Pheromone trapping models for pest control: Effects of mating patterns and immigration

Several models are presented which examine pest population behaviour with the release of female sex pheromones for the attraction and annihilation of males. These models include male polygamy and female monogamy, various mating frequencies, delayed mating of females, immigration of one or all individual types, and differential survivorship of males and females. In all the models there are two steady states, a stable s.s. at the origin and an unstable s.s. in the positive domain for a given value of pheromone release rate. In all the models, control relies on the reduced ability of males to fertilize virgin females following trapping and male annihilation. As such, control is very sensitive to mating frequency, being very difficult when males mate frequently. Control is also very difficult with the immigration of even a moderate number of fertilized females. Control is much easier when mating is delayed, especially if survivorship is low, or with density dependent population regulation.     

Models for mating disruption by means of pheromone for insect pest control

Models are presented to investigate the population dynamic behavior of a pest population with the release of pheromone for mating disruption. Three mechanisms of mating disruption are considered: (i) confusion of males, (ii) competition with female pheromone trails yielding false trail following, (iii) emigration of males prior to mating. In addition, several refinements to confusion are considered. Confusion and emigration of males were found to be very similar both quantitatively and dynamically; also, a combination of both mechanisms was very little more efficient than either one separately. False trail following is difficult to compare with the other two, since competition with wild females is involved and thus the total population size enters the equations. Density dependence of the action of pheromones results in some cases in which mating disruption cannot control the pest population. Similarly, aggregation of the pest population decreases the efficiency of the method unless the pheromone action is density independent. Delayed mating of females makes control easier, and may constitute one mechanism for mating disruption.     

Modeling intra-sexual competition in a sex pheromone system: how much can female movement affect female mating success?

Mating disruption theory predicts that high concentrations of female pheromone, and/or large numbers of release sites, should confuse males orienting to "calling" females, reduce the number of successful matings, and decrease the reproductive potential of the population. In this scenario, females are regarded as stationary point sources of pheromone. Past behavioral observations, however, have shown virgin female grape root borers, Vitacea polistiformis Harris, significantly alter their behavior in mating disruption treatments. Treated females call at different heights, move less before call initiation, and move more after call initiation than control females. Pheromone gland dragging and wing fanning also increase significantly during pheromone treatments. These behavioral differences are significant only if they alter the mating success of females. Because long-term field studies are impractical, we used known behavior of male and female GRB to build a Fortran language time step model, adding the effects of female movement to past models of male pheromone plume following. Females were distributed randomly, and then assigned a conditional movement strategy. If females were within the competitive portion of another female's plume, the downwind female moved. Except in the lowest population density tested, females moving upwind and crosswind when in a competing female's pheromone plume mated significantly more often than females remaining stationary. In all population simulations, mating success was significantly reduced when females moved downwind. These field and simulation studies provide strong evidence for female movement as a previously overlooked potential mechanism for resistance to mating disruption treatments, as well as a shaping behavior in the evolution of pheromone communication systems.     

Mate choice evolution, dominance effects, and the maintenance of genetic variation

Female mate choice influences the maintenance of genetic variation by altering the mating success of males with different genotypes. The evolution of preferences themselves, on the other hand, depends on genetic variation present in the population. Few models have tracked this feedback between a choice gene and its effects on genetic variation, in particular when genes that determine offspring viability and attractiveness have dominance effects. Here we build a population genetic model that allows comparing the evolution of various choice rules in a single framework. We first consider preferences for good genes and show that focused preferences for homozygotes evolve more easily than broad preferences, which allow heterozygous males high mating success too. This occurs despite better maintenance of genetic diversity in the latter scenario, and we discuss why empirical findings of superior mating success of heterozygous males consequently do not immediately lead to a better understanding of the lek paradox. Our results thus suggest that the mechanisms that help maintain genetic diversity also have a flipside of making female choice an inaccurate means of producing the desired kind of offspring. We then consider preferences for heterozygosity per se, and show that these evolve only under very special conditions. Choice for compatible genotypes can evolve but its selective advantage diminishes quickly due to frequency-dependent selection. Finally, we show that our model reproduces earlier results on selfing, when the female choice strategy produces assortative mating. Overall, our model indicates that various forms of heterozygote-favouring (or variable) female choice pose a problem for the theory of sexual ornamentation based on indirect benefits, rather than a solution.     

A simple criterion for successful biological control on annual crops

Population dynamics of pest insect-natural enemy systems on annual crops is quite different from those seen in classic biological control programes. On an annual crop, for example, the persistence of populations of pest insects is forced to terminate when crops are harvested. Pest control on annual crops aims to suppress the maximum density of the pest below a certain level, and a low level equilibrium is not always the aim. It is important to determine the initial impact just after release of a natural enemy in order to determine the success of a biological control program. Therefore, effectiveness of natural enemies should be evaluated by prediction of such short-term population dynamics. This paper presents a new and simple analytical model for successful biological control on annual crops. A criterion of successful biological control is given as the ratio of the pest and natural enemy populations just when the pest begins to decrease. This ratio is derived from the intrinsic rates of natural increase of both populations and the daily total predation by natural enemies. Using this model, criteria on appropriate number and time of release of natural enemies are obtained. The practical applications of this model are discussed with respect to evaluating the success or failure of natural enemy releases in future biological control programs.     

Double impact of sterilizing pathogens: added value of increased life expectancy on pest control effectiveness

Sterilizing pathogens are commonly assumed not to affect longevity of infected individuals, and if they do then negatively. Examples abound, however, of species in which the absence of reproduction actually increases life expectancy. This happens because by decreasing the energy outlay on reproduction individuals with lowered reproduction can live longer. Alternatively, fertile individuals are more susceptible to predators or parasitoids if the latter can capitalize on mating signals of the former. Here we develop and analyze an SI epidemiological model to explore whether and to what extent does such a life expectancy prolongation due to sterilizing pathogens affect host dynamics. In particular, we are interested in an added value of increased life expectancy on the possibility of successful pest control, that is, the effect of increased lifespan and hence increased potential of the infected individuals to spread the disease on pest control effectiveness. We show that although the parameter range in which we observe an effect of increased lifespan of the sterilized individuals is not large, the effect itself can be significant. In particular, the increase in pest control effectiveness can be very dramatic when disease transmission efficiency is close to birth rate, mortality rate of susceptibles is relatively high (i.e., the species is relatively short-lived), and sterilization efficiency is relatively high. Our results thus characterize pathogens that are promising candidates for an effective pest control and that might possibly be engineered if not occurring naturally.     

Replicator-dynamics models of sexual conflict

Evolutionary conflict between the sexes has been studied in various taxa and in various contexts. When the sexes are in conflict over mating rates, natural selection favors both males that induce higher mating rates and females that are more successful at resisting mating attempts. Such sexual conflict may result in an escalating coevolutionary arms race between males and females. In this article, we develop simple replicator-dynamics models of sexual conflict in order to investigate its evolutionary dynamics. Two specific models of the dependence of a female's fitness on her number of matings are considered: in model 1, female fitness decreases linearly with increasing number of matings and in model 2, there is an optimal number of matings that maximizes female fitness. For each of these models, we obtain the conditions for a coevolutionary process to establish costly male and female traits and examine under what circumstances polymorphism is maintained at equilibrium. Then we discuss how assumptions in previous models of sexual conflict are translated to fit to our model framework and compare our results with those of the previous studies. The simplicity of our models allows us to consider sexual conflict in various contexts within a single framework. In addition, we find that our model 2 shows more complicated evolutionary dynamics than model 1. In particular, the population exhibits bistability, where the evolutionary outcome depends on the initial state, only in model 2.     

Effect of mating delay on the reproductive performance of Cnephasia jactatana (Lepidoptera: Tortricidae)

The leafroller species, Cnephasia jactatana Walker, is an important pest of kiwifruit in New Zealand. The effect of mating delay on its reproductive performance was investigated in the laboratory to provide information for the development of pheromonal pest control measures such as mating disruption. Reproductive performance of both sexes is adversely affected by mating delay. Females are more severely affected by mating delay than males in terms of reproductive potential. Delaying mating in females for 3 and 4 d reduced the reproductive potential by 29 and 88%, respectively. It is suggested that mating disruption may have potential for the control of this species.     

Aggregation and mating success of Capnodis tenebrionis （Coleoptera： Buprestidae）

An understanding of the relative importance of extrinsic and intrinsic factors in determining the potential distribution and mating success of individuals is critical for the successful monitoring and management of pest species. Using a combination of field observations and a caged field experiment, we explored the roles of environmental and individual variation on the formation of mating aggregations and mating success in the buprestid beetle Capnodis tenebrionis （Linnaeus, 1767）, a pest species of stone fruit trees. Our field observations revealed that the formation of aggregations is influenced by a range of environmental factors including temperature, photoperiod, and population density. However, aggregations were not at random and were more likely to occur on the section of the plant with highest incidence of solar radiation and thus higher temperatures. Data from our experiment with caged beetles in the field further indicate that the reproductive behavior of this species varies with temperature. The probability of a successful mating occurring was also positively related to both male and female size. Females of C. tenebrionis mate several times over a 4-h period, but generally not with the same male. Information obtained from these studies is useful to define the most appropriate time for pest control, especially adopting strategies that interfere with reproduction.     

Polyandry and female control: the red flour beetle Tribolium castaneum as a case study

Females of many animal species are polyandrous, and there is evidence that they can control pre- and post-mating events. There has been a growing interest in consequences of polyandry for male and female reproductive success and offspring fitness, and its evolutionary significance. In several taxa, females exhibit mate choice both before and after mating and can influence the paternity of their offspring, enhancing offspring number and quality, but potentially countering male interests. Studying female mating biology and in particular post-copulatory female control mechanisms thus promises to yield insights into sexual selection and the potential of male-female coevolution. Here, we highlight the red flour beetle Tribolium castaneum (Herbst), a storage pest, as a model system to study polyandry, and review studies addressing the effects of polyandry on male sperm competitive ability and female control of post-mating events. These studies show that the outcome of sperm competition in the red flour beetle is influenced by both male and female traits. Furthermore, recent advances suggest that sexual conflict may have shaped reproductive traits in this species.     

Effect of Age, Body Weight and Multiple Mating on Copitarsia decolora (Lepidoptera: Noctuidae) Reproductive Potential and Longevity

Successful behavioral-based control methods rely on the accurate knowledge of the mating dynamics of the target insect. Age at first mating affects reproductive potential and the chance of multiple mating. The cabbage moth, Copitarsia decolora (Guenée) is an important pest of a number of commodities. We investigated combinations of age, body size and mating history to determine how these variables affect insect reproductive capacity. Fecundity and fertility decreased as the age of mating pairs increased, heavy and average sized females laid more eggs than light females. Female multiple mating did not enhance fecundity nor fertility potential. Furthermore, spermatophore size did not determine female re-mating behavior. However, female fecundity and fertility was related to the male mating history. Our results show that SIT is a valuable tool for controlling this pest.     

The effect of genetic incompatibility of demes on total population development

The change of absolute deme frequencies in a discrete-time model of multiple, mutually genetically incompatible subpopulations (demes) which are still in mating contact has been studied. The attempt was made to answer the question of which initial conditions concerning deme frequencies lead to extinction or survival of certain demes. A complete answer could be given for the density-independent model and, with some restrictions, for a particular kind of density-dependent model assuming essentially complete niche overlap. For a more general model of density dependence, necessary initial conditions for deme extinction have been derived. Some implications for pest control have been briefly outlined.     

Modeling ecological traps for the control of feral pigs

Ecological traps are habitat sinks that are preferred by dispersing animals but have higher mortality or reduced fecundity compared to source habitats. Theory suggests that if mortality rates are sufficiently high, then ecological traps can result in extinction. An ecological trap may be created when pest animals are controlled in one area, but not in another area of equal habitat quality, and when there is density‐dependent immigration from the high‐density uncontrolled area to the low‐density controlled area. We used a logistic population model to explore how varying the proportion of habitat controlled, control mortality rate, and strength of density‐dependent immigration for feral pigs could affect the long‐term population abundance and time to extinction. Increasing control mortality, the proportion of habitat controlled and the strength of density‐dependent immigration decreased abundance both within and outside the area controlled. At higher levels of these parameters, extinction was achieved for feral pigs. We extended the analysis with a more complex stochastic, interactive model of feral pig dynamics in the Australian rangelands to examine how the same variables as the logistic model affected long‐term abundance in the controlled and uncontrolled area and time to extinction. Compared to the logistic model of feral pig dynamics, the stochastic interactive model predicted lower abundances and extinction at lower control mortalities and proportions of habitat controlled. To improve the realism of the stochastic interactive model, we substituted fixed mortality rates with a density‐dependent control mortality function, empirically derived from helicopter shooting exercises in Australia. Compared to the stochastic interactive model with fixed mortality rates, the model with the density‐dependent control mortality function did not predict as substantial decline in abundance in controlled or uncontrolled areas or extinction for any combination of variables. These models demonstrate that pest eradication is theoretically possible without the pest being controlled throughout its range because of density‐dependent immigration into the area controlled. The stronger the density‐dependent immigration, the better the overall control in controlled and uncontrolled habitat combined. However, the stronger the density‐dependent immigration, the poorer the control in the area controlled. For feral pigs, incorporating environmental stochasticity improves the prospects for eradication, but adding a realistic density‐dependent control function eliminates these prospects.     

The role of prey taxis in biological control: a spatial theoretical model

We study a reaction-diffusion-advection model for the dynamics of populations under biological control. A control agent is assumed to be a predator species that has the ability to perceive the heterogeneity of pest distribution. The advection term represents the predator density movement according to a basic prey taxis assumption: acceleration of predators is proportional to the prey density gradient. The prey population reproduces logistically, and the local population interactions follow the Holling Type II trophic function. On the scale of the population, our spatially explicit approach subdivides the predation process into random movement represented by diffusion, directed movement described by prey taxis, local prey encounters, and consumption modeled by the trophic function. Thus, our model allows studying the effects of large-scale predator spatial activity on population dynamics. We show under which conditions spatial patterns are generated by prey taxis and how this affects the predator ability to maintain the pest population below some economic threshold. In particular, intermediate taxis activity can stabilize predator-pest populations at a very low level of pest density, ensuring successful biological control. However, very intensive prey taxis destroys the stability, leading to chaotic dynamics with pronounced outbreaks of pest density.     

Local adaptation to developmental density does not lead to higher mating success in Drosophila melanogaster

In this study, we investigate the effect of local adaptation to developmental density on male mating success in laboratory populations of Drosophila melanogaster. Mating success is known to be influenced by body condition which can in turn be influenced by local adaptation. We test the hypothesis that males adapted to a given environment have higher mating success when assayed in that environment. We used males selected for adaptation to high larval density and their controls which are reared at low larval density. We grew assay males in low and high densities whereas the focal females (raised at low larval density) used for the experiment belonged to the common ancestor of selected and control populations. We considered selected males grown at high density and control males grown at low density as ‘adapted’. Similarly, we considered selected males grown at low density and control males grown at high density as ‘nonadapted’. Selected male belonging to a given treatment (larval density) was made to compete with control male of the same treatment for mating with ancestral female. We quantified components of reproductive fitness: mating latency, copulation duration, mating success and number of progeny sired by the ‘adapted’ and ‘nonadapted’ males. The results show that local adaptation does not lead to higher mating success in populations adapted to their own larval rearing environment.     

Mate search and mate-finding Allee effect: on modeling mating in sex-structured population models

Many demographic and other factors are sex-specific. To assess their impacts on population dynamics, we need sex-structured models. Such models have been shown to produce results different from those predicted by asexual models, yet need to explicitly consider mating dynamics. Modeling mating is challenging and no generally accepted formulation exists. Mating is often impaired at low densities due to difficulties of individuals in locating mates, a phenomenon termed a mate-finding Allee effect. Widely applied models of this Allee effect assume either that only male density determines the rate at which females mate or that male and female densities are equal. Contrarily, when detailed models of mating dynamics are sometimes developed, the female mating rate is rarely reported, making quantification of the mate-finding Allee effect difficult. Here, we develop an individual-based model of mating dynamics that accounts for spatial search of one sex for another, and quantify the rate at which females mate, depending on male and female densities and under a number of reasonable mating scenarios. We find that this rate increases with male and female densities (hence observing a mate-finding Allee effect), in a decelerating or sigmoid way, that mating can be most efficient at either low or high female densities, and that the mate search rate may undergo density-dependent selection. We also show that mate search trajectories evolve to be as straight as possible when targets are sedentary, yet that when targets move the search can be less straight without seriously affecting the female mating rate. Some recommendations for modeling two-sex population dynamics are also provided.     

Evolution of disassortative and assortative mating preferences based on imprinting

A two-locus haploid model of sexual selection is investigated to explore evolution of disassortative and assortative mating preferences based on imprinting. In this model, individuals imprint on a genetically transmitted trait during early ontogeny and choosy females later use those parental images as a criterion of mate choice. It is assumed that the presence or absence of the female preference is determined by a genetic locus. In order to incorporate such mechanisms as inbreeding depression and heterozygous advantage into our haploid framework, we assume that same-type matings are less fertile than different-type mating. The model suggests that: if all the females have a disassortative mating preference a viability-reducing trait may be maintained even without the fertility cost of same-type matings; a disassortative mating preference can be established even if it is initially rare, when there is a fertility cost of same-type matings. Further, an assortative mating preference is less likely to evolve than a disassortative mating preference. The model may be applicable to the evolution of MHC-disassortative mating preferences documented in house mice and humans.     

Can non‐directional male mating preferences facilitate honest female ornamentation?

Recent studies have demonstrated male mate choice for female ornaments in species without sex-role reversal. Despite these empirical findings, little is known about the adaptive dynamics of female signalling, in particular the evolution of male mating preferences. The evolution of traits that signal mate quality is more complex in females than in males because females usually provide the bulk of resources for the developing offspring. Here, we investigate the evolution of male mating preferences using a mathematical model which: (i) specifically accounts for the fact that females must trade-off resources invested in ornaments with reproduction; and (ii) allows male mating preferences to evolve a non-directional shape. The optimal adaptive strategy for males is to develop stabilizing mating preferences for female display traits to avoid females that either invests too many or too few resources in ornamentation. However, the evolutionary stability of this prediction is dependent upon the level of error made by females when allocating resources to either signal or fecundity.     

Host-Parasitoid Dynamics and the Success of Biological Control When Parasitoids Are Prone to Allee Effects

In sexual organisms, low population density can result in mating failures and subsequently yields a low population growth rate and high chance of extinction. For species that are in tight interaction, as in host-parasitoid systems, population dynamics are primarily constrained by demographic interdependences, so that mating failures may have much more intricate consequences. Our main objective is to study the demographic consequences of parasitoid mating failures at low density and its consequences on the success of biological control. For this, we developed a deterministic host-parasitoid model with a mate-finding Allee effect, allowing to tackle interactions between the Allee effect and key determinants of host-parasitoid demography such as the distribution of parasitoid attacks and host competition. Our study shows that parasitoid mating failures at low density result in an extinction threshold and increase the domain of parasitoid deterministic extinction. When proned to mate finding difficulties, parasitoids with cyclic dynamics or low searching efficiency go extinct; parasitoids with high searching efficiency may either persist or go extinct, depending on host intraspecific competition. We show that parasitoids suitable as biocontrol agents for their ability to reduce host populations are particularly likely to suffer from mate-finding Allee effects. This study highlights novel perspectives for understanding of the dynamics observed in natural host-parasitoid systems and improving the success of parasitoid introductions.     

Mating disruption method against the vine mealybug,Planococcus ficus: effect of sequential treatment on infested vines

The vine mealybug, Planococcus ficus (Signoret) (Hemiptera: Pseudococcidae), is a major pest of vineyards. Here, we tested the efficacy of the mating disruption method against the pest when applied during one or two successive years in high and low infestation levels. Following 1 year of treatment, at low initial infestation levels a shutdown of pheromone traps was observed, along with a significant reduction in infested vines. With initially high infestation levels, a gradual reduction in infested vines was observed, with a trap shutdown seen only after the second year of pheromone application. We discuss the implications of the male mating disruption method for this pest in which the wingless females are aggregated with limited movement among vines, offering multiple mating opportunities for the flying male.