable future. Reefs are subject to many of the same processes that affect other human-dominated ecosystems, but some special features merit emphasis: (i) Many dominant reef builders spawn eggs and sperm into the water column, where fertilization occurs. They are thus particularly vulnerable to Allee effects, including potential extinction associated with chronic reproductive failure. (ii) The corals likely to be most resistant to the effects of habitat degradation are small, short-lived “weedy” corals that have limited dispersal capabilities at the larval stage. Habitat degradation, together with habitat fragmentation, will therefore lead to the establishment of genetically isolated clusters of inbreeding corals. (iii) Increases in average sea temperatures by as little as 1°C, a likely result of global climate change, can cause coral “bleaching” (the breakdown of coral–algal symbiosis), changes in symbiont communities, and coral death. (iv) The activities of people near reefs increase both fishing pressure and nutrient inputs. In general, these processes favor more rapidly growing competitors, often fleshy seaweeds, and may also result in explosions of predator populations. (v) Combinations of stress appear to be associated with threshold responses and ecological surprises, including devastating pathogen outbreaks. (vi) The fossil record suggests that corals as a group are more likely to suffer extinctions than some of the groups that associate with them, whose habitat requirements may be less stringent.

The timing and interval of mate encounter affects investment during mating

The benefits obtained from mating are usually condition-dependent, favouring the evolution of flexible investment during copulation, for instance, in terms of invested time, energy, or sperm. Flexible investment strategies are predicted to depend on the likelihood of acquiring alternative mates and therefore they should depend on the timing of mate encounter. However, scarce experimental evidence for this hypothesis exists. Here we manipulated the time delay until first mating and the interval between first and second mating in the polygynandrous common lizard, Zootoca vivipara. We determined treatment effects on fertilisation success and copulation duration, the latter being a proxy for investment in mating and for quantity of transferred sperm. The duration of the second copulation decreased with increasing inter-mating interval and depended on the fertilisation success of first mates. The former provides evidence for time-dependent investment strategies, most likely resulting from the progression of the female's reproductive cycle. Fertilisation success of first mates increased with increasing inter-mating interval and was higher when females were closer to ovulation, showing that flexible investment strategies significantly affected male reproductive success. This points to fertilisation assurance, which may mitigate negative effects of low population density on reproductive success, e.g. Allee effects.

Towards a population ecology of stressed environments: the effects of zinc on the springtail Folsomia candida

1. To understand population dynamics in stressed environments it is necessary to join together two classical lines of research. Population responses to environmental stress have been studied at low density in life table response experiments. These show how the population's growth rate (pgr) at low density varies in relation to levels of stress. Population responses to density, on the other hand, are based on examination of the relationship between pgr and population density. 2. The joint effects of stress and density on pgr can be pictured as a contour map in which pgr varies with stress and density in the same way that the height of land above sea level varies with latitude and longitude. Here a microcosm experiment is reported that compared the joint effects of zinc and population density on the pgr of the springtail Folsomia candida (Collembola). 3. Our experiments allowed the plotting of a complete map of the effects of density and a stressor on pgr. Particularly important was the position of the pgr= 0 contour, which suggested that carrying capacity varied little with zinc concentration until toxic levels were reached. 4. This prediction accords well with observations of population abundance in the field. The method also allowed us to demonstrate, simultaneously, hormesis, toxicity, an Allee effect and density dependence. 5. The mechanisms responsible for these phenomena are discussed. As zinc is an essential trace element the initial increase in pgr is probably a consequence of dietary zinc deficiency. The Allee effect may be attributed to productivity of the environment increasing with density at low density. Density dependence is a result of food limitation. 6. Synthesis and applications. We illustrate a novel solution based on mapping a population's growth rate in relation to stress and population density. Our method allows us to demonstrate, simultaneously, hormesis, toxicity, an Allee effect and density dependence in an important ecological indicator species. We hope that the approach followed here will prove to have general applicability enabling predictions of field abundance to be made from estimates of the joint effects of the stressors and density on population growth rate.

One Step Forward: Contrasting The Effects Of Toe Clipping And Pit Tagging On Frog Survival And Recapture Probability.

Amphibians have been declining worldwide and the comprehension of the threats that they face could be improved by using mark-recapture models to estimate vital rates of natural populations. Recently, the consequences of marking amphibians have been under discussion and the effects of toe clipping on survival are debatable, although it is still the most common technique for individually identifying amphibians. The passive integrated transponder (PIT tag) is an alternative technique, but comparisons among marking techniques in free-ranging populations are still lacking. We compared these two marking techniques using mark-recapture models to estimate apparent survival and recapture probability of a neotropical population of the blacksmith tree frog, Hypsiboas faber. We tested the effects of marking technique and number of toe pads removed while controlling for sex. Survival was similar among groups, although slightly decreased from individuals with one toe pad removed, to individuals with two and three toe pads removed, and finally to PIT-tagged individuals. No sex differences were detected. Recapture probability slightly increased with the number of toe pads removed and was the lowest for PIT-tagged individuals. Sex was an important predictor for recapture probability, with males being nearly five times more likely to be recaptured. Potential negative effects of both techniques may include reduced locomotion and high stress levels. We recommend the use of covariates in models to better understand the effects of marking techniques on frogs. Accounting for the effect of the technique on the results should be considered, because most techniques may reduce survival. Based on our results, but also on logistical and cost issues associated with PIT tagging, we suggest the use of toe clipping with anurans like the blacksmith tree frog.

Impact Of Benign Prostatic Hyperplasia Pharmacological Treatment On Transrectal Prostate Biopsy Adverse Effects.

Background. Benign prostatic hyperplasia (BPH) pharmacological treatment may promote a decrease in prostate vascularization and bladder neck relaxation with theoretical improvement in prostate biopsy morbidity, though never explored in the literature. Methods. Among 242 consecutive unselected patients who underwent prostate biopsy, after excluding those with history of prostate biopsy/surgery or using medications not for BPH, we studied 190 patients. On the 15th day after procedure patients were questioned about symptoms lasting over a week and classified according to pharmacological BPH treatment. Results. Thirty-three patients (17%) were using alpha-blocker exclusively, five (3%) 5-alpha-reductase inhibitor exclusively, twelve (6%) patients used both medications, and 140 (74%) patients used none. There was no difference in regard to age among groups (P = 0.5). Postbiopsy adverse effects occurred as follows: hematuria 96 (50%), hematospermia 53 (28%), hematochezia 22 (12%), urethrorrhagia 19 (10%), fever 5 (3%), and pain 20 (10%). There was a significant negative correlation between postbiopsy hematuria and BPH pharmacological treatment with stronger correlation for combined use of 5-alpha-reductase inhibitor and alpha-blocker over 6 months (P = 0.0027). Conclusion. BPH pharmacological treatment, mainly combined for at least 6 months seems to protect against prostate biopsy adverse effects. Future studies are necessary to confirm our novel results.

Inhibitory Effects Of A Cured Antibacterial Bonding System On Viability And Metabolic Activity Of Oral Bacteria.

To evaluate the antimicrobial efficacy of Clearfil SE Protect (CP) and Clearfil SE Bond (CB) after curing and rinsed against five individual oral microorganisms as well as a mixture of bacterial culture prepared from the selected test organisms. Bacterial suspensions were prepared from single species of Streptococcus mutans, Streptococcus sobrinus, Streptococcus gordonii, Actinomyces viscosus and Lactobacillus lactis, as well as mixed bacterial suspensions from these organisms. Dentin bonding system discs (6 mm×2 mm) were prepared, cured, washed and placed on the bacterial suspension of single species or multispecies bacteria for 15, 30 and 60 min. MTT, Live/Dead bacterial viability (antibacterial effect), and XTT (metabolic activity) assays were used to test the two dentin system's antibacterial effect. All assays were done in triplicates and each experiment repeated at least three times. Data were submitted to ANOVA and Scheffe's f-test (5%). Greater than 40% bacteria killing was seen within 15 min, and the killing progressed with increasing time of incubation with CP discs. However, a longer (60 min) period of incubation was required by CP to achieve similar antimicrobial effect against mixed bacterial suspension. CB had no significant effect on the viability or metabolic activity of the test microorganisms when compared to the control bacterial culture. CP was significantly effective in reducing the viability and metabolic activity of the test organisms. The results demonstrated the antimicrobial efficacy of CP both on single and multispecies bacterial culture. CP may be beneficial in reducing bacterial infections in cavity preparations in clinical dentistry.

In Vitro And In Vivo Anti-angiogenic Effects Of Hydroxyurea.

Hydroxyurea (HU), or hydroxycarbamide, is used for the treatment of some myeloproliferative and neoplastic diseases, and is currently the only drug approved by the FDA for use in sickle cell disease (SCD). Despite the relative success of HU therapy for SCD, a genetic disorder of the hemoglobin β chain that results in red-cell sickling, hemolysis, vascular inflammation and recurrent vasoocclusion, the exact mechanisms by which HU actuates remain unclear. We hypothesized that HU may modulate endothelial angiogenic processes, with important consequences for vascular inflammation. The effects of HU (50-200 μM; 17-24 h) on endothelial cell functions associated with key steps of angiogenesis were evaluated using human umbilical vein endothelial cell (HUVEC) cultures. Expression profiles of the HIF1A gene and the miRNAs 221 and 222, involved in endothelial function, were also determined in HUVECs following HU administration and the direct in vivo antiangiogenic effects of HU were assessed using a mouse Matrigel-plug neovascularization assay. Following incubation with HU, HUVECs exhibited high cell viability, but displayed a significant 75% inhibition in the rate of capillary-like-structure formation, and significant decreases in proliferative and invasive capacities. Furthermore, HU significantly decreased HIF1A expression, and induced the expression of miRNA 221, while downregulating miRNA 222. In vivo, HU reduced vascular endothelial growth factor (VEGF)-induced vascular development in Matrigel implants over 7 days. Findings indicate that HU is able to inhibit vessel assembly, a crucial angiogenic process, both in vitro and in vivo, and suggest that some of HU's therapeutic effects may occur through novel vascular mechanisms.

Angiogenic Effects Of Cryosurgery With Liquid Nitrogen On The Normal Skin Of Rats, Through Morphometric Study.

Cryosurgery is an efficient therapeutic technique used to treat benign and malignant cutaneous diseases. The primary active mechanism of cryosurgery is related to vascular effects on treated tissue. After a cryosurgical procedure, exuberant granulation tissue is formed at the injection site, probably as a result of angiogenic stimulation of the cryogen and inflammatory response, particularly in endothelial cells. To evaluate the angiogenic effects of freezing, as part of the phenomenon of healing rat skin subjected to previous injury. Two incisions were made in each of the twenty rats, which were divided randomly into two groups of ten. After 3 days, cryosurgery with liquid nitrogen was performed in one of incisions. The rats' samples were then collected, cut and stained to conduct histopathological examination, to assess the local angiogenesis in differing moments and situations. It was possible to demonstrate that cryosurgery, in spite of promoting cell death and accentuated local inflammation soon after its application, induces quicker cell proliferation in the affected tissue and maintenance of this rate in a second phase, than in tissue healing without this procedure. These findings, together with the knowledge that there is a direct relationship between mononuclear cells and neovascularization (the development of a rich system of new vessels in injury caused by cold), suggest that cryosurgery possesses angiogenic stimulus, even though complete healing takes longer to occur. The significance level for statistical tests was 5% (p<0,05).

Core-valence Correlation Effects On Ir Calculations: The Bf3 And Bcl3 Cases.

The first theoretical results of core-valence correlation effects are presented for the infrared wavenumbers and intensities of the BF3 and BCl3 molecules, using (double- and triple-zeta) Dunning core-valence basis sets at the CCSD(T) level. The results are compared with those calculated in the frozen core approximation with standard Dunning basis sets at the same correlation level and with the experimental values. The general conclusion is that the effect of core-valence correlation is, for infrared wavenumbers and intensities, smaller than the effect of adding augmented diffuse functions to the basis set, e.g., cc-pVTZ to aug-cc-pVTZ. Moreover, the trends observed in the data are mainly related to the augmented functions rather than the core-valence functions added to the basis set. The results obtained here confirm previous studies pointing out the large descrepancy between the theoretical and experimental intensities of the stretching mode for BCl3.