Parasitism of house fly (Musca domestica) pupae by four species of Pteromalidae (Hymenoptera): effects of host–parasitoid densities and host distribution

Parasitoid-induced mortality of house fly, Musca domestica L., pupae and parasitoid progeny emergence by four species of pteromalid parasitoids, Muscidifurax raptor Girault & Sanders, M.zaraptor Kogan & Legner, Spalangia cameroni Perkins and S.endius Walker, were determined for a 24 h exposure period using parasitoid: host ratios ranging from 1:2 to 1:50. When the number of parasitoids was held constant (n = 5) and the numbers of hosts varied, and when the number of hosts was held constant (n = 100) and the number of parasitoids varied, both the number of pupae killed per parasitoid and the number of parasitoid progeny per parasitoid increased with increasing parasitoid:host ratios to reach an upper limit asymptotically. Maximum values were, respectively: M.raptor (14.7, 11.1), M.zaraptor (12.3, 9.3), S.cameroni (16.9, 5.5), S.endius (14.8, 9.7) with no consistent effects attributed to parasitoid interference. For M.raptor and S.cameroni at parasitoid:host ratios of 1:10, the pupal mortality and progeny emergence were determined for a 24 h exposure period when hosts were distributed in poultry manure at four levels of aggregation ranging from clumped to uniform. Pupal mortality was least in clumped distributions, while parasitoid progeny emergence was not significantly different.     

Functional response and mutual interference of Peristenus spretus (Hymenoptera: Braconidae), a parasitoid of Apolygus lucorum (Heteroptera: Miridae)

Peristenus spretus Chen & van Achterberg (Hymenoptera: Braconidae) is a solitary endoparasitoid, which is considered for augmentative biological control of Apolygus lucorum Meyer-Dür (Heteroptera: Miridae) in Chinese cotton fields. Since the association of P. spretus with A. lucorum was only recently discovered, the biology of the parasitoid remains unknown. In order to understand its reproductive biology, the mutual interference and functional response of P. spretus were investigated by altering either the parasitoid or the host density while keeping the other constant. In both experiments, the effects of parasitoid and host densities on parasitism, superparasitism, progeny production and sex ratio were assessed. P. spretus exhibited a Holling type II functional response to changing host densities, indicating that parasitism increases with increasing host density until the parasitoid reaches its maximum reproductive capacity. The model suggested that a single P. spretus female could parasitise a maximum of 88 nymphs per day or four nymphs per hour. Increasing the wasp-nymph ratio from 1:10 to 1:80 significantly increased the offspring production more than fivefold from ±5.8 to ±35.6; further increasing the host densities (above 80 nymphs) did not significantly increase offspring production. Strong mutual interference of foraging P. spretus females occurred only at high parasitoid densities. Parasitoids foraging alone produced an average progeny of 33.4, whereas parasitoids foraging in groups of 16 produced only 2.6. The optimal wasp-nymph ratio for mass-rearing P. spretus is 4:100, given that resources of parasitoids and nymphs are unlimited.     

Effect of mating combinations on the host parasitisation and sex allocation in solitary endoparasitoid,Aenasius arizonensis (Hymenoptera: Encyrtidae)

Aenasius arizonensis (Girault) is an important solitary endoparasitoid of Phenacoccus solenopsis Tinsley. To optimise the mass production of high-quality females, it is important to assess the influence of mating regimes on the progeny fitness and sex allocation. We, therefore, hypothesise that mating combinations in A. arizonensis adults emerged from different host instars may influence parasitism and sex allocation in the subsequent generation. Therefore, we compared three nymphal instars (1st, 2nd and 3rd) and adults host stages of P. solenopsis for parasitism and sex allocation by A. arizonensis. Further, F₁ female progeny of the parasitoid emerged from different host instars was henceforth evaluated for its fitness in six mating combinations. A. arizonensis females parasitised all the host stages except the 1st instar nymphs. The parasitised 2nd instar nymphs yielded only males, while the sex ratio in the later host instars was strongly female-biased. The parasitoid females preferred 3rd instar nymphs with respect to higher parasitism (74.0–84.0%) and produced more females in the F₁ progeny as compared to other host stages. F₁ females that emerged from 3rd instar nymphs produced significantly higher parasitism (74.0–79.0%). These mating combinations also yielded more female progeny in the F₂ generation. However, parasitism by F₁ females was significantly lower (9.0–12.0%) when mated with males that emerged from 2nd instar P. solenopsis nymphs. Moreover, latter combinations yielded only male progeny in F₂ generation. These findings can be used in laboratory mass rearing of this parasitoid vis-à-vis biological control of P. solenopsis.     

The reproductive strategy of the gregarious parasitoid,Pteromalus puparum (Hymenoptera: Pteromalidae)

Summary Host size of Pteromalus puparum, a gregarious pupal parasitoid, shows a wide inter- and intraspecific variation. Experiments were made to study the regulation of the number and sex ratio of progeny per host by the parasitoid. The parasitoid could discriminate inter- and intraspecific size differences of the host and regulate the number of eggs according to the host size when a single female attacked the host. The sex ratio of progeny (proportion males) was about 0.1. The number of progeny laid by the female agreed with the energetically most efficient number og eggs in order to maximize total weight of progeny per host but not with the reproductively most efficient number of eggs to maximize the total fecundity of the progeny. The parasitoid laid smaller number of eggs in a half buried host, but the number was much larger than a half of those in a fully exposed host. When more than one female attacked a single host, the number and sex ratio of progeny per host increased with the number of females attacking the host, but the number of progeny per female decreased. The change of the sex ratio agreed with the prediction of the local mate competition model.     

Sex ratio regulation in Coccygomimus turionella Linnaeus (Hymenoptera: Ichneumonidae) and its ecological implications

Abstract. 1. Sex regulation and its relevance to the ecology of a k-selected pupal parasitoid was investigated in Coccygomimus turionellae.
2. The ratio varied with host size, females predominating in large hosts.
3. Egg transfer experiments and comparative mortality rates among the progeny of virgin and inseminated females demonstrated that the phenomenon was due to parental behaviour.
4. The study of the mechanism confirmed Aubert's hypothesis of host size estimation with the addition that the host had to be exposed from the poles and had to contain the proper host kairomones.
5. Host size was highly correlated to parasitoid fecundity via influences on size and longevity but not the number of ovarioles per female or daily egg production.
6. Host encounters are more limiting than egg production and host size had no effect on host acceptance.
7. Sex regulation allows a maximal host encounter rate at the same time that it maximizes the reproductive potential of female progeny.
8. Low host density increased the production of female progeny resulting in more offspring searching for the limited resource. Concealed hosts and a high host density resulted in a shift towards a Fisher 1:1 sex ratio.     

Biology of a thelyotokous biotype of Eretmocerus mundus (Hymenoptera: Aphelinidae) on Bemisia tabaci (Homoptera: Aleyrodidae)

Abstract Thelyotokous biotype of Eretmocerus mundus Mercet (Hymenoptera: Aphelinidae), a parasitoid of Bemisia tabaci (Gennadius) (Homoptera: Aleyrodidae), was recently recorded in northern Iran. Reproductive biology of this biotype was studied as part of an evaluation of its potential for biological control of B. tabaci. The parasitoid deposited more eggs under 2nd and 3rd nymphal instars than 1st or 4th instars. Adult females fed honey, with no access to whitefly nymphs, lived significantly longer (13.6 ± 4.7 d) than those given access to nymphs, but not fed honey (7.6 ± 2.21 d). Lifetime fecundity averaged 81.7 ± 26.9 female progeny per female parasitoid, ranging from 11–132. Daily fecundity, measured as the number of whitefly nymphs parasitized by per female each day for 10 d, averaged 18.06 ± 3.95 for the first 6 d of life, and then declined to < 11. Developmental time from oviposition to parasitoid emergence was significantly shorter in the 3rd instar of the host (15.9 ± 1.06 d) than in the 1st instar (18.7 ± 2.3 d), but not in the 2nd instar (16.4 ± 1.3 d).     

Influence of host size variation on the development of a koinobiont aphid parasitoid, Lysiphlebus ambiguus Haliday (Braconidae, Hymenoptera)

To determine whether host body size is the currency used by the aphidiine parasitoid, Lysiphlebus ambiguus Haliday (Hymenoptera: Braconidae), in assessing host quality, the aphid, Aphis fabae Scopoli (Homoptera: Aphididae), was reared at either high or low temperature to yield hosts of the same instar with different body sizes. Cohorts of A. fabae raised at 15 degrees C and 30 degrees C and exposed to individual female L. ambiguus in no-choice tests were successfully parasitized in all host stages from 1st instar nymphs to adults. However, younger and smaller aphids were more susceptible to parasitism than older and larger nymphs or adults, as measured by the number of mummies produced. For aphid cohorts reared at 15 degrees C, the proportion of female progeny, progeny adult size, and development time all increased linearly with aphid size at the time of attack. In contrast, for aphid cohorts raised at 30 degrees C, the proportion of female progeny and progeny adult size declined with aphid size, while development time remained unaffected. Through manipulation of host rearing temperature, we have shown that at cooler temperatures the koinobiont parasitoid, L. ambiguus, responds to host size in the same way as an idiobiont parasitoid, but that this response is compromised at higher temperatures. Our results suggest that differential mortality during development is likely to influence the observed secondary sex ratio in relation to aphid size for aphid cohorts raised at higher temperatures due to disruption of the activity of the host's primary endosymbiont and that such reduced nutritional quality of aphids cannot be compensated by increased development time.     

Influence of parasitoid-host density and host availability on the laboratory propagation ofMicroctonus aethiops [Hym.: Braconidae] parasitoid ofHypera postica [Coleop.: Curculionidae]

Laboratory studies of the arrhenotokous braconid wasp,Microctonus aethiops (Nees) were conducted relative to maximizing parasitoid production without adversely affecting sex ratios of the progeny. The influence of hostHypera postica (Gyllenhal) and parasitoid densities on parasitoid productivity was evaluated. Maximum production or a mean 25.8M. aethiops progeny were obtained per female when the host parasitoid ratio was 50∶1. More than one parasitoid per rearing cage resulted in fewer parasitoid progeny per female and increased host mortality. Oviposition significantly increased when female parasitoids were exposed to 25 different weevils every 24 hours. The most intense ovipositional activity usually occurred during the first 48 hours of exposure. However, superparasitism occurred if exposure to 25 hosts continued for more than 24 hours. Continuous and discontinuous oviposition patterns did not affect the numbers of parasitoid progeny produced. However, fewer females were produced when new weevils were provided every 24 hours as in the continuous oviposition group.     

Determination of the optimal parasitoid‐to‐host ratio for efficient mass‐rearing of the parasitoid,Sclerodermus pupariae (Hymenoptera: Bethylidae)

Sclerodermus pupariae Yang et Yao (Hymenoptera: Bethylidae) is used as a potential biocontrol agent for several buprestid and cerambycid larvae. This study aimed to enhance the efficiency of mass‐rearing of this parasitoid by investigating the fitness gain of this bethylid wasp, including the proportion of successful parasitism and development, brood size, sex ratio, proportion of winged female offspring, body size and longevity of female offspring, under eight different maternal parasitoid density treatments using Thyestilla gebleri Faldermann as host in the laboratory. The results indicated that the foundress densities did not affect the parasitism or emergence rate of this parasitoid. Brood size of the parasitoids increased significantly when the number of maternal wasps ranged from one to four. However, further increases in foundress number did not affect the parasitoid brood size. The sex ratios of S. pupariae were always female‐biased. The proportions of male in the progeny colonies were <10% throughout all experimental treatments. The percentage of winged female progeny was not significantly influenced by the density of adult maternal parasitoids. Body sizes of parasitoids significantly declined with increasing maternal parasitoid densities. Although the parasitoid body size reduced when maternal wasp number was higher, it could be compromised by the relatively higher number of female offspring produced. Further, more than 70% of the parasitoids remained alive when they were stored at 12°C for four months throughout the experiments. These findings suggest that exposure of four female wasps to a single host larva would result in the highest fitness of S. pupariae. Our findings might provide a new approach to enhance the efficiency of mass‐rearing of this bethylid wasp.     

Fitness consequences of superparasitism and mechanism of host discrimination in the stemborer parasitoid Cotesia flavipes

The fitness consequences of superparasitism and the mechanism of host discrimination in Cotesia flavipes, a larval parasitoid of concealed stemborer larvae was investigated. Naive females readily superparasitized and treated the already parasitized host as an unparasitized host by allocating the same amount of eggs as in an unparasitized host. However, there was no significant increase in the number of emerging parasitoids from superparasitized hosts due to substantial mortality of parasitoid offspring in superparasitized hosts. Furthermore, the developmental time of the parasitoids in a superparasitized host was significantly longer than in a singly parasitized host and the emerging progeny were significantly smaller (body length and head width). Naive females entered a tunnel in which the host was parasitized 4 h previously and accepted it for oviposition. Experienced females (oviposition experience in unparasitized host) refused to enter a tunnel with a host parasitized by herself or by another female. In experiments where the tunnel and/or host was manipulated it was demonstrated that the female leaves a mark in the tunnel when she parasitizes a host. The role of patch marking in C. flavipes is discussed in relation to the ecology of the parasitoid.     

Sex ratios in natural populations ofAphelinus mali (Hym.: Aphelinidae) in relation to host size and host density

In an apple orchard at Armidale, the Northern Tablelands of NSW, population sex ratios ofAphelinus mali (Haldeman), an endoparasitoid of the woolly apple aphid,Eriosoma lanigerum (Hausmann) varied from 0.51 (proportion of males) at low host densities to female-biased at high host densities (proportion of males ranged from 0.35–0.39). This shift in sex ratio seems to be caused by the differences in allocation of sons and daughters to hosts of different sizes. In the fieldA. mali parasitizes all life stages (four nymphal instars and adult) of the woolly aphid upon encountering. According to Hughes'(1979) optimal diet model, such general host acceptance seems to be the best strategy. However, it allows the host nymphs or adults to continue to develop or reproduce until about to mummify (pupate). No mortality was observed when first or second-instar hosts were parasitized in the laboratory. Field collected small mummified hosts yielded male-biased sex ratios whereas large mummified hosts produced mainly females. In the laboratory, progeny from smaller hosts (first to third-instars) produced sex ratios which were not significantly different from 0.5 whereas progeny from larger hosts (third and fourth-instars) produced female-biased sex ratio. During winter (June–August) and early spring (September–October) when the host populations in the orchard were predominantly nymphs, the parasitoid tended to allocate equal resources to male and female offspring. In contrast, at peak population densities in summer and autumn (December–May) when larger hosts were available, the sex ratios were female-biased. The host size ofE. lanigerum andA. mali is, therefore, an important component in the dynamics of host-parasitoid interactions.     

Functional response to host density by the egg parasiteTrichogramma pretiosum

The effect of host density on parasitism byTrichogramma pretiosum Riley was studied by exposing groups of 150, 300, 600 or 1200 eggs of potato tuber moth to 2, 4 or 8 female parasites per group. The parasite exhibited a type 2 functional response. As host density increasedT. pretiosum parasitised more hosts, but at a decreasing rate. The attack coefficient (a′) decreased as parasite density increased, whereas the handling time (T _h ) remained almost constant. The search rate (a) decreased with increasing host density.T. pretiosum responded to increasing host density by increasing the number of its encounters with hosts and the number of hosts it parasitised only up to host density of 300 when the parasite density was 2 and up to host density of 600 when the parasite densities were greater and then remained almost constant. The observed incidence of parasitism was higher than that expected on the assumption that the parasites behaved the same at higher host densities as at the lowest. When parasite density was raised from 2 to 8 females per group the percentage of female progeny fell from about 73 to about 48%. A 2-fold increase in the number of female progeny was observed when parasite density was reduced from 8 to 2 and also when the host density was raised from 150 to 1200 eggs.     

The reproductive strategy of the gregarious parasitoid,Pteromalus puparum (Hymenoptera: Pteromalidae)

Summary Pteromalus puparum is a gregarious parasitoid of many butterfly pupae. Adult size, mortality, and sex ratio of P. puparum, as a parasitoid of Papilio xuthus, were unit weight of the host. Effects of female size on fecundity, wing load, and longevity were also examined.The highest total weight of progeny from the host was attained when the number of eggs per gram of the host was approximately 150. Positive correlations were observed between the size of the females and their fecundity and wing load. The maximum longevity of the female kept with honey but without hosts was attained when the initial number of parasitoids per g of the host was 150.Considering the total fecundity of all female progeny, the reproductively most efficient number of eggs to be deposited per g of the host was estimated to be approximately 300. However, as shortage of food for the adult females strongly affects their fecundity, the reproductively most efficient number of eggs to be deposited per g of the host was about 70 when the adult female progeny was not provided with food.The optimal number of eggs to be deposited when the emale oviposits in the host under field conditions is discussed.     

拟澳洲赤眼蜂和短管赤眼蜂在米蛾卵上的种间竞争

By means of single and mixed inoculation, this paper studied the interspecific competition between T. confusum and T. pretiosum on the factitious eggs of Corcyra cephaloica under different parasitoid densities, host densities and inoculated spaces. The results showed that for both singly and mixed inoculated groups, the parasitism increased with parasitoid density but decreased with host density, whereas the percentage of female progeny dropped with parasitoid density but enhanced with host density. No significant effect was observed on adult emergence for all parasitoid and host density treatments. In mixed inoculated group, the proportion of T. pretiosum in the progeny decreased with parasitoid density but increased with host density, and was more than 50% in all treatments, indicating that T. pretiosum had a stronger competitive ability than T. confusum. In the spaces ranging from 4cm^3 to 102cm^3, the parasitism decreased gradually in both singly and mixed inoculated groups. The percentage of female progeny and adult emergence had no significant difference among different inoculated spaces. In mixed inoculated group, the proportion of T. pretiosum in the progeny was more than 50% in all treatments except space 102 cm3, but decreased with space, which suggested that T. confusum could improve their competitive ability through increasing their search areas and looking for more hosts.     

Host stage selection of the mealybug parasitoid Anagyrus spec. nov near sinope

The mealybug parasitoid Anagyrus spec. nov near sinope (Hymenoptera: Encyrtidae) is an undescribed parasitoid of the Madeira mealybug, Phenacoccus madeirensis Green (Homoptera: Pseudococcidae). We investigated the preference of Anagyrus spec. nov near sinope for six developmental stadia (first‐ and second‐instar nymphs, third‐instar immature females, third‐ or fourth‐instar immature males, pre‐reproductive adult females, and ovipositing adult females) of P. madeirensis and the fitness consequences of the host stage selection behavior. In the no‐choice test, Anagyrus spec. nov near sinope parasitized and completed development in all host stadia except third‐instar immature males. When all host stadia were offered simultaneously, the parasitoids preferred third‐instar immature and pre‐reproductive adult females. Dissection of the stung mealybugs revealed that the clutch size (number of eggs per host) was approximately four and three in the third‐instar and pre‐reproductive females, respectively, and one egg per first‐instar nymph. Parasitoids emerged from P. madeirensis parasitized at third‐instar or pre‐reproductive adult female completed development in the shortest duration, achieved a higher progeny survival rate, larger brood and body size, and the lowest proportion of males. We showed that the continued development of mealybugs had significant influence on the fitness of the parasitoids. Although deposited as eggs in first‐ or second‐instar nymphs, parasitoids emerged from mummies that had attained third‐instar or adult development achieved similar progeny survival rate, brood size, body size, and sex ratio as those parasitoids deposited and developed in third‐instar or adult mealybugs. By delaying larval development in young mealybugs, Anagyrus spec. nov near sinope achieved higher fitness by allowing the parasitized mealybugs to grow and accumulate body size and resources. We suggest that the fitness consequence of host stage selection of a koinobiont parasitoid should be evaluated on both the time of parasitism and the time of mummification.     

The Influence of Host Species on Some Biological and Behavioural Aspects of Dibrachys boarmiae (Hymenoptera: Pteromalidae), Parasitoid of Kermania pistaciella (Lepidoptera: Tineidae)

Dibrachys boarmiae was recently found as a parasitoid of the pistachio twig borer moth, Kermania pistaciella, an important pistachio pest in Iran. Several biological and behavioural aspects of the wasp were studied under controlled conditions using three different lepidopterous host species, K. pistaciella, Sitotroga cerealella and Galleria mellonella. Development time from egg to adult decreases from 54 days at 15°C to 12.6 days at 32.5°C. The thermal constant was estimated 270°D, and the lower development threshold was at 9.9°C. Longevity of females that had the opportunity to oviposit and access to food (honey) was on average 23 days, and 134 offspring were produced during 13 days of oviposition. Ninety percent of ovipositions occur during the first 10 days of the parasitoid's life, although no pre-oviposition period was found. If females were deprived of food, longevity as well as fecundity, were drastically reduced to 8 days and only 79 offspring respectively. Females were able to mate immediately after emergence and the sex ratio of the progeny was strongly female biased on all examined hosts, especially on the largest host G. mellonella (0.08 male). When females were kept with a male throughout their life, the total number of progeny decreased to 92 wasps on average but the sex ratio was unaffected. The parasitoid significantly preferred to attack the pre-pupal stage, and this influenced the size of clutches allocated to different host stages. The parasitoid laid larger clutches on bigger hosts.     

Mating and host density affect host feeding and parasitism in two species of whitefly parasitoids

Abstract The parasitoids in the genera of Encarsia and Eretmocerus (Hymenoptera: Aphelinidae) are important biological control agents of whiteflies, and some of them not only parasitize hosts but also kill them with strong host‐feeding capacity. Two whitefly parasitoid species, Encarsia sophia and Eretmocerus melanoscutus were examined to determine if mating and host density affected their host feeding and parasitism. The whitefly host, Bemisia tabaci, was presented to these two wasp species in densities of 10, 20, 30, 40, 50 and 60 third‐instar nymphs per clip cage. Mated whitefly parasitoid females fed on more hosts than unmated females under a range of host densities (under all six host densities for En. sophia; under the densities of 40 nymphs or more for Er. melanoscutus). Meanwhile, mated females parasitized more whitefly nymphs than unmated females under all host densities for both species. With increase of host density, mated or unmated Er. melanoscutus females killed more hosts by host feeding and parasitism. Mated En. sophia females killed more hosts by host feeding with increase of host density, whereas unmated females did not parasitze whitefly nymphs at all. Our results suggest that only mated female parasitoids with host‐feeding behavior should be released in crop systems to increase their bio‐control efficiency.     

Modelling age‐ and density‐structured reproductive biology and seasonal survival of Apanteles galleriae Wilkinson (Hym., Braconidae)

Abstract: The biology of Apanteles galleriae Wilkinson, an important biological control agent of wax moths, is well described in the literature. We developed models simulating the functional response of fecundity and female progeny proportion of adult females as a function of age, host and/or parasitoid density to integrate current knowledge. Daily pattern of age‐related fecundity and female progeny proportion of different parasitoids was also examined. We investigated the effect of sex, mating status and seasonal time on adult longevity. We derived survival data of females in two different seasonal periods. We found that 50% of adult life span is important for an efficient fecundity. The patterns of host and/or parasitoid density‐dependent fecundity and sex ratio varied considerably. The highest fecundity and female progeny proportion occurred with one parasitoid and one female equivalent host. Longevity of adults was affected by sex and month periods, but mating status did not affect their longevity. Female survival was greater between December and May relative to June and November. Our results indicated that age, host and parasitoid density, and the timing of rearing influenced the life processes of parasitoids.     

蝇蛹金小蜂对家蝇蛹的寄生策略

蝇蛹金小蜂Pachycrepoideus vindemmiae Rondani是家蝇Musca domestica蛹期常见寄生蜂种类。本文探讨蝇蛹金小蜂对寄主日龄的选择策略以及该寄生蜂的寿命、产卵历期和后代数量等规律。结果表明寄生蜂可利用各日龄的蝇蛹,寄生高龄期蝇蛹时,寄生蜂后代产量显著降低,既未出蜂也未出蝇的死亡蝇蛹比例显著增加;寄生蜂寿命为(11.89±6.99)d,产卵历期为(9.58±6.67)d,单个雌蜂后代产量为(33.74±18.08)头,雄性后代的发育历期显著短于雌性后代,随着寄生蜂产卵历期的延长,寄生蜂后代产量下降,雄性后代比例增加。     

Reproductive biology and related host-parasitoid interactions between the gypsy moth,Lymantria dispar and Glyptapanteles flavicoxis,a gregarious endoparasitoid*

The mean total progeny produced by female Glyptapanteles flavicoxis was significantly greater when the parasitoid attacked 4th instar gypsy moth rather than younger larvae. The development of parasitoids within older instars was faster than that in younger hosts. The proportion of female progeny was not altered by the host instar parasitised. The total reproductive output per female G. flavicoxis increased as the number of host larvae increased. However, since the reproductive output was spread among more available hosts, the reproductive output per host declined as the number of host larvae increased. There was no trend in the relationship between total progeny produced or the proportion of female progeny and the number of matings of parental females.