Oviposition height increases parasitism success by the robber fly Mallophora ruficauda (Diptera: Asilidae)

Abstract

For parasitoids, host finding is a central problem that has been solved through a variety of behavioural mechanisms. Among species in which females do not make direct contact with hosts, as is the case for many dipteran parasitoids, eggs must be laid in an appropriate part of the host habitat. The asilid fly Mallophora ruficauda lays eggs in clusters on tall vegetation. Upon eclosion, pollen-sized larvae fall and parasitize soil-dwelling scarab beetle larvae. We hypothesized that wind dissemination of M. ruficauda larvae is important in the host-finding process and that females lay eggs at heights that maximize parasitism of its concealed host. Through numerical and analytical models resembling those used to describe seed and pollen wind dispersal, we estimated an optimal oviposition height in the 1.25- to 1.50-m range above the ground. Our models take into account host distribution, plant availability and the range over which parasitic larvae search for hosts. Supporting our findings, we found that the results of the models match heights at which egg clusters of M. ruficauda are found in the field. Generally, work on facilitation of host finding using plants focuses on plants as indicators of host presence. We present a case where plants are used in a different way, as a means of offspring dispersal. For parasitoids that carry out host searching at immature stages rather than as adults, plants are part of a dissemination mechanism of larvae that, as with minute seeds, uses wind and a set of simple rules of physics to increase offspring success.

Appendices

Appendix A

The number of hosts parasitized by larvae issued from a single egg cluster is derived in two steps. First, the distribution of larvae on the ground after release from the plant is calculated, and then the number of host parasitized is evaluated.

A basic mechanistic model of seed dispersion by wind shows that the horizontal distance (x) a seed (here a larva) can travel by the wind is a linear function of the height of release (h), the mean horizontal wind speed during larvae flight (u) and the terminal velocity (T) (Grenne and Johnson 1989, 1996; Nathan et al. 1996, 2001a,b).

$$ x = \frac{{uh}} {T} $$

(2)

T is the falling velocity reached by the larvae shortly after release; this quantity depends on the characteristics of the larva (shape and weight).

Here, we further assume that the larvae are uniformly distributed within the shadow (the area that encompasses all the larvae after landing on the ground, see text). This shadow is a sector whose bisecting line length is given by Eq. 2 with u=U, the maximum wind speed the larvae experience during their drop.

Assuming random encounters between hosts and parasitoids, the probability that r larvae parasitize a given host is given by a Poisson distribution. The parameter of this distribution, the mean number of larvae per unit area, is given by

$$ \lambda = \frac{Q} {{a{\left( h \right)}}}, $$

(3)

where Q is the number of larvae in the cluster and a(h) is the non-isotropic shadow area (see text). The shadow being a sector of angle 2θ (θ  takes values between 0 and π) and radius Uh/T, one gets

$$ a{\left( h \right)} = \theta {\left( {\frac{{Uh}} {T}} \right)}^{2} . $$

(4)

Finally, the number of hosts parasitized by the Q larvae is the number of hosts present in the ground within the shadow (with density p), weighted by the probability that each host is found by at least one larva

$$ f{\left( h \right)} = pa{\left( h \right)}{\left( {1 - e^{{ - \lambda }} } \right)}. $$

(5)

Similarly, the number of hosts superparasitized is given by the probability that each host is found by at least two larvae,

$$ pa{\left( h \right)}{\left( {1 - e^{{ - \lambda }} - \lambda e^{{ - \lambda }} } \right)} $$

(6)

To take into account the possible heterogeneity in host distribution, we substitute the Poisson distribution, by the negative binomial distribution (see discussion on aggregation in host distribution in the main text). The probability of a given host being found by at least one larva becomes

$$ f{\left( h \right)} = pa{\left( h \right)}{\left( {1 - {\left( {1 + \frac{\lambda } {k}} \right)}^{{ - k}} } \right)}, $$

(7)

where k is the shape parameters of the negative binomial distribution. As k departs from 0 and becomes larger, the host distribution becomes less aggregated, and at the limit $k \to + \infty$ one recovers the Poisson distribution. The second parameter of the negative binomial distribution is its mean, here equal to λ (see Eq. 3).

Appendix B

Numerical simulation model

Larvae dispersal was simulated by means of a spatially explicit model, using a grid of 200×200 cells, each cell representing an area of 400 cm². The grid represents the soil surface where the larvae drop, and contains only one egg cluster at variable height, placed in the centre of the grid (oviposition site). Hosts are distributed in patches of variable size of constant density (1,600 hosts per grid on average).

Larvae are dislodged from the oviposition site and can fall in any cell, depending on the dispersal direction and the distance travelled (x). Dispersal direction is fixed and it is assumed constant during the larvae falling. Travel distance, the horizontal distance covered by a larva while dropping, is given by Eq. 2 with u=U′, where U′ is the mean horizontal wind velocity during the falling of the larvae and T is the terminal velocity of one larva that falls without wind. Terminal velocity depends of both the size and weight of the particle and the fluid in which it displaces (Okubo 1980). Host distribution inside patches is modelled through a cell occupation probability. Density in each patch is assigned by means of an occupation probability, which by default is set at 50% on average. The wind spreads the larvae in the grid at random with given angle spans and degrees of variation in intensity, leading to a cone-shaped dispersion pattern (Nathan et al. 2001a; Wagner et al. 2004).

The definition and numerical values of the physical and biological parameters of the model related to the movement of larvae are given in Table 1 (see main text).

With this model, for each height of egg laying, we simulated different host distributions changing parameter values (a “grid”). A total of 90 grids were considered for each height, and 100 larvae falling cycles (100 egg clusters) were simulated for each grid. We thus obtained a total 9,000 cycles per oviposition height. We considered 16 height values, from 0 to 4 m, in intervals of 0.10 m.

We assumed the following: the larval drop is uniform due to its terminal velocity; the larva reaches quickly the terminal velocity after its release from the egg cluster, so that travelled vertical distance is negligible; there are no interactions or turbulence during the drop process; each cell may be only occupied by a single host and all larvae falling on an occupied cell will parasitize or superparasitize; and dispersal direction is randomly defined.

Appendix C

The oviposition strategy is defined by the probabilities p _i of choosing each type-i plant upon encounter. This strategy is obtained by maximizing the rate of fitness gain (fitness over time), which comes from calculating the following (Stephens and Krebs 1986):

$$ \frac{\partial } {{\partial p_{j} }}{\left( {\frac{{{\sum\limits_{i = 1}^n {r_{j} f_{i} p_{i} } }}} {{1 + \tau {\sum\limits_{i = 1}^n {r_{j} p_{i} } }}}} \right)} $$

(8)

One can show that p _j is either 0 or 1, the latter occurring if

$$ \frac{{f_{j} }} {\tau } > \frac{{{\sum\limits_{i \ne j} {r_{i} f_{j} } }}} {{1 + \tau {\sum\limits_{i \ne j} {r_{{ii}} } }}} $$

(9)

This leads to the guess that higher plants are better since the fitness they allow is larger. This can be proven by recurrence, and one can derive a procedure for choosing the optimal plants (Stephens and Krebs 1986). Finally, the optimal oviposition strategy consists of accepting taller plants, those whose type j is larger or equal to i*. The threshold i* is the smallest j such that inequality (Eq. 1) in text, derived from Eq. 9, is verified.