A Theoretical Approach to Study the Evolution of Aggregation Behavior by Larval Codling Moth, Cydia pomonella (Lepidoptera: Tortricidae)

Abstract

Pupation site-seeking larvae of the codling moth, Cydia pomonella, aggregate in response to aggregation pheromone produced by cocoon-spinning conspecific larvae. Larvae that pupate in an aggregation rather than in solitude may experience a lower rate of parasitism by the parasitoid Mastrus ridibundus. Additionally, adults eclosing from a larval aggregation may encounter mates more rapidly at the site of eclosion (on-site) than away from that site (off-site). We employed an evolutionary simulation to determine the effect of several ecological parameters on the evolution of larval aggregation behavior. These parameters included (i) the probability of mate encounter off-site; (ii) the time available for finding a mate; and (iii) the population density of parasitoids and their rate of larval parasitism. The model predicts that larval aggregation behavior is selected for when the probability of off-site mate encounter is low, the time to locate mates is short, and egg-limited parasitoids are at high population levels. We also show that aggregations reduce the risk of parasitism through dilution effects. The parameters found to favour the evolution of larval aggregation behavior are consistent with life history traits exhibited by C. pomonella.

Appendix A1

Model Functions (see Table A1)

Probability of a Larva Accepting Site, p_accept(α,n)

When a larva encounters a pupation site, it accepts the site based on some probability, p _accept (α,n), which is a function of α and the number of other individuals present (n), such that:

$$ {p_{{accept}}}(\alpha, n) = \left\{ {\begin{array}{*{20}{c}} {\left[ {1 - \frac{\alpha }{7}} \right],\;if\;n = 0} \hfill \\{\left[ {\frac{\alpha }{7}} \right],\;if\;0 < n \leqslant {n_{{\max }}}} \hfill \\\end{array} } \right\} $$

(A1)

We assume an aggregation can contain a maximum of 10 larvae (n _max  = 10). We further assume that foraging larvae do not discern between the number of larvae within an aggregation based on the amount of aggregation pheromone they produce.

Probability of a Pupa Being Parasitized, p _parasitism (n)

During the pupal stage individuals risk being parasitized. This risk is expressed as a probability of being parasitized, p _parasitism (n), during each time step, and is the product of: (i) the probability of a parasitoid being present in the current cell, p _present ; (ii) the probability that the parasitoid finds the pupa, p _find (n); and (iii) the probability that the parasitoid attacks the pupa successfully, p _attack (n):

$$ {p_{{parasitism}}}(n) = {p_{{present}}} \times {p_{{find}}}(n) \times {p_{{attack}}}(n) $$

(A2)

The probability that a particular cell contains a parasitoid is described by the total number of parasitoids in the environment (ϕ) divided by the total number of cells in the environment (E). To gain a generalised understanding of the effects of a natural enemy (Mastrus ridibundus) on C. pomonella larval aggregations, we maintain simple parasitoid-host interactions and assume that parasitoids randomly and independently of one another search the environment for pupal aggregations:

$$ {p_{{present}}} = \frac{\phi }{E} $$

(A2.1)

If a parasitoid is present in the current cell, its probability of finding an aggregation is described by the baseline probability of a parasitoid finding an aggregation (β) which was fixed at 0.66 and the number of other individuals present in an aggregation (n):

$$ {p_{{find}}}(n){ } = \left\lfloor {\beta {{\left( {\frac{n}{{{n_{{\max }}}}}} \right)}^{\sigma }}} \right\rfloor $$

(A2.2)

The shape of the curve depends on σ, such that σ < 1 yields a decelerating curve, σ = 1 yields a straight line, and σ > 1 yields an accelerating curve.

Once an aggregation is found by a parasitoid, we describe the probability of an individual pupa being attacked as inversely related to the number of moth pupae present (n). The rate is an average of rates approximated from Bezemer and Mills (2001) and Jumean et al. (2009a) such that:

$$ {p_{{attack}}}(n) = \frac{1}{n},\;if\;n > 0 $$

(A2.3)

Probability of Mating, p(mate)

For a newly eclosed on-site adult moth, its probability of accepting a mate depends on its on-site mating preference (M), and is a linearly increasing function of this trait value (μ) such that:

$$ {p_{{mate(on - site)}}} = \frac{\mu }{7} $$

(A3.1)

Once the moth moves off-site, the probability of accepting a mate is a fixed parameter of the environment such that:

$$ {p_{{mate(on - site)}}} = \delta $$

(A3.2)

Therefore, the probability of a successful mate encounter between two moths is:

$$ {p_{{mate}}} = {p_{{mate}}}\left\{ {\hbox{individual 1}} \right\} \times {p_{{mate}}}\left\{ {{\hbox{individual}}\;{2}} \right\} $$

(A3.3)

Fitness function, w(τ)

One objective of our model is to determine whether the aggregation trait can be evolutionarily selected for based on the benefits of expedient mating. Delayed mating linearly decreases the net reproductive rate of C. pomonella adults (Vickers 1997). Therefore, our fitness function for a mated individual is based directly on the time remaining to locate a mate (τ), and it is described by the following function:

$$ w\left( \tau \right) = \frac{\tau }{T} $$

(A4)

where T is the maximum number of time steps available during the mating phase of the simulation.

Table A1 Descriptions of variables and functions used in the model