Impact of lek mating on the sterile insect technique: A modeling study

Summary Modelling studies are presented which describe the effect of lek mating on the control of a wild population by sterile male release. The mixed leks are assumed to follow a Poisson-binomial distribution and the system includes three parts: territory defense, matings inside a lek and matings outside a lek. The effects of parameters on the hatchability are discussed. Among the parameters, sterile type effect (W _s ), female choice (f _s ) and mating competitiveness (C _m ) are the most important. The application to determining the effects of sterile male release and on the proportion of sterile males required for eradication are also discussed.     

The screw-worm flyChrysomya bezziana villeneuve (Diptera: Calliphoridae) in a sterile insect release trial in Papua New Guinea

Summary The feasibility of the sterile insect release method (SIRM) was tested against natural populations of the Old World screw-worm fly,Chrysomya bezziana in the Musa Valley, Papua New Guinea. Sterile mating frequencies were determined from egg masses laid by native females on wounded, sentinel cattle. The aerial release of sterilised puparia resulted in low frequencies of sterile matings and few trap recaptures of released material. The release of chilled adult flies resulted in higher frequencies of sterile matings and many trap recaptures. The mean density of males released was 230 males per km² per week over a target area of 361 km² (48% of the valley). Sterile masses were first detected 2 weeks after the release of chill flies commenced, reaching a weekly peak of 33% after 5 weeks of releases with 15% of egg masses found to be sterile during the final month. The levels of sterile matings achieved in this trial were similar to comparable SIRM studies made in the USA, Mexico and Guatemala to control the New World screw-worm fly,Cochliomyia hominivorax.     

Eradication of the melon fly,Dacus cucurbitae, from Kume is., Okinawa with the sterile insect release method

Summary The sterile insect release method was applied to eradicate the melon fly,Dacus cucurbitae, from the 58.5 km² island of Kume, in the Okinawa Islands group. Weekly releases of 1 to 1.5 million flies irradiated as pupae with 6–7 kR from a cobalt-60 source did not decrease the wild melon fly population. Releases of 1.5–2 million pupae per week made from September, 1975 to January, 1976 decreased the percent egg-hatch of females caught on Kume Is., but did not decrease the percent infestation significantly. The number of pupae released was increased from February, 1976 to accelerate the eradication process. When the number of pupae released exceeded 3.5 million per week, a rapid increase in the ratio of marked (sterile) to unmarked (wild) flies, a remarkable decrease in percent egg-hatch, and a decrease in percent infestation of fruits were observed. There has been no sign of melon fly infestation in wild cucurbit fruits from October, 1976 to the present time (April, 1977), despite the fact that more than 70,000 fruits were carefully examined. The eradication of the melon fly from Kume Is. was thus achieved by April, 1977, after the release of 264 million sterile fly pupae.     

Lek mating system and its impact on male annihilation technique

Summary Simulation models were presented which describe the matings inside a lek. The size of the lek was assumed to follow a poisson distribution, the dominance factor of each of the males was drawn from a gamma distribution, and the mating probability for each male was determined by its mating effectiveness raised to female mating factor divided by the sum of all the mating effectivenesses raised to this power. The mating probatility for each male and the actual matings were determined by Monte Carlo simulation. Based on the simulation data, the effects of female mating factor and size of the lek on the frequency of actual matings accomplished by the males inside the lek were discussed. In the case of male annihilation, the mean number of effective matings per male in the lek, calculated from the frequency of actual matings weighted by the effective mating ratio, was used to evaluate the efficiency of male annihilation method.     

The sterile release method for population control with interspecific competition

Summary A differential equations model of competing species with the release of sterile individuals of one of the species is examined. The system is found to have two positive steady states for certain parameter values; one of these is stable and the other is unstable. The system is quite resilient around the stable steady state. The release of steriles causes the nontarget species to increase in numbers. There exists a value of the release rate above which the pest species collapses to extinction. The existence of the competitor species assists the sterile release program since the pest equilibrium at any release rate is lower with the competitor species present than without it; in addition the release rate required to cause collapse of the pest species is lower with the competitor species present than without it. The effects of the parameters on the ease of eradication were examined. It was found that the ideal competitor species should have a high rate of increase, a large carrying capacity and exert strong competitive depression on the pests. The ideal pest would have a low rate of increase, a low carrying capacity and be a poor competitor.     

The sterile insect release method on species with two-stage life cycles

Summary A continuous-time density dependent model was constructed of a species with a two stage life cycle. This model has a unique stable equilibrium. With the introduction of steriles at constant rate a second positive unstable steady state appears; this condition does not depend on the mode of action within the life cycle of the density dependence or its relative strength. A comparison was made of the effects of having the density dependence in each of larval and adult recruitment and larval and adult losses. It was found that if only adult recruitment is denisty dependent, then adult numbers can actually increase with the release of steriles provided density independent recruitment greatly exceeds density independent losses. Sterile releases were often more effective against larvae than against adults, although in some cases not importantly so. Density dependence in recruitment gives much lower equilibrium values than when density dependence of comparable strength is in the mortality. The release rates needed to cause extinction were generally between 0.1 and 0.5 of the larval equilibrium with no sterile releases except when the density dependence is predominantly in adult recruitment, in which case much higher release rates are required.     

Analysis of changes of insect-plant ratio-improvement of key-factor analysis for evaluating bottom-up effects in insect population dynamics

A revised key-factor analysis was presented for analyzing the temporal changes in the ratio of insect absolute number to plant resource. Ten data sets for 5 insect species were then analyzed. In this key-factor analysis, the key factor is defined as the factor contributing highly to between-year variation inR _r , the log rate of the inter-year change of the insect-plant ratio. The yearly change of plant resource was handled as a separate factor, expressed byr _pl , log ratio of plant resource in yearn to plant resource in yearn+1. The following was revealed: 1) In 7 of the 10 data sets examined,r _pl influenced variations ofR _r ; in particular in 3 casesr _pl was the main key factor. 2) Generation-to-generation fluctuations of absolute insect densities showed density dependence in 4 cases, while those of insect-plant ratios, in 8 cases. 3) The Royama model or a linear model, explained well the relationship between log insect-plant ratio (X _r ) andR _r and the relationship betweenX _r and log yearly change rate of absolute insect density (R _abs ). However, in the 7 cases in whichr _pl was a critical factor for variations ofR _r , with, increase ofX _r ,R _r showed a steeper, decrease around the equilibrium point (the point for whichR _r is 0) thanR _abs . This occurred becauser _pl tended to be negatively correlated withX _r . Consequently, in two casesX _r fluctuated cyclicly or chaotically although without the changes in plant resource, fluctuations ofX _r would be damped oscillations approaching equilibrium.     

Combining methods of insect pest control: Partitioning mortality and predicting complementarity

Summary An age-structured population model is used as a vehicle for presenting a method for the analysis of interactions between pairs of insect pest control methods. This analysis is based on partitioning the total mortality acting on a population into its constituent components from all known sources. Pairwise critical mortality curves are then constructed which represent the combined mortality required for eradicating the pest population. Effort curves are then constructed from computing the mortality resulting from a given amount of control effort. The convolution of the critical mortality curves and the effort curves then yields the isoclines formed by the effort required of two control methods in combination to achieve eradication. This analysis allows the prediction of either synergism or interference between the control methods and also helps explain patterns observed in previous modelling of such combinations of pest control methods.     

Combining pheromone-baited and food-baited traps for insect pest control: Effects of developmental period

Summary An age-structured population dynamics model is presented that incorporates pheromone-trapping and food-trapping as control methods for an insect pest. The model yields the following results. Low rates of pest survivorship allow lower trapping rates for control. Species with long developmental periods are easier to control than those with shorter developmental periods (other factors being equal) due to lower net survival. The rates of pheromone trapping alone for effective control are usually very high. The combination of pheromone and food trapping allows control with much lower trapping rates than either method alone. Even small amounts of immigration of adult pests into the control area renders pheromone control ineffective, whereas food traps suppress both the immigrants and the resident population. Food- (or odor-) baited traps which attract both males and females are only somewhat more efficient than those which attract females alone. The existence of density-dependent population regulation assists the control program substantially, but this assistance declines as food trapping becomes a more important part of the control program. Larval competition strongly affects the required trapping rates for eradication; species in which all larvae exert strong competition are much easier to control than those in whic the younger larvae contribute little to the total competitive depression.     

Effects of sterile insect releases on a population under predation or parasitism

Summary A continuous-time differential equation model was constructed which describes the population dynamics of a predator prey system in which sterile prey are released in a program designed to eradicate or reduce the prey population. It was found that the dynamics of the system behave quite differently when predators are present. Two conditions were found which have differing implications for the control program. If the predators still exist when the wild prey population declines to extinction, then the SIRM is assisted by the predators, sometimes to a considereble extent. If the predators decline to extinction before the wild prey population goes extinct, then the predators may or may not assist the SIRM depending on the parameters of the system. If the predators do assist the SIRM, then a potentially dangerous situation exists in which an explosion of the prey population could occur after the predators go extinct. Predator polyphagy would probably minimize this danger of an explosion since it would stabilize the predator population.     

Persistence of abnormal females that produce only female progeny with occasional recovery to normal females in Lepidoptera

In Lepidoptera, females that produce only female progeny have been found in wild populations of at least 12 species. In some species, recoveries, where abnormal females return to normal females, have been observed. A mathematical model of the population dynamics with recovery was developed to identify the conditions for realizing the persistence of abnormal females. Analysis indicated normal and abnormal females coexist and reach an equilibrium state at certain recovery rate values. The equilibrium values of normal and abnormal females were determined. When a population was in equilibrium it was shown that the ratio of normal to abnormal females and the sex ratio after reproduction are always functions of the recovery rate and the proportion of female offspring from an abnormal female to that from a normal female. Using the simulation it was found that, even when a population fluctuates under variable environmental conditions, the two ratios mentioned above reach equilibrium. Equilibrium relationships were applied to published data, and it was concluded that recovery from abnormal to normal females explains the persistence of abnormal females in some species of Lepidoptera. The model developed in this paper can also be used for analysing the persistence of abnormal females of other insect species.     

Economic structure and fertility: A comparative analysis

This study empirically investigates the relationship between the economic structure of populations and their level of fertility, using data from censuses recently conducted in some 50 nations. Findings show that high rates of female labor force participation outside the home and low rates of economic activity of children depress a society’s fertility level, as measured by the crude birth rate or the child-woman ratio. It is also hypothesized, but not confirmed, that the per cent of unpaid family workers in a society is positively related to its fertility level. A model is presented that treats these three components of economic structure as intervening variables through which the exogenous variables, urbanization, industrialization, and education, operate in influencing the fertility level of a society.     

Towards a theory of insect epidemiology

Summary An attempt is made to consolidate and extend some of our current thoughts on insect epidemiology using graphical reproduction models. Starting with a simple model with a single equilibrium point, the elementary hypothesis is proposed that epidemics erupt when this equilibrium point increases substantially through improvement of the insect's habitat. The extension of this model to more than one coincident equilibria, some of which may be locally stable, is discussed and generalized using the theory of habitat suitability. Use of equilibrium manifolds is suggested to permit greater dimensionality. Lastly, an explanation of insect epidemics, based on the effects of time delays in the response of density-dependent processes, is elaborated and generalized. The influence of spatial dimensions and insect dispersal on the theory is discussed. Scientific Paper No. 4890, College of Agriculture Research Center, Washington State University. Modified from a paper presented at the joint meeting of the Sociedad Mexicana de Entomologia and the Pacific and Southwestern Branches of the Entomological Society of America, held at Guadalajara, Mexico, April 17–22, 1977. This work was conducted under Project 102 and was supported by the State of Washington and the National Science Foundation (Grant Nos. GB-30752 and GB-34718).     

Simple mathematical models to describe the rate of mating in insect populations

Summary Simple models are constructed to describe the rate of mating in insect populations. The models are based on the assumption of random mate-searching in a closed habitat, including four parameters, i.e., population size, sex ratio, searching efficiency and male's capacity on mating frequency. The modes of effects of these parameters on the rate of mating are analyzed and some principles deduced are discussed in relation to the mating process in natural populations. This study was supported by science research fund from the Ministry of Education.     

Impact of developmental variance on behavior of models for insect populations II. Models for populations with density dependent restrictions on growth

Summary The impact of variation in developmental times on behavior of models for insect populations is investigated with special reference to models which include various types of intraspecific competition. At low densities, increases in developmental variation led to decreases in reproductive rate. At high densities, increases in developmental variation led to increases in reproductive rate. There was little change in the relationship between developmental variance and generation time as density increased.     

A reformulation of the two-sex problem

The ability of classical stable population theory to determine the equilibrium growth rate and age structure of a population from its vital rates in a single period depends on assuming that the observed maternity rates are equilibrium rates. This paper resolves the two-sex problem by replacing the fixed, age-specific fertility schedule of classical stable population theory by two basic relationships: a “birth matrix” and a “mating rule.” Placing certain restrictions on the birth matrix and the mating rule (BMMR), I establish that under certain plausible conditions, the BMMR model solves the two-sex problem by allowing matings and births to adjust to changes in population structure. The BMMR model thus provides an equilibrating mechanism in place of a fixed maternity schedule of classical stable population theory.     

Pest population stability under sterile releases

Summary The stability of a pest population is one of the critical features to be examined when considering a control strategy for a given pest species. Four models involviing sterile male releases are examined for various stability characteristics; the models examined were: (i) a simple one stage model with no species interactions, (ii) a two life-stage model, (iii) a model involving two competing species, (iv) a model in which the pest is under predation. Of the four, the simple model was the most stable and the predation model was the least stable under continued sterile releases.     

Survey on sex ratio of the children from one-child families in Shihezi in the Xinjiang Uigur autonomous region]

A survey of 1 child families in the Shihezi area showed a higher ratio of boys, 920 boys vs. 822 girls (1.12:1.00). There was also a higher ratio of boys among children born between 1975-1980, but the proportion of girls was higher among children born before 1974. The ratio of boys was higher among firstborn children born between 1976-1980 (1.086:1.00), while the sex ratio was 1.00 among 2nd born children born between 1976-1980. School children between age 6-18 showed 6266 boys and 6218 girls (1.01:1.00). The sex ratio of the total population in the Shihezi area was 1.05:1:00; this coincides with our national ratio of 1.08:1.00 (1953 census) and the world sex ratio of 1.0035:1.00 in 1975. The universal occurrence of more males than females is probably a result of physiological factors. It is actually beneficial to the country to have a slightly higher ratio of males because many jobs are more suitable for men because of their physical condition and the accidental death rate is also higher for men. The slightly higher percentage of boys among single child families was not statistically significant (P0.05).     

Evolutionary character changes and population responses in an insect host-parasitoid experimental system

In an insect host (the cowpea weevilCallosobruchus maculatus)- parasitoidHeterospilus prosopidis) experimental system, the population densities of the component species oscillated for the first 20 generations and then abruptly stabilized as the parasitoid density decreased. Examination of the host and parasitoid after the 40th generation in the long-term experiment showed that (1) host larvae exhibited contest-type competition (killing other larvae inhabiting the same bean), in contrast to the founder population being scramble-type competitors and (2) the parasitoid attack rate on the host did not change. There was also an evolutionary trade-off between body size and the rates of larval survival and development, suggesting a cost of contest competition on larval survivorship and development. I tested model predictions (Tuda and Iwasa 1998) that (1) host equilibrium population size should gradually decrease as the proportion of the contest type increases and that (2) random attacks of the parasitoid on the host should reduce the rate of increase in proportion of the contest type, and the effect should become manifest especially during the first 20 generations. Two of three host-only replicates showed significant decrease in population sizes. Although the density of emerging adults per bean did not differ between replicates of the host-only and host-parasitoid systems, comparison of the host body size between them on day 270 (at the 13th generation) showed that the host was more contest-type in the host-only system than in the host-parasitoid system, as the model predicted, and later on day 650 the effect of the parasitoid had disappeared.     

Midwifery continuity of care and vaginal birth after caesarean section: A randomised controlled trial

Problem and backgroundCaesarean section (CS) rates in Australia and many countries worldwide are high and increasing, with elective repeat caesarean section a significant contributor.AimTo determine whether midwifery continuity of care for women with a previous CS increases the proportion of women who plan to attempt a vaginal birth in their current pregnancy.MethodsA randomised controlled design was undertaken. Women who met the inclusion criteria were randomised to one of two groups; the Community Midwifery Program (CMP) (continuity across the full spectrum — antenatal, intrapartum and postpartum) (n = 110) and the Midwifery Antenatal Care (MAC) Program (antenatal continuity of care) (n = 111) using a remote randomisation service. Analysis was undertaken on an intention to treat basis. The primary outcome measure was the rate of attempted vaginal birth after caesarean section and secondary outcomes included composite measures of maternal and neonatal wellbeing.FindingsThe model of care did not significantly impact planned vaginal birth at 36 weeks (CMP 66.7% vs MAC 57.3%) or success rate (CMP 27.8% vs MAC 32.7%). The rate of maternal and neonatal complications was similar between the groups.ConclusionModel of care did not significantly impact the proportion of women attempting VBAC in this study. The similarity in the number of midwives seen antenatally and during labour and birth suggests that these models of care had more similarities than differences and that the model of continuity could be described as informational continuity. Future research should focus on the impact of relationship based continuity of care.