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PREDPREY
A Simulation Model of Podisus maculiventris (Say) (Heteroptera: Pentatomidae) and Mexican Bean Beetle, Epilachna varivestis (Mulsant) (Coleoptera: Coccinellidae), Population Dynamics in Soybean, Glycine max (L.).
Many crops have a complex of generalist predators that serve to "buffer" pest population growth. The simulation model "PREDPREY", uses as example, the predator Podisus maculiventris(Heteroptera: Pentatomidae) attacking Mexican bean beetle, Epilachna varivestis (Coleoptera: Coccinellidae) in soybeans, to better understand and describe the impact of these predators on prey dynamics in crops.
PREDPREY is a state-variable model that uses a distributed-delay function to represent the temperature-dependent development of both predator and prey species. The model tracks changes in plant size, and predator and prey populations over a single growing season using a one-day time step. Model parameters, inputs and outputs are scaled to a m2 basis, thus, predators and prey are assumed to be distributed uniformly in the field. The soybean plant model describes the accumulation of leaf area over time. The predator submodel includes descriptions of immigration, predator searching, functional response to prey density, survivorship, development and reproduction. The prey submodel includes immigration, survivorship, development and reproductive characteristics. The search strategy of P. maculiventris and consequent attack on Mexican bean beetle, provide a link between the three components. Model output is numbers of adult (female) P. maculiventris. Numbers of P. maculiventris are used rather than density (e.g. numbers/m2 of leaf area) as the predator's search for prey incorporates the size-effect of the soybean plant.
Soybean Plant Growth: Figure 1 shows the changes in plant size over time. Starting with soybean plants of an initial size, an increase in leaf area proceeds linearly for a defined time period. Following this period of growth, plant size remains constant, and then begins to decline, first linearly and then exponentially. Leaf area is computed based on two surfaces of a leaf, as prey are found on both leaf surfaces, and predators must traverse both surfaces to find them. Based on the typical soybean planting period in Indiana (early-May to mid-June), June 1 was set as the starting date for simulation. On that date, soybeans have a leaf area index of 1.1
Figure 1 Mexican bean beetle: The prey submodel is diagrammed in Figure 2. The population begins with an initial number of adults (0.25 adults/m2) that enter the field on June 1. The adults are assumed to be 1-5 days old, with 20% allocated into each age class. Incoming adults were assumed to be either newly-emerged from overwintering sites or progeny of overwintered adults that emerged early and developed on alternate hosts. The timing, magnitude and age structure of the in-coming population (referred to as an "influx pattern") can be specified as part of the model inputs.
The rate of oviposition of the Mexican bean beetle is age dependent. In the model, after a 6-day preoviposition period, the number of eggs laid increases linearly to a peak value of 25 eggs per day at 18 days. Subsequently, there is a linear decline in daily egg production until females cease reproduction at 30 days. Females produce 300 eggs in their lifetime.
Immature development is temperature-dependent, with a lower developmental threshold of 10°C. Eggs take about 5 days to hatch at 25°C, giving a value of 75 degree-day (DD) for egg development. Following the typical hatching pattern of coccinellids, all eggs hatch simultaneously after the accumulation of 75 DD. Larvae and pupae were considered a single stage for developmental purposes.
Immature and adult Mexican bean beetle are subject to mortality from factors other than predation. Egg mortality is imposed at hatching, whereas larval/pupal mortality is imposed on a daily basis. Daily adult mortality and larval mortality rates are set at 0.0385 and 0.0450, respectively. Total egg survival is set as 0.8. To account for plant size, "prey density" is defined as the number of Mexican bean beetle larvae per m2 of leaf area (both surfaces).
P. maculiventris: The general structure of the predator submodel is similar to the prey submodel with the addition of a predator searching component (see Figure 3). Only females are tracked by the model due to incomplete data on male and immature life history and/or searching behavior. In the model, the population begins with an influx of overwintered adults, ages 65-75 days, entering the field on June 1. The reproductive status of immigrating P. maculiventris females correspond to predators that have been attacking one prey daily. The influx magnitude was set as 0.1 adults/m2. A range of predator influx patterns (timing, age, reproductive status and magnitude) can be specified as part of the input data.
Immature (eggs and nymphs) development is temperature-dependent, with a developmental threshold of 10°C. Earliest and latest development values of 360 DD and 520 DD, respectively.
The pre-ovipositional period, the number of eggs laid per egg mass, the inter-oviposition interval, and adult survivorship depend on the predation rate. The maximum clutch size is set at 14 female eggs/egg mass. Egg survivorship is set at 94%. Survival through the nymphal stage was set as 55%. Adult survivorship follows a Type I schedule (linear decline in survival), with a daily mortality value of 0.058
The predation rate for P. maculiventris is directly related to the area searched. The area searched by P. maculiventris is described as a negative exponential function of prey density:
S = C1 e -C2 (N/A) + C3, [1.]
where S is the leaf area searched (m2), N/A is the prey density, with N being the number of prey and A the leaf area (m2, both surfaces). Figure 4 shows the form of this relationship.
Figure 4 The per capita attack rate (Na) is given by:
Na = S (N/A). [2.]
Inserting equation 1 into 2 gives the equation for P. maculiventris attacking Mexican bean beetle in soybeans:
Na= [C1 e -C2 (N/A) + C3] (N/A) [3.]
The search and attack functions are based on the assumptions that P. maculiventris searches at random and that it attacks all encountered prey.
Leaf area: Leaf area growth is shown in Figure 1. Starting with a leaf area of 1.1 on June 1, leaf area reaches a maximum of ca. 12 m2 on July 25. Following a period where leaf area is maintained, leaf area declines, first linearly, then exponentially. Mexican bean beetle and P. maculiventris: The standard simulation shows two generations of Mexican bean beetle per season, with the first-generation density lower than the second generation. Peak prey density of 6.7 Mexican bean beetle larvae per m2 of leaf area occurred on August 19. Predator population growth shows a gradual increase in numbers over time. At the end of the season, there were approximately 1.5 predators per m2.
Standard Run (June 01/Mid-aged/Medium/Normal) |
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Please send feedback to bob_oneil@entm.purdue.edu Copyright © Midwest Institute for Biological Control, 2000 This page was last updated 08.21.00 www.biocontrol/theoriesmodels/predprey/aboutpredprey.html |
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