Chapter 8 Biology of Red Scale and its Parasitoids {# redscale}
In California, red scale, Aonidiella aurantii (Maskell) (Diaspididae: Homoptera) is a major insect pest of citrus, especially in California’s San Joaquin Valley where most of the State’s citrus in now grown. At moderate densities, the scale infests the fruit, while at higher densities they cause leaf and twig death, which can reduce fruit production. Dense scale populations can kill branches or portions of the tree with the subsequent loss of all or part of the crop. California’s citrus is marketed as fresh fruit. Fruit with scale are downgraded or culled and most culled fruit are juiced, which does not cover production and processing costs. Thus, marketing conditions make cosmetic damage economic.
Growers in the San Joaquin Valley traditionally suppressed scale infestations with broad-spectrum insecticides. Recently red scale has evolved resistance to these pesticides, making them ineffective (Grafton-Cardwell 1994). An alternative suppression tactic employs the release of a small wasp, Aphytis melinus DeBach (Aphelinidae: Hymenoptera). Aphytis parasitizes specific stages of the scale insect to produce its offspring, killing the scale as a consequence. When sufficient scales are parasitized, the scale population is suppressed at densities below those of economic concern. Release of this wasp in the absence of broad-spectrum insecticides can suppress the scale at a cost equal to or less than that achieved with the traditional insecticide program. Moreover, the quality of the fruit harvested under such a program is equal to or better than that harvested under the traditional program. (Haney et al. 1992; Luck et al. 1997).
8.1 Detailed life histories
8.1.1 Red Scale Life History
Red scale’s life cycle begins with the crawler stage, a brief mobile stage that allows the young scale to find a suitable location on a branch, leaf or fruit on which to “settle”. It then inserts its mouthparts into the substrate and transforms into a sedentary feeding stage. Once settled, a female scale remains immobile for the rest of her life. In contrast, the male once settled remains immobile until its adult stage when it transforms into a winged adult and seeks a virgin female with which to mate. Both the male and female grows by molting periodically, alternating between a feeding instar and a non-feeding or molting stage. During the molting stage the scale sheds its exoskeleton and increases its size so that it can grow when it initiates feeding during the next instar. A female red scale has three feeding stages (instars) with two intervening molts. At the end of the third instar, it mates and transforms into a gravid female, maturing its eggs, and subsequently produces crawlers. The eggs develop within the female. Immature males have two feeding instars separated by a molt stage. Following the second molt the male transforms into a prepupa followed by a pupa, finally emerging as a winged adult. The winged adult locates a virgin female with whom to mate via a sex pheromone. This is illustrated in Figure 1.
<<Figure 1 about here>>
Since red scale’s development is temperature dependent, the average time it takes the scale to complete its development during an instar or molt is represented in degree-days (DDo), which are approximately the cumulative degrees (?C) above 11?C (Yu and Luck 1988). It takes both female and male scales about 330 DDo to reach the end of the second instar. Males remain prepupae for an additional 30 DDo before molting to a pupa, and, after 20 DDo as a pupa, emerge as a winged adult. In contrast to males, second instar females, on the other hand, molt, which last approximately 50 DDo after which they reinsert its rostrella and feed as third instars. Red scale is subject to parasitism during the development process, until it becomes a mature adult. A mated female becomes attached to her scale cover and begins to mature her eggs. In approximately 90 DDo the mature female begins to produce crawlers. The cycle for a female from crawler to crawler producing female takes approximately 650 DDo.
8.1.2 Aphytis Life History
Aphytis melinus is a small wasp that lays its eggs externally on the body of red scale (= host) but beneath the scale cover (Forster et al. 1995). It paralyzes the scale before it lays its egg. Normally, Aphytis lays its egg on a second or a third instar female or on a second instar male scale. Aphytis prefers instar stages to molt stages of red scale. During the instar stage the scale cover is free of the body and Aphytis can lay eggs on either or both the dorsal and ventral surfaces of the scale (Abdelrahman 1974; Luck et al. 1982). During the molt and mature female stage the cover is rigidly fused to a hardened body. The wasp larva hatching from the egg feeds on the paralyzed scale, consuming the contents of the scale, which kills it. This is referred to as parasitization. The food available to the developing Aphytis is determined by the size of the scale body at the time the scale is paralyzed. Aphytis passes through four immature stages during its development: egg, several larval stages, prepupa, and pupa. Generally, Aphytis allocates a male offspring on second instar scales and on male and female scales. About 20% of the male scales are allocated a female Aphytis. About 70% of the third instar female scales are allocated a female Aphytis offspring, about 25% are allocated a male Aphytis offspring, and about 5% are allocated two Aphytis off spring (usually a male and a female) (Luck et al. 1982; Luck and Podoler 1985). The two eggs are laid during the same host visit and represent a case of gregariousness (Luck et al 1982).
Once having allocated an offspring to a host scale, the Aphytis egg or larva is vulnerable to usurpation of the host by a second female Aphytis encountering the host. A previously laid Aphytis egg or the first instar larva arising from it may be killed when a second female encounters and oviposits on the previously parasitized host (Forster and Luck pers obs). The second female distinguishes the scale as previously parasitized and, while walking on the scale cover or probing the scale, detects chemical cues that were left by an Aphytis that previously oviposited on the scale (van Lenteren and DeBach 1981). It punctures the previously laid egg and then lays its egg on the host, usurping the scale as a resource for its offspring (= super-parasitism) (Forster and Luck pers obs). This usurpation increases in frequency as the ratio of unparasitized to parasitized scales decreases. This form of intraspecific competition can occur more than once on a host but, with each usurpation, the survival of the wasp larva arising from each newly laid egg decreases.
<<Figure 2 about here>>
Aphytis melinus development is also temperature dependent. At 26.70C”, in a parasitized or super-parasitized host, a wasp egg hatches after about two days. The resulting larva feeds for approximately five days before becoming a prepupa for one day. It pupates for four to five days before chewing a hole through the scale cover and emerging as an adult Aphytis. Thus, the entire process from egg to adult takes twelve to thirteen days. Aphytis prefers instar stages to molt stages of red scale. During the instar stage the scale cover is free from the body. The development of Aphytis is illustrated in Figure 2, while parasitism is shown in Figure 3.
<<Figure 3 about here>>
Female Aphytis usually mature their first batch of eggs, approximately 12% of its lifetime egg supply, within 24 hours of emergence using resources from their larval stage. They produce eggs during their entire adult lifetime, relying on periodic feeding on body fluids of small, immature hosts for sustenance (Opp and Luck,1986; Heimpel and Rosenheim 1998; Collier 1995; Luck and Nunney 1999). Adult Aphytis host-feed by probing the scale body more extensively than when they oviposit, feeding on the body fluids that ooze from the wound. Aphytis feed on small hosts (scales) while searching for larger scales to serve as suitable hosts on which to lay eggs. Host-feeding kills a substantial percentage of California red scale beyond those killed through parasitism. Within 12 to 18 hours of host-feeding, the female develops approximately 1.3 eggs if it has not recently oviposited, or about 2.7 eggs if it has. Host feeding appears to provide resource for both metabolic maintenance and egg production. Collier (1995) showed that Aphytis that do not have access to hosts for either oviposition or host feeding will re-absorb about one egg per day. However, egg re-absorption will not supply the metabolic needs of the wasp in the absence of honey or other carbohydrates.
Aphytis, as with most parasitoids, controls the sex of its offspring by optional fertilization of eggs: males normally arise from unfertilized eggs while females arise from fertilized eggs (Yu and Luck 1988; Godfray 1994). Larger scales are allocated female eggs as large daughters are more reproductively successful on average than smaller daughters. Thus scales growing on fruit are more likely to be parasitized due to their larger size (Luck and Podoler 1985; Hare and Luck 1991).
8.5 Search algorithms
8.5.4 Simulations
A simulation system has been developed using the event-driven competing risk structure outlined above. The initial implementation focuses on the California red scale-Aphytis system, although the software module has no code specific to this system except details of event handling. Our parameterization can dramatically reduce disk storage needs and run time for simulations. Calculations involve no integration, reducing to an exponential random variate, a pair of linear transformations and an evaluation of M-1. The structure of an individual is divided into the “static” properties, such as physical attributes and relationships with other individuals, and the “dynamic” event structure, influenced by the competing risks and other individuals in the community.
Since red scale is temperature dependent (approximated by degree-days, the integral of degrees above 11?C) while Aphytis is diurnal (active from about 9am to 4pm), we allow the two species to operate on different biological clocks. Mean value functions for future events are by default linear in the species-specific biological clock (degree-day or diurnal), but can be tuned using a graphical interface. The software is written in the R language, which is graphical, extensible, and in the public domain (Venables and Ripley 2000; see http://www.r-project.org). We compute M and M-1 and the hour/degree-day translation using forward and backward cubic splines via library(splines) in R, and efficiently generate standard exponential pseudo-random numbers using the R implementation of algorithms by Ahrens and Dieter (1974, 1988). Details of the simulation and access to public domain software can be found at http://www.stat.wisc.edu/~yandell/ewing.
The simulation uses life history information from Forster et al. (1995) as summarize earlier in this paper. A temperature range of 15?C to 30?C is used to represent springtime conditions in the interior regions of California or the San Joaquin Valley. The cool evenings slow development of red scale. We simulate the red scale-Aphytis system with varying number of individuals of each species. Here we present a limited set of simulations to demonstrate proof of concept. The orange tree is simulated as one four-sided orange, one two-sided leaf, and a twig connecting them. Pragmatic choices were made about movement among these locations for red scale crawlers and Aphytis adults. Initial simulations are run for up to 10,000 events, or several generations of each species.
An isolated population of red scale demonstrates, as expected, an exponential increase in total population over generation (not shown). Since the underlying orange resource is not restricted, we see uncontrolled growth. However, both gravid females and crawlers tend to show inherently discontinuous dynamics, with periods of growth and decline.
<<Figure 7 about here>>
A simulation with 200 red scale and 200 Aphytis, weighted initially toward immature individuals, shows the characteristic lag in response to parasitization (Figure 7). The number of red scale initially rises, and then is dramatically reduced by the emerging adult Aphytis. Both decline for some time, but the red scale shows evidence of recovery with an increased number of crawlers, and subsequent increase in instars that can serve as Aphytis hosts. The decline in Aphytis appears to be arrested late in the simulation, but there are only a few individuals left. The frequent vertical spikes in number of Aphytis young represent male offspring that are born and immediately removed from the simulation. This crash in parasite population may be due to the artificial isolation of this simulation. In a larger simulation, there could be immigration of new adult Aphytis from neighboring orange fruits as well as the emigration of males.
<<Figure 8 about here>>
The next example differs in having initial populations of 300 red scale and 50 Aphytis, and a slower depletion of adult Aphytis egg resources. Figure 8 shows that Aphytis can maintain its population for a few generations. However as the number of adult Aphytis stabilizes at around 35, they begin to seriously reduce the host population. The Aphytis population drops as well, as the adults fail to find red scale that are mature enough to support female Aphytis eggs. Eventually the remaining Aphtis adults would perish for lack of food.
8.6 Simulations from QPE Paper
A simulation was developed (see www.stat.wisc.edu/~yandell/ewing) to implements our event-driven quantitative population ethology structure using the R language (www.r-project.org). The initial implementation focuses on the red scale/Aphytis/Encarsia dynamics, although software modules are not code specific to this system except for some details of event handling. In the next few paragraphs we discuss the input requirements for the simulation and then we examine some of the properties of an event-driven simulation.
Information concerning organism life stages and their inter-relationships are extracted from field data and stored as ordinary tables. These encode system features, schedules for future events, and information concerning interactions among organisms. The simulation initializes an event structure and partially orders future events by species in priority queues (Knuth 19xx) such that the next future event has minimal time. The simulation then processes the next future event, updating the priority queues by rescheduling an new future event for that individual. In addition, future events for other individuals may be rescheduled (e.g. due to interaction) or de-queued (e.g. due to death).
8.6.1 Model Span and Resolution
Luck et al. (19xx) showed that relevant organisms develop from an egg to adult stage in roughly 2-4 weeks (red scale 24-25 days, Aphytis 13-14 days, Encarsia 19-28 days). Oranges mature in about 8 months, roughly 10 or more generations for each species. Thus our simulation span is 240 days or 3,500 degree-days (DD, cumulative degrees cumulative degrees above 11?C). Resolution for the simulation is more difficult to determine. Yu and Luck (1988) recorded red scale life histories to 1-3 DD precision, while Aphytis and Encarsia data are recorded to 1 day precision. However, multiple events of feeding and ovipositing may occur during a day for adults. For simplicity, we consider the resolution to be approximately 1 DD or 1 hour, depending on species. Thus a simulation with 500 individuals at a time, roughly 20 events per individual, and 10 generations, will process approximately 100,000 events.
Orange fruit are mature for about 8 months. Luck (see Yu and Luck 1988 and references in Ewing et al. 2001) suggests that the time in days from egg to gravid adult for the insect species involved are roughly 2-4 weeks (red scale 24-25 days; Aphytis 13-14 days; Encarsia 19-28 days). Thus, 8 months corresponds to 10 or more generations for each species. This gives us our span of roughly 240 days or 6400 degree-days (DD), using 1 day = approximately 26.7 DD on average.
Resolution is more difficult to determine. Luck (cf. Yu and Luck 1988) often recorded red scale life histories to the precision of 1-3 DD, with a recognition of inherent variability. Information on Aphytis and Encarsia is often recorded to the precision of 1 day. However, multiple events of feeding and ovipositing probably occur on any given day for adults. For simplicity, we consider the resolutions of approximately 1 DD and 1 hour. These are roughly equivalent on average.
Given a particular span and resolution, what are the implications for the size of the simulation? Consider roughly 500 individuals at any one time, with on average 20 events per individual. We are running 10 generations, which makes 100,000 events. Version 3 of the software can handle about 3000 events per hour on a Pentium II 150Mhz system. Thus one simulation could be completed in a day or two. There are some issues about space management that need to be redesigned to make this happen, however, but they are solvable.
Suppose one were to use classical modeling techniques, running each individual a DD at a time. Assuming there are 500 individuals, there would be 3,200,000 steps (500 individuals times 6400 DD), or if you consider cycling through say 10 types of events per individual, 32,000,000 operations. This is a considerably more costly and time-consuming operation.
Notice also that we do not explicitly need to set things up rounded to the smallest resolution. In fact, it can be useful to have a smaller precision to resolve ties. Order is resolved because events are schedule asynchronously. The important thing is to have a resolution that is relevant to the events under study, and vice versa. Note further that the choice of future events implicitly determines the resolution; coarser events correspond to coarser time resolution.
8.6.2 Model Results
We ran simulations with a small number of events to demonstrate the apparent discreteness implicit in the event-driven modeling paradigm. Changes in spatial and temporal descriptions of red scale and Aphytis populations involve discrete, discontinuous changes.
[New simulations here.]
One reason that A. aurantii/A. melinus exhibits this type of dynamics may be attributed to the fact that A. melinus and A. aurantii operate using different constraints. The development of A. aurantii is essentially a temperature dependent process, whereas parasitism by A. melinus is a time dependent phenomenon. Note that A. melinus ability to adapt to changes in the structure and dynamics ultimately determines its ability to survive. One of the techniques used by A. melinus is to control the sex ratios of its offspring (Luck and Nunney 1999).
Is this model capable of obtaining results one would expect under field conditions? The answer to that question is dependent on the fidelity of the simulation. If, for example, A. melinus uses a search algorithm based on possible pheremone queues and the simulation uses an ad-hoc search algorithm, or alternatively the migration pattern of A. aurantii does not account for mortality rates due to environmental factors, then the probability that the simulation will be realistic must be suspect. Perhaps this is the true value of this simulation philosophy. The relationship to what the researcher perceives of the system he or she is studying is directly related to the results the model produces. The model now becomes primarily a tool for rapidly testing various scenarios, not for discerning the global properties of a biological model. Implicit in this technique is the understanding of the role of the field biologist.