We combined two models to investigate the theoretical dynamics of five exotic and native blowfly species in response to the Allee effect by using demographic parameters estimated from experimental populations. Most of the results suggest stabilization of dynamic behavior in response to the Allee effect. However, the results depended on the magnitude of the demographic parameters of each species, and also indicated chaotic fluctuations and limit cycles. The results are discussed in the context of larval aggregation, an important biological process for blowflies, which naturally incorporates the Allee effect.

In this study we investigated the population dynamics of Chrysomya albiceps (Wiedemann) with laboratory experiments, employing survival analysis and stage structure mathematical models, emphasizing survival among life stages. The study also assessed the theoretical influence of density dependence and cannibalism during immature stages, on the population dynamics of the species. The survival curves were similar, indicating that populations of C. albiceps exhibit the same pattern of survival among life stages. A strong nonlinear trend was observed, suggesting density dependence, acting during the first life stages of C. albiceps. The time-series simulations produced chaotic oscillations for all life stages, and the cannibalism did not produce qualitative changes in the dynamic behavior. The bifurcation analysis shows that for low values for survival, the population reaches a stable equilibrium, but the cannibalism results in chaotic oscillations practically over all the parametric space. The implications of the patterns of dynamic behavior observed are discussed.

Neste estudo, a variação sazonal da fecundidade, comprimentos de asa e tíbia foram investigadas em populações naturais de Chrysomya albiceps (Wiedemann, 1819) como uma forma de determinar as variações bionômicas da espécie em função da sazonalidade. Uma trajetória temporal constante foi encontrada para fecundidade, comprimentos de asa e tíbia durante vinte e quatro meses. Correlações positivas entre fecundidade e comprimento de asa, fecundidade e comprimento de tíbia e comprimentos de asa e tíbia foram observadas. As implicações destes resultados para a dinâmica populacional de C. albiceps foram discutidas.

In this study, the seasonal variation of fecundity, wing and tibia length were investigated in natural populations of Chrysomya albiceps (Wiedemann, 1819) in an attempt to determine the changes in life history of the species as a function of seasonality. A relative constant temporal trajectory was found for fecundity, wing and tibia length over twenty-four months. Positive correlations between fecundity and wing size, fecundity and tibia size and wing and tibia sizes were observed. The implications of these results for population dynamics of C. albiceps are discussed.

A razão sexual é um componente essencial da biologia de organismos a ser considerado em crescimento populacional. Chrysomya albiceps é uma espécie de mosca varejeira que exibe um desvio na razão sexual em relação à proporção 1:1. Neste estudo avaliamos o impacto de alterações na razão sexual sobre o comportamento dinâmico de C. albiceps utilizando um modelo matemático dependente da densidade que incorpora parâmetros demográficos como sobrevivência e fecundidade. Os parâmetros foram obtidos por regressão exponencial, com sobrevivência e fecundidade sendo estimadas experimentalmente em função da densidade larval. O diagrama de bifurcação gerado pelos resultados indicou a evolução de pontos de equilíbrio estável em função da razão sexual. A sucessão contínua dos valores da razão sexual resultou em uma hierarquia de pontos de equilíbrio estável produzida por bifurcações, resultando em regime caótico. Os parâmetros demográficos obtidos por regressão exponencial foram também mudados para valores máximos e mínimos, a fim de analisar a influência deles sobre o comportamento dinâmico da espécie, tendo a razão sexual como variável independente. Bifurcações com janelas de periodicidade intercaladas com o regime caótico também foram encontradas.

Sex ratio is an essential component of life history to be considered in population growth. Chrysomya albiceps is a blowfly species with a naturally biased sex ratio. In this study, we evaluated the impact of changes in sex ratio on the dynamic behavior of C. albiceps using a density-dependent mathematical model that incorporated demographic parameters such as survival and fecundity. These parameters were obtained by exponential regression, with survival and fecundity being estimated experimentally as a function of larval density. Bifurcation diagram of the results indicated the evolution of stable equilibrium points as a function of sex ratio. A continually increasing sex ratio yielded a hierarchy of bifurcating stable equilibrium points that evolved into a chaotic regime. The demographic parameters obtained by exponential regression were also changed to maximum and minimum values in order to analyze their influence on dynamic behavior with sex ratio being considered as an independent variable. Bifurcations with periodicity windows between chaos regimes were also found.

The equilibrium dynamics of native and introduced blowflies is modelled using a density-dependent model of population growth that takes into account important features of the life-history in these flies. A theoretical analysis indicates that the product of maximum fecundity and survival is the primary determinant of the dynamics. Cochliomyia macellaria, a blowfly native to the Americas and the introduced Chrysomya megacephala and Chrysomya putoria, differ in their dynamics in that the first species shows a damping oscillatory behavior leading to a one-point equilibrium, whereas in the last two species population numbers show a two-point limit cycle. Simulations showed that variation in fecundity has a marked effect on the dynamics and indicates the possibility of transitions from one-point equilibrium to bounded oscillations and aperiodic behavior. Variation in survival has much less influence on the dynamics.

An indirect estimate of consumable food and probability of acquiring food in a blowfly species, Chrysomya putoria, is presented. This alternative procedure combines three distinct models to estimate consumable food in the context of the exploitative competition experienced by immature individuals in blowfly populations. The relevant parameters are derived from data for pupal weight and survival and estimates of density-independent larval mortality in twenty different larval densities. As part of this procedure, the probability of acquiring food per unit of time and the time taken to exhaust the food supply are also calculated. The procedure employed here may be valuable for estimations in insects whose immature stages develop inside the food substrate, where it is difficult to partial out confounding effects such as separation of faeces. This procedure also has the advantage of taking into account the population dynamics of immatures living under crowded conditions, which are particularly characteristic of blowflies and other insects as well.