Annotated Bibliography On Female Parenting

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1-1-2012

Modelling female mating success during mass trapping and natural competitive attraction of searching males or females
John A. Byers
USDA-ARS, [e-mail]

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Byers, John A., "Modelling female mating success during mass trapping and natural competitive attraction of searching males or females" (2012). Publications from USDA-ARS / UNL Faculty. Paper 1095. http://digitalcommons.unl.edu/usdaarsfacpub/1095

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DOI: 10.1111/eea.12006

Modelling female mating success during mass trapping and natural competitive attraction of searching males or females
John A. Byers*
US Arid-Land Agricultural Research Center, USDA-ARS, 21881 North Cardon Lane, Maricopa, AZ 85138, USA Accepted: 3 September 2012

Key words: computer simulation, monitoring, mating disruption, integrated pest management, IPM, mating systems, semiochemicals, effective attraction radius

Abstract

Simulation models of insects encountering sex pheromone with or without mass trapping in which the searching sex is either male (moths and many insect species) or female (some true bugs, beetles, and flies) were developed. The searching sex moved as a correlated random walk, while the opposite sex remained stationary (calling) and released an attractive sex pheromone. The searching sex was caught when encountering a pheromone-baited trap, and females mated when encountering a male. An encounter with pheromone was defined by the searcher’s interception of a circle termed the effective attraction radius (EARc). Parameters of movement (speed and duration), initial numbers of calling sex and searching sex, number of traps, area, and EARc of traps and calling sex were varied individually to evaluate effects on the percentage of females mating. In the natural condition without traps, female mating success in both models was identical. Increasing the EARc of the calling sex caused diminishing increases in female mating success, suggesting that evolution of larger pheromone release and EARc is limited by increasing costs (production/sensitivity) relative to diminishing increases and benefits of mating encounters. With mass trapping, increasing the EARc of traps or density of traps caused similar declines in female mating in both models, but the female-searching model predicted slightly lower mating success than the male-searching model. Increasing the EARc of calling insects or the initial density of insects caused similar increases in female mating in both models, but again the female-searching model had slightly lower mating success than the malesearching model. The models have implications for mating lek formation and for understanding the variables affecting the success of mass trapping programs for insect pests with either male or female sex pheromones.

Introduction
Pheromones with attractive properties appear to be ubiquitous in insect mating systems. These pheromones can be characterized in regard to their attraction distances and the responding and producing sexes. Furthermore, attractive pheromones may be characterized by whether they act only on the opposite sex (sex pheromone), or act on both sexes (aggregation pheromone); there is a continuum between sex and aggregation pheromones. Pheromones are also characterized by which sex produces the pheromone. Usually, only one gender in a species produces the

*Correspondence: E-mail: [e-mail]

attractive pheromone (www.pherobase.net). Long-range sex pheromones in practically all moth species (Lepidoptera) have been shown to be produced only by the female and to attract only the male (Byers, 2006). Many other species across various insect orders (cockroaches, aphids, mealybugs, bugs, beetles, and flies) have female-produced sex pheromones to which males (male-searching model) are the only sex responding (www.pherobase.net). In contrast to the male-searching model, there are more than a few species where males produce a sex pheromone that only attracts (or nearly so) females, which can be described as a female-searching model. For example, the male dried bean beetle, Acanthoscelides obtectus (Say) produces a sex pheromone attractive to females (Halstead, 1973), as do male desert beetles Parastizopus armaticeps

No claim to original US government works Entomologia Experimentalis et Applicata 145: 228–237, 2012

228

Entomologia Experimentalis et Applicata © 2012 The Netherlands Entomological Society
This article is a U.S. government work, and is not subject to copyright in the United States.

Simulated mating encounters and mass trapping 229

´ (Peringuey) (Geiselhardt et al., 2008). Several cockroach species (Dictyoptera) have males that release sex pheromone to which only females respond (Sreng, 1990; Farine et al., 1994, 2007). At least one longhorn male beetle, the coffee white stemborer, Xylotrechus quadripes Chevrolat, produces a sex pheromone attracting females (Hall et al., 2006). Also, some stink bug species (Pentatomidae) have been discovered where males produce a sex pheromone ´ that appears only to cause females to respond (Brezot et al., 1994; McBrien et al., 2001, 2002; Borges et al., 2007). Leks (mating swarms) are invariably formed by males that produce an aggregation pheromone and ‘call’ for females, which join briefly to mate and then leave. Leks appear common in Hymenoptera and Diptera, for example, males of wood wasps (Cooperband et al., 2012) and many species of flies (Hoglund & Alatalo, 1995; Field et al., 2002; Wicker-Thomas, 2007). Many important fruit fly pests (Tephritidae) as well as human disease-vectoring sand flies (Psychodidae) have male-produced sex pheromones that attract conspecific females (Jacobson et al., 1973; Chuman et al., 1987; Robacker, 1988; Hamilton et al., 1996; Khoo et al., 2000). However, in many cases the males can call singly as well as form lek mating swarms (Jarvis & Rutledge, 1992; Shelly, 2001; Field et al., 2002; Quilici et al., 2002; Segura et al., 2007; Robacker et al., 2009). Thus, in many important pest species the males produce the sex pheromone that is attractive only to females, and some of these species may also form leks. Mass trapping commonly uses many traps with pheromone dispensers in an area to attract one or both sexes and remove them before females mate and lay viable eggs (Shorey, 1977; El-Sayed et al., 2006, 2009; Byers, 2007, 2008). A similar method is mating disruption, which uses only dispensers that waste the time of one or both sexes orienting in pheromone plumes and/or become disoriented so mating occurrences are greatly reduced (Shorey, ´ ´ 1977; Carde, 1990; Carde & Minks, 1995; Miller et al., 2006a,b). In these control methods, competitive attraction occurs when natural sources of pheromone from calling insects compete with sources of synthetic pheromone or semiochemicals from lures (Miller et al., 2006a,b). Byers (2007) used the ‘effective attraction radius’ (EAR) to represent the catching power of natural pheromone as well as an attractive trap’s dispenser (competitive attraction) in models of mass trapping. The EAR of a pheromone source is defined as a theoretical sphere that would intercept the same number of insects as that caught by a trap releasing the pheromone. A specific EAR in meters for a particular species and pheromone release rate is calculated from the trap catch and the silhouette area of the trap compared to the catch on an unattractive (blank control) trap that catches at least one individual (Figure 1; Byers et al., 1989;

Figure 1 Two cylindrical sticky traps, a blank catching one insect (Cb = 1) and a pheromone trap catching 40 insects (Ca = 40), are each 0.09 m2 in silhouette area (S), giving a spherical EAR ¼ ½ðCa Á SÞ=ðp Á Cbފ0:5 ¼ 1:070 m that can be converted to a circular EARffic = p Á EAR2/(2 Á FL) = 0.539 m (where pffiffiffiffiffiffiffiffi FL ¼ SD Á 2 Á p ¼ 3:33 m) (Byers, 2008). The black wavy lines represent a pheromone plume, whereas the small dots represent 1 000 insects distributed vertically in a normal distribution (SD = 1.33 m).

Byers, 2008, 2009). An EAR indicates the strength of a pheromone source and depends on the chemical blend, release rate, and ecological function (e.g., short- or longrange) with regard to a species. In addition, multiple EAR conveniently represent pheromone sources in models instead of attempting to simulate complex spatial-temporal dimensions of attractive odor plumes interacting with insect orientation behaviors in the field (Figure 1). The spherical three-dimensional EAR, measured from catches in the field, needs to be transformed into a circular EAR (termed EARc) for use in two-dimensional encounter-rate simulations of competitive attraction and camouflage (Byers, 2008). The conversion equation requires an estimation of the standard deviation (SD) of the vertical flight distribution (Byers, 2011) to obtain an effective flight layer, FL (Figure 1). Thus, the EARc can be estimated from the vertical catch data of the species of interest and from the catch on the synthetic sex pheromone and blank traps such that models of mass trapping can be made predictive. The simulations also require estimates of average distance searched (or average flight speed and time of flight) that can be estimated from flight mill tests (e.g., 23 km for male pink bollworm moths; Wu et al., 2006). Densities of the searching and the calling sex can be measured in the field using EAR-related methods (Byers, 2012) along with determinations of EARc of calling sex and pheromone-baited traps. These predetermined values (or values varied) can then be used in simulations to explore the effect of different numbers of traps on female mating success.

230 Byers

The first objective of this study was to explore differences in mating encounters, if any, between male- and female-searching systems when no pheromone traps were present. This would occur in natural environments or before mass trapping and mating disruption attempts of the last 40 years. The second objective was to compare the male-searching system of moths and many other insects as modelled earlier (Byers, 2007) with a new model of search by females when numerous pheromone-baited traps were employed. General assumptions of the models are that (1) the sex ratio is 1:1 as in most species, and (2) females mate only once, whereas moving or stationary males can mate repeatedly during the simulated period. In both the maleand the female-searching models, the searching sex can be caught by pheromone traps, but only the female (stationary or moving) is removed after mating (to begin egg laying). Implications for lek mating systems, such as female-searching with fewer sources of male-produced pheromone, will also be considered.

Materials and methods
A simulation model was constructed for females searching for stationary males competing with each other and sometimes with pheromone-baited traps to compare this to a previous model of male-searching moths (Byers, 2007). The new model had males represented by EARc of specified radius, remaining stationary, whereas females moved at specified speeds and durations (distances) within a rectangular area (female-searching model). The alternative model reversed the role of the sexes in producing and orienting to pheromone. In both models, males were never removed after mating encounters with females, whereas females were removed. Simulations proceeded until either the searching male or female had (1) taken the number of steps of constant length (depending on speed in m sÀ1) required for the specified duration, or (2) all the searching sex were caught by traps, or (3) all the females were mated (Figure 2). Various numbers of searching females or males were placed at random within a rectangular area of specified xa and ya axes [e.g., in Java: Math.random()*xa] to obtain specific initial densities. Pheromone traps, also represented by a specified EARc (usually 2 m) were usually placed at random, but with all centers spaced apart at least a minimum allowed distance (MAD) that was half the maximal spacing for a hexagonal pattern, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi MAD ¼ 0:5 Á ð1:0746= n Á xa Á yaÞ, where n is the number of traps. For high-density trap placements, the traps were placed at random, but with no overlap of EARc. Individuals of the searching sex were initially placed at random points and usually moved a step (s) of 1 m each second in a correlated random walk. After initial directions
Figure 2 Flow diagram of simulation model 2 for femalesearching insects (see Figure 1 in Byers, 2007, for flow diagram of model 1, male-searching moths).

(a in radians) were chosen at random for each individual, each took steps between successive coordinates (e.g., x1, y1 to x2, y2) based on polar coordinates [x2 = x1 + s Á cos (a + φ), y2 = y1 + s Á sin (a + φ)] that deviated from their previous direction by an angle (φ) taken at random from a normal distribution with a standard deviation of 6° (Byers, 2001). Thus, each individual’s a direction changed at each step according to a = a + φ. A mating or catch encounter was determined when any of the searching sex stepped into or through an EARc of the stationary sex or trap [line segment intersecting a circle algorithm in Figure 3 of Byers (1991)]. Individuals that otherwise would leave the simulation area were made to take one or more new directions at random until they remained in the area. The two models were programmed in Java 6 (Oracle, Redwood Shores, CA, USA) and implemented visually in a Java application on a personal computer. A Java applet was made for demonstration on the Internet in a web browser (see http://www.chemicalecology.net/java2/model2.htm). Simulation results were graphed using QuickBASIC 4.5 code (Microsoft, Redmond, WA, USA) generating PostScript files for processing by Adobe Acrobat 6.0 (Adobe Systems, San Jose, CA, USA) and ReaConverter Pro v3.5 (ReaSoft Development, Seattle, WA, USA).

Simulated mating encounters and mass trapping 231

A

B

C

Figure 3 (A) Percentage of females mated when no traps were present in model 1 (males searching, stationary females; solid line, filled circles) or model 2 (females searching, stationary males; dashed line, open circles) depending on area. (B) Percentage of females mated when no traps were present (models as in A) depending on EARc of stationary sex. (C) Percentage of females mated when no traps were present (models as in A) depending on flight speed of searching sex. In all cases, 1 000 searching sex began to travel for up to 18 km (or 5 h) at a speed of 1 m sÀ1 unless varied, in an area of 10 km2 unless varied, and 1 000 stationary sex had an EARc of 0.5 m unless varied.

Simulations were performed in specified areas with an initial number of stationary sex and searching sex placed in the male-searching (model 1) and female-searching (model 2) systems. To determine whether or not there

were differences in the percentage of females mating during 5 h of searching (up to 18 000 steps) in natural environments (no mass trapping), both models were compared without traps in which either area (5–100 km2), EARc (0.05–1 m), or speed (0.1–2 m sÀ1) was varied, while other parameters were kept constant (see figures and captions for specific simulation parameters). As in all simulations, females that encountered a male were mated and removed from further consideration. Mobile males continued to search after mating (male searching) and stationary males continued to call after mating (female searching). In subsequent simulations, traps were added to the models, and the hours of searching flight were varied from 0.25 to 1.75, with initially 1 000 of each sex (stationary sex EARc = 0.5 m). The percentages of females and males that had mated within each 30 min period over the first 2 h were compared in the two models in which the searching sex could fly up to 10 h in a 1-km2 area with 100 pheromone traps (each 2 m EARc). In addition, the average distance traveled by the searching sex was calculated during the 10-h simulations. In additional simulations, the EARc of pheromone traps in both models was varied from 0.25 to 5 m (n = 8 simulations for each value) to determine the effect of EARc size on female mating success. Each simulation had initially 100 of each sex (calling sex EARc = 0.5 m) and 100 traps in a 9-ha area (300 9 300 m). The searching sex flew at 1 m sÀ1 for up to 5 h. Similarly, the EARc of stationary callers was varied from 0.1 to 2 m in both types of models that had trap EARc of 2 m. The initial number of each sex in a 9-ha area was varied from 20 to 450 in both models in which the calling sex had an EARc of 0.5 m and there were 100 traps of 2-m EARc. As mentioned above, the searching sex flew at 1 m sÀ1 for up to 5 h (eight simulations per value) and the percentage of the females mated was calculated. Similarly, the number of traps was varied from 10 to 300 (trap EARc of 2 m) to determine the effect of trap number on the percentage of females mating. The percentages of 1 000 of each sex in each model that were still searching, had been caught, or had mated by the end of the 5 h simulation (up to 18 km search distance) in increasingly larger areas (5–100 km2) were determined and graphed. The percentages of females mating in the two models were compared in a two-dimensional simulation array by varying the initial number of each sex (from 50 to 500) and the number of pheromone traps (from 10 to 100 of 4 m EARc) in a 100 9 100 m area. Female mating success in the female-searching model (1 000 females in a 4-km2 area) was compared between a case with 1 000 males (each of EARc = 0.25 m) to a case with male lek formation comprising 100 leks (each lek with 10 males and a larger EARc = 2.5 m proportional to lek size).

232 Byers

Means of the simulations were determined as well as in many cases the 95% confidence limits of the means. Best fitting regression equations of female mating success as a function of various simulation variables were analyzed using TableCurve 2D v5.01 (Systat Software, Chicago, IL, USA).

A

Results
Varying the area from 5 to 100 km2 with an initial 1 000 of each sex when no traps were present caused the percentage of females mating to decline from 98 to about 15% in both the male- and the female-searching model (Figure 3A). The same parameters were used in the two models except that females and males had opposite roles of calling and searching. The curves of mating decline were not significantly different between the models and best fit a reciprocal model [Y = 1/(a + bX), R2>0.99] that should represent the natural mate-finding situation without mass trapping (Figure 3A). More simulations without traps showed that an increase in the EARc of the stationary sex had decreasing benefits with regard to mating success in both models (Figure 3B). Similarly, increases in speed of the searching sex had diminishing benefits on mating success in both models (Figure 3C). These logarithmiclike increases in mating success due to increases in EARc or speed best fit the function Y = 100 À aebX (R2>0.99) (Figure 3). Therefore, the male- and female-searching models are identical in mating success of females when traps are not present. However, when traps are present, there are differences (Figure 4). In the male-searching model with initially 1 000 males (Figure 4A), the average (± 95% confidence limits) distance a male traveled was 2 367 ± 149 m, which was also the distance before capture as all males were caught by the 100 traps before the 10 h period expired. Of the females, 703 mated before all males were captured, leaving 297 females unmated. The percentage of females mating and males captured was summarized every 30 min until males were nearly all caught and showed that female mating percentages were consistently lower than percentages of searching males captured (Figure 4A). This is in contrast to the female-searching model (Figure 4B) in which the percentage of females mating was higher than the percentage of searching females captured. Also, the rate of decline in mating and capture of the searching sex is less in the male-searching model than that in the female-searching model (Figure 4A and B). In the female-searching model with initially 1 000 females (Figure 4B), the average distance a female traveled was 700 ± 84 m, whereas one female was never mated or captured in the 10 h period. The number of females eventually mating was 697 (nearly
B

Figure 4 (A) Percentage of initial 1 000 male-searching insects (solid line) caught by 100 traps (EARc = 2 m) and percentage of initial 1 000 stationary females (EARc = 0.5 m) mating per 30min period during the first 2 h of 10-h maximum search time. Males flew at 1 m sÀ1 and any encounters with a female caused her to be removed and counted as ‘mated’ (dashed line), whereas males continued to search in 1 000 9 1 000 m area, unless caught by a trap. (B) Percentage of female-searching insects (solid line) caught by traps in competition with stationary males (parameters as above) and percentage of females mating per 30min period during the first 2 h of 10-h maximum search time. Females (B) flew as males (A), but any encounters with males caused the females to be removed and counted as ‘mated’ (dashed line). Percentages after equal signs are the total percentage mated or trapped during the 10-h search.

identical to 703 above), whereas 302 females were captured before mating (Figure 4B). This clearly shows that there are differences in mating rates between the two models when traps are present. If pheromone traps are competing under the model parameters above, and the searching sex travels less distance (0.99; Table 1 in Byers, 1988]. If EARc of attractive pheromones increases in a logarithmic relationship with release rate, then we should not expect leks to evolve, because larger leks (e.g., 20 males) would not have proportionately larger EARc compared to the sum of 20 single males of smaller EARc. So is there another reason why males form leks? Leks of fruit flies appear more often to form on certain fruit tree species, larger trees and nearby trees (Shelly & Whittier, 1993), or on fruit (Kaspi & Yuval, 1999; Quilici et al., 2002), or in sunlit areas in the morning (Segura et al., 2007). Thus, considering these reports and that EARc appears logarithmically related to male numbers, it is more likely that males of some species evolved leks because of the ‘hotspots’ theory (Field et al., 2002), which is supported by the models here. Hotspots are places in the habitat where females are concentrated or pass through, and if males form leks in these areas then they can attain a higher frequency of mating (Hoglund & Alatalo, 1995; Field et al., 2002). The simulations show that relatively more mating occurs when a constant number of insects are placed in an increasingly smaller area (Figures 3A and 7) or when increasingly higher numbers are in a constant area (Figures 6A and 8), showing that higher densities of insects cause higher percentages of mating. Thus, males and females that congregate in a limited area of the habitat, such as on host plants can increase their density and mating frequency. Males that did not join a lek would likely be in low-density areas and not encounter as many females. Females may have little choice but to seek the highest densities of males (a lek), but the females could also gain even more fitness if they are able to choose higher quality males in the group, or if the males are territorial and only the best males can stay inside the lek (Hoglund & Alatalo, 1995; Field et al., 2002). Furthermore, as males are the calling sex in fruit flies, it is more likely that any such female choice and male territoriality evolved after male leks evolved. Females do not form leks because additional mating after fertilization of eggs yields little or no benefit and would delay searching for suitable oviposition sites (Jarvis & Rutledge, 1992; Cabrera & Jaffe, 2007).

236 Byers

The models here have pheromone traps that compete with natural pheromone (competitive attraction), but also have a possible second mechanism of camouflaging the stationary sex. Camouflage occurs if a caller’s EARc circle is partially or completely within a trap’s EARc circle, which reduces or prevents encounters by the searching sex (Figure 2). The female-searching model can accommodate leks by making fewer and larger EARc for the male groups. For example, 100 males were partitioned into 10 leks of 10 males each. However, the size of the EARc would be difficult to estimate and in nature the mating groups would be expected to be of all sizes from a single male to leks up to tens of males (Shelly, 2001; Field et al., 2002). Dose-response tests in the field are needed for fruit flies along with EAR measurements before meaningful models can be attempted. In any case, a lek model of male searching is not easily compared to the male-searching model of moths, whereas sex pheromones of single males are straightforward to compare. Mass trapping with competitive attraction by natural pheromone is always more efficient than mating disruption when both have an equal number of pheromone sources of the same EARc. This is because mating disruption only delays the searching sex, whereas a trap delays them indefinitely (Byers, 2007). However, the EARc in many species cannot be made as large as desired by increasing pheromone release rates. This is because (1) logarithmic dosage curves indicate that amounts needed for a linear increase in catch or EARc require exponential increases in release rate, which is increasingly expensive (Byers, 2007); (2) based on models here (Figure 3), a linear increase in EARc results in a logarithmic-like increase in mate finding; and (3) many insects are inhibited by a high release rate such that the EARc can even become ´ smaller (e.g., male moths; Roelofs & Carde, 1977). Therefore, mating disruption can be more cost-effective than mass trapping because many more sources of pheromone can be employed at a sufficiently large EARc without the need of relatively higher expenses of traps and their deployment. The models show that insects with sex pheromones with either female- or male-searching behavior are equally efficient in finding mates in natural systems. However, with mass trapping (or mating disruption) the female-searching system has somewhat less mating than the male-searching system.

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