Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Time correlation function in systems with two coexisting biological species

We study a stochastic lattice model describing the dynamics of coexistence of two interacting biological species. The model comprehends the local processes of birth, death, and diffusion of individuals of each species and is grounded on interaction of the predator-prey type. The species coexistence can be of two types: With self-sustained coupled time oscillations of population densities and without oscillations. We perform numerical simulations of the model on a square lattice and analyze the temporal behavior of each species by computing the time correlation functions as well as the spectral densities. This analysis provides an appropriate characterization of the different types of coexistence. It is also used to examine linked population cycles in nature and in experiment.

Effect of crab size and habitat type on the locomotory activity of juvenile shore crabs, Carcinus maenas

Post-settlement processes are a major focus in the study of the dynamics of marine populations and communities. Post-settlement movement of juveniles is an important, but often ignored, process which affects local predator-prey and competitive interactions. We used benthic suction sampling and pitfall traps to examine density and locomotory activity of Carcinus maenas juveniles in different intertidal habitat types in the Rio Mira Estuary, Portugal, to better understand intra-specific interactions in a system where density-dependent processes are known to regulate population dynamics. As expected, significantly higher densities of juvenile shore crabs were found from bare mud compared to densely vegetated habitats. At the time of sampling, small and intermediate stages together outnumbered by far the larger juveniles. Conversely, larger crabs were much more frequent than smaller ones in traps. A locomotory index (LI), i.e. the ratio between crab catch in pitfall traps and their density within their moving range, is proposed as a measure of movement. LI analyses indicated that: (1) movement is an order of magnitude higher in large than small juveniles and much higher in sparse than dense vegetation cover; (2) activity of small juveniles is mostly crepuscular, regardless of vegetation cover; and (3) movement of large juveniles is very limited in dense Zostera patches, but very high in sparsely vegetated areas, during the day and night. These results suggest that small juveniles are relatively protected under dense vegetation cover due to lower mobility of larger crabs, and provide evidence of temporal segregation of activity windows between juvenile crabs of different sizes, which may be a key mechanism to reduce cannibalism and therefore increase the carrying capacity of nursery habitats. (C) 2008 Elsevier Ltd. All rights reserved.

Shelf and estuarine transport mechanisms affecting the supply of competent larvae in a suite of brachyuran crabs with different life histories

Supply of competent larvae to the benthic habitat is a major determinant of population dynamics in coastal and estuarine invertebrates with an indirect life cycle. Larval delivery may depend not only on physical transport mechanisms, but also on larval behavior and physiological progress to the competent stage. Yet, the combined analysis of such factors has seldom been attempted. We used time-series analyses to examine tide- and wind-driven mechanisms responsible for the supply of crab megalopae to an estuarine river under a major marine influence in SW Spain, and monitored the vertical distribution of upstream moving megalopae, their net flux and competent state. The species Panopeus africanus (estuarine), Brachynotus sexdentatus (euryhaline) and Nepinnotheres pinnotheres (coastal) comprised 80% of the whole sample, and responded in a similar way to tide and wind forcing. Tidal range was positively correlated to supply, with maxima 0 to 1 d after spring tides, suggesting selective tidal stream transport. Despite being extensively subjected to upwelling, downwind drift under the effect of westerlies, not Ekman transport, explained residual supply variation at our sampling area. Once in the estuary, net flux and competence state matched the expected trends. Net upstream flux increased from B. sexdentatus to P. africanus, favoring transport to a sheltered coastal habitat (N. pinnotheres), or to the upper estuary (P. africanus). Competence state was highest in N. pinnotheres, intermediate in B. sexdentatus and lowest in P. africanus, as expected if larvae respond to cues from adequate benthic habitat. P. africanus megalopae were found close to the bottom, not above, rendering slower upstream transport than anticipated.

Colonization and extinction of land planarians (Platyhelminthes, Tricladida) in a Brazilian Atlantic Forest regrowth remnant

Long-term assessments of species assemblages are valuable tools for detecting species ecological preferences and their dispersal tracks, as well as for assessing the possible effects of alien species on native communities. Here we report a 50-year-long study on population dynamics of the four species of land flatworms (Platyhelminthes, Tricladida, Terricola) that have colonized or become extinct in a 70-year-old Atlantic Forest regrowth remnant through the period 1955-2006. On the one hand, the two initially most abundant species, which are native to the study site, Notogynaphallia ernesti and Geoplana multicolor have declined over decades and at present do not exist in the forest remnant. The extinction of these species is most likely related with their preference for open vegetation areas, which presently do not exist in the forest remnant. On the other hand, the neotropical Geoplaninae 1 and the exotic Endeavouria septemlineata were detected in the forest only very recently. The long-term study allowed us to conclude that Geoplaninae 1 was introduced into the study area, although it is only known from the study site. Endeavouria septemlineata, an active predator of the exotic giant African snail, is originally known from Hawaii. This land flatworm species was observed repeatedly in Brazilian anthropogenic areas, and this is the first report of the species in relatively well preserved native forest, which may be evidence of an ongoing adaptive process. Monitoring of its geographic spread and its ecological role would be a good practice for preventing potential damaging effects, since it also feeds on native mollusk fauna, as we observed in lab conditions.

Rotifer abundance, biomass, and secondary production after the recovery of hydrologic connectivity between a river and two marginal lakes (Sao Paulo, Brazil)

Rotifera density, biomass, and secondary production on two marginal lakes of Paranapanema River were compared after the recovery of hydrologic connectivity with the river (Sao Paulo State, Brazil). Daily samplings were performed in limnetic zone of both lakes during the rainy season immediately after lateral inflow of water and, in the dry period, six months after hydrologic connectivity recovery. In order to identify the factors that affect rotifer population dynamics, lake water level, volume, depth, temperature, transparency, dissolved oxygen, pH, alkalinity, conductivity, suspended solids, nutrients, and chlorophyll-a were determined. Variations of water physical and chemical factors that affect rotifer population were related to the lake-river degree of connection and to water level rising after drought. The water lateral inflow from the river resulted in an increase in lake water volume, depth, and transparency and a decrease in water pH, alkalinity, and suspended solids. The lake with the wider river connection, more frequent biota exchange, and larger amount of particulate and dissolved materials was richer and more diverse, while rotifer density, biomass, and productivity were lower in both periods studied. Density, biomass, and secondary production were higher in the lake with the smaller river connection and the higher physical and chemical stability. Our results show that the connectivity affects the limnological stability, associated to seasonality. Stable conditions, caused by low connectivity in dry periods, were related with high density, biomass and secondary production. Conversely, instability conditions in rainy periods were associated to elevated richness and diversity values, caused by exchange biota due to higher connectivity. (C) 2008 Elsevier GmbH. All rights reserved.

Continuous reproduction and recruitment in the narrowback mud crab Panopeus americanus (Brachyura, Panopeidae) in a remnant human-impacted mangrove area

The population structure, reproductive period, and juvenile recruitment of Panopeus americanus were studied in order to enhance knowledge of its life cycle and reproductive strategy and promote the maintenance of its natural stocks in an impacted region. Specimens were collected in the remnant human-impacted mangrove at Araca, state of Sao Paulo, Brazil, at two-month intervals from January to November 2005, at low tide, with a capture effort by three people. The crabs were measured (carapace width, CW) and sexed. The total catch was 275 animals, including 132 males (48.0%); 127 females (46.2%), of which 39 were ovigerous (14.2% of total catch); and 16 individuals whose sex could not be identified (5.8%). No correlation was observed between water temperature and the number of collected individuals; however, there was a significant, positive correlation with salinity. Males were significantly larger than females. The size-frequency distribution was bimodal, reflecting the occurrende of more than one recruitment pulse and the differential abundance of adults during the period of study. The overall sex ratio was 1:0.97 favoring males, and was not significantly different from the expected value, i.e., this population fits the anomalous pattern of sex occurrence in size classes. Ovigerous females were captured in all sampled months, which explain the continuous recruitment observed. Expected low levels of individuals of different size classes in the population were not confirmed. All population aspects found here allowed us to infer that this population of P. americanus is well established in the impacted mangrove by virtue of its reproductive strategy.

THE TEMPO AND MODE OF EVOLUTION OF TRANSPOSABLE ELEMENTS AS REVEALED BY MOLECULAR PHYLOGENIES RECONSTRUCTED FROM MOSQUITO GENOMES

Although many mathematical models exist predicting the dynamics of transposable elements (TEs), there is a lack of available empirical data to validate these models and inherent assumptions. Genomes can provide a snapshot of several TE families in a single organism, and these could have their demographics inferred by coalescent analysis, allowing for the testing of theories on TE amplification dynamics. Using the available genomes of the mosquitoes Aedes aegypti and Anopheles gambiae, we indicate that such an approach is feasible. Our analysis follows four steps: (1) mining the two mosquito genomes currently available in search of TE families; (2) fitting, to selected families found in (1), a phylogeny tree under the general time-reversible (GTR) nucleotide substitution model with an uncorrelated lognormal (UCLN) relaxed clock and a nonparametric demographic model; (3) fitting a nonparametric coalescent model to the tree generated in (2); and (4) fitting parametric models motivated by ecological theories to the curve generated in (3).

An optimization model for antibiotic use

There is a positive correlation between the intensity of use of a given antibiotic and the prevalence of resistant strains. The more you treat, more patients infected with resistant strains appears and, as a consequence, the higher the mortality due to the infection and the longer the hospitalization time. In contrast, the less you treat, the higher the mortality rates and the longer the hospitalization time of patients infected with sensitive strains that could be successfully treated. The hypothesis proposed in this paper is an attempt to solve such a conflict: there must be an optimum treatment intensity that minimizes both the additional mortality and hospitalization time due to the infection by both sensitive and resistant bacteria strains. In order to test this hypothesis we applied a simple mathematical model that allowed us to estimate the optimum proportion of patients to be treated in order to minimize the total number of deaths and hospitalization time due to the infection in a hospital setting. (C) 2007 Elsevier Inc. All rights reserved.

Dog culling and replacement in an area endemic for visceral leishmaniasis in Brazil

Measures employed to control visceral leishmaniasis in Brazil have focused on vector control by residual insecticide spraying and diagnosis of infection with elimination of positive dogs. We describe dog culling and replacement in a Brazilian endemic area (the Alvorada District, Aracatuba, SP) in order to better understand dog population dynamics when elimination of the dog reservoir is adopted as the main control measure. From August 2002 to July 2004, 60.9% of the estimated dog population for the area was culled with a mean age of 34 months old. The presence of anti-Leishmania sp. antibodies was recorded for only 26.7% of the euthanized canines. Replacement was observed in 38.8% of the cases, some of them by 2 or more dogs and in a mean time of 4 months. Dogs were replaced mostly by puppies of both sexes with a mean age of 6.8 months. From August 2002 to April 2005 we were able to follow-up 116 of these dogs, during a mean time of 8.7 months. Canine visceral leishmaniasis seropositivity by ELISA was observed in 42.2% of the followed dogs, 30.6% of which were already positive at the first evaluation. By the end of the follow-up period 37% of the dogs were submitted to euthanasia, with a mean age of 18.3 months. In the studied CVL endemic area of Brazil, euthanasia and the subsequent replacement ratio were high, increasing the dog population turnover and leading to a younger population that might be more susceptible to a variety of other infectious diseases in addition to CVL. Dog culling as a control strategy for VL should be reassessed. (C) 2008 Elsevier B.V. All rights reserved.

The risk of chikungunya fever in a dengue-endemic area

Background. Chikungunya, an alphavirus of the Togaviridae family, causes a febrile disease transmitted to humans by the bite of infected Aedes mosquitoes. This infection is reaching endemic levels in many Southeast Asian countries. Symptoms include sudden onset of fever, chills, headache, nausea, vomiting, joint pain with or without swelling, low back pain, and rash. According to the World Health Organization, there are 2 billion people living in Aedes-infested areas. In addition, traveling to these areas is popular, making the potential risk of infections transmitted by the bite of infected Aedes mosquitoes very high. Methods. We proposed a mathematical model to estimate the risk of acquiring chikungunya fever in an Aedes-infested area by taking the prevalence of dengue fever into account. The basic reproduction number for chikungunya fever R-0chik can be written as a function of the basic reproduction number of dengue R-0dengue by calculating the ratio R-0chik/R-0dengue. From R-0chik, we estimated the force of infection and the risk of acquiring the disease both for local residents of a dengue-endemic area and for travelers to this area. Results. We calculated that R-0chik is 64.4% that of R-0dengue. The model was applied to a hypothetical situation, namely, estimating the individual risk of acquiring chikungunya fever in a dengue-endemic area, both for local inhabitants (22% in steady state) and for visiting travelers (from 0.31% to 1.23% depending on the time spent in the area). Conclusions. The method proposed based on the output of a dynamical model is innovative and provided an estimation of the risk of infection, both for local inhabitants and for visiting travelers.

Modelling the control strategies against dengue in Singapore

Notified cases of dengue infections in Singapore reached historical highs in 2004 (9459 cases) and 2005 (13 817 cases) and the reason for such all increase is still to be established. We apply a mathematical model for dengue infection that takes into account the seasonal variation in incidence, characteristic of dengue fever, and which mimics the 2004-2005 epidemics in Singapore. We simulated a set of possible control strategies and confirmed the intuitive belief that killing adult mosquitoes is the most effective strategy to control an ongoing epidemic. On the other hand, the control of immature forms was very efficient ill preventing the resurgence of dengue epidemics. Since the control of immature forms allows the reduction of adulticide, it seems that the best strategy is to combine both adulticide and larvicide control measures during an outbreak, followed by the maintenance of larvicide methods after the epidemic has subsided. In addition, the model showed that the mixed strategy of adulticide and larvicide methods introduced by the government seems to be very effective in reducing the number of cases in the first weeks after the start of control.

FOR DEBATE A hypothesis for the 2007 dengue outbreak in Singapore

A previous mathematical model explaining dengue in Singapore predicted a reasonable outbreak of about 6500 cases for 2006 and a very mild outbreak with about 2000 cases for 2007. However, only 3051 cases were reported in 2006 while more than 7800 were reported in the first 44 weeks of 2007. We hypothesized that the combination of haze with other local sources of particulate matter had a significant impact on mosquito life expectancy, significantly increasing their mortality rate. To test the hypothesis a mathematical model based on the reproduction number of dengue fever and aimed at comparing the impact of several possible alternative control strategies was proposed. This model also aimed at contributing to the understanding of the causes of dengue resurgence in Singapore in the last decade. The model`s simulation demonstrated that an increase in mosquito mortality in 2006 and either a reduction in mortality or an increase in the carrying capacity of mosquitoes in 2007 explained the patterned observed in Singapore. Based on the model`s simulation we concluded that the fewer than expected number of dengue cases in Singapore in 2006 was caused by an increase in mosquito mortality due to the disproportionate haze affecting the country that year and that particularly favourable environmental conditions in 2007 propitiated mosquitoes with a lower mortality rate, which explains the greater than expected number of dengue cases in 2007. Whether our hypothesis is plausible or not should be debated further.

Brood cell size of Apis mellifera modifies the reproductive behavior of Varroa destructor

We undertook a field study to determine whether comb cell size affects the reproductive behavior of Varroa destructor under natural conditions. We examined the effect of brood cell width on the reproductive behavior of V. destructor in honey bee colonies, under natural conditions. Drone and worker brood combs were sampled from 11 colonies of Apis mellifera. A Pearson correlation test and a Tukey test were used to determine whether mite reproduction rate varied with brood cell width. Generalized additive model analysis showed that infestation rate increased positively and linearly with the width of worker and drone cells. The reproduction rate for viable mother mites was 0.96 viable female descendants per original invading female. No significant correlation was observed between brood cell width and number of offspring of V. destructor. Infertile mother mites were more frequent in narrower brood cells.

Ecological aspects of the free-living ticks (Acari: Ixodidae) on animal trails within Atlantic rainforest in south-eastern Brazil

In a recent ecological study of the ticks on animal trails within an area of Atlantic rainforest in south-eastern Brazil, Amblyomma aureolatum, A. brasiliense, A. incisum, A. ovale and Haemaphysalis juxtakochi were found questing on the vegetation. Most of the ticks recorded by a small, man-made dam on the forest border were A. dubitatum but a few A. brasiliense and A. cajennense, one A. incisum and one H. juxtakochi were also found. The seasonal activity of the ticks indicated that A. incisum and A. brasiliense had one generation/year. On the animal trails, most tick species and stages quested on the vegetation at a height of 30-40 cm above ground level. The questing larvae and adults of A. incisum tended to be found higher, however, with the greatest numbers recorded 40-50 cm (larvae) or 60-70 cm (adults) above ground level. Most of the adult ticks (81.1% -100%), nymphs (78.6%-100%) and larval clusters (100%) found on a forest trail remained questing at the same location over a 24-h period. Carbon-dioxide traps in the rainforest attracted, 50% of the ticks observed questing on the nearby vegetation and, curiously, the CO(2) traps set deep in the forest attracted far fewer ticks than similar traps set by the dam. The ecological relationships between the ticks, their hosts and the rainforest environment are discussed.