Random foraging by herbivores: complex patterns may be due to plant architecture

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Insect herbivores can have detrimental effects on the growth and reproduction of the plants they eat. For the plant, the consequences of losing a leaf to a forager may depend on the location of that leaf in relation to other leaves and flowers or seeds (Marquis 1988). To enable better predictions of the impact of herbivory, it is important to analyse the relationship between insect foraging behaviour and the resulting spatial distribution of tissue loss within the structure of the plant.   Recently, Alonso & Herrera (1996) studied whether noctuid larvae foraging on the shrub Daphne laureola (Thymelaeaceae) exhibited within-plant selection with respect to plant architecture. They found that within plants, leaf whorls visited by larvae were at significantly lower branching orders and with shorter supporting stems than whorls where no noctuid larvae were recorded. They used these data to speculate that the larvae may use plant architectural traits as cues to select food in a way that reduces the cost of travel, but can such patterns be considered valid evidence of non-random foraging? After considering this issue, I outline an alternative null hypothesis that is appropriate for the relationship between patterns of herbivory and plant architecture.   The larvae studied by Alonso & Herrera (1996) are inactive during the day in the litter beneath the plants, and climb at night to the leaf whorls to feed. The two most abundant species (Trigonophora flammea and Noctua janthe), which together comprise over 80% of records, may also feed on flowers and unripe fruits (Alonso & Herrera 1996). The simplest assumption about the foraging behaviour of these caterpillars does not involve the use of information about costs and benefits to select a foraging path. Rather, when they climb up a stem and meet a branching fork, larvae randomly select one of the branches and continue along it until they find a leaf whorl (and then stay there feeding until they return back to hide at the base of the plant). The simplest case (dichotomous branching; Fig. 1) is when the branch forks are of about similar size and the probability of selecting each of the two forks is 0.5.   If insects forage randomly according to the rules just described, the relative visitation frequency (RVF) of leaf whorls decreases as a function of branching order (n) according to the relationship RVF = 0.5n (Fig. 1). An average branching order can be predicted for those leaf whorls that are visited by larvae by weighting the number of whorls of each order by the RVF of that order [mean branching order of visited whorls = Σ(RVFkümh-480Ý*nk), such that Σ(RVFk) = 1]. A similar value can be calculated for all available whorls, and it is inevitably higher than the value for visited whorls (Fig. 2). Thus, an essentially random foraging behaviour of herbivores, when filtered through host-plant architecture, results in a non-random pattern of herbivory. The data point from Alonso & Herrera (1996) falls within the scatter of points generated from random visitation frequencies for a variety of branch patterns (Fig. 2), and thus there is no reason to conclude that noctuid larvae on D. laureola exhibit within-plant selection with respect to plant architecture.   We can easily extend the discussion/analysis to more complex architectural structures by formulating a null hypothesis that states that the probability of selecting a branch is proportional to its size (projection) in relation to the circumference of the stem at that node. The dichotomous branching considered in Fig. 1 and related discussion is just a specific case of a model that also includes cases where branches arise from nodes on a main axis. The relative visitation frequency of each leaf whorl is obtained by multiplying the probabilities at each fork leading to that leaf whorl [note that Σ(RVFk) is again equal to 1]. To illustrate the calculations with an example, imagine a plant with four branches at the first node (each with 1 cm diameter) and four branches at the second node (each with 0.5 cm diameter) and one leaf whorl at the top of the plant (as well as at the end of each branch); the diameter of the main stem at the first and second node is 3 and 1.5 cm, respectively (Fig. 3). We can approximate the size of the projection of the branches by their diameter (Fig. 3, insert); thus, the probability of selecting each branch at the first node is 1 cm/π*3 cm (the total circumference of the main stem at that node) = 10.6%, and the probability of continuing upwards along the main stem is 1–4*(1/π*3) = 57.5%. The probability of selecting each branch at the second node is conditional on the larva having continued upwards at the first node: 57.5%*(0.5 cm/π*1.5 cm) = 6.1% the probability of continuing upwards along the main stem after the second node (and thus selecting the leaf whorl at the top of the main stem) is 100–(4*10.6 + 4*6.1)% = 33.2%. This example illustrates that in cases with a main stem and (relatively thin) branches, the highest RVF can be at the topmost leaf whorl, and that the average branching order of visited leaf whorls can be higher than that of all available leaf whorls (Fig. 3).   When testing data against the above null hypothesis, it may not be appropriate to combine samples from different stems (ramets). In fact, one should realize that there is a hierarchy of selection/foraging behaviours: (i) selection of plants; (ii) selection of stems; (iii) selection of branching whorls within a stem. Selection of plants is probably done mostly by the ovipositing females and the plant traits involved may be largely different from those associated with larval behaviour. Furthermore, architectural differences between, for example, plants growing solitarily vs. in dense stands may confound an analysis of larval behaviour if data from different plants are combined. The selection of stems (within a plant) and branching whorls within a stem is probably determined solely by larval behaviour. Noctuid larvae on D. laureola do not discriminate between stems on the basis of their basal diameter (Alonso & Herrera 1996, their Table 2). However, Alonso & Herrera’s (1996) observation that supporting stem length (from ground level to the leaf whorl) was shorter for branches with noctuid larvae than branches without larvae may be an incidental result of random foraging behaviour according to rules described above (given the obvious positive correlation between branch order and supporting stem length). Overall ‘population level’ averages of plant traits may not be sufficient to allow informative analyses. The frequency distribution of all the different architectural types available, as well as their use by insects, would allow each type to be analysed separately (as in Fig. 1). Only then could statistical risk levels be combined for an overall test (Sokal & Rohlf 1981).   Regardless of whether patterns of herbivore visitation within plants result from real selective foraging behaviour, or from nearly random behaviour, it is evident from Fig. 1 that the risks of leaf and/or flower/seed predation may differ according to position within the structure of a small plant. The same principle may apply to branches of larger trees with a main trunk (Fig. 3). However, this reasoning is relevant only in cases where herbivores must regularly return to the ground, for example to escape predators or desiccation, and then re-climb the stems of the plant to access food. Thus, knowledge of the life history and foraging behaviour of herbivores is also necessary if we are to understand the patterns of browsing within plants and the fitness consequences to plants resulting from those patterns.

Figure 1.

The probability (0.5) of choosing each branching fork, and the resulting relative visitation frequencies (italics) above each leaf whorl (a). The relative visitation frequencies above leaf whorls for differentbranching patterns (b–f). Inset: the relative visitation frequency of individual leaf whorls as a function of their branching order assuming random and equal probability of choosing each branching fork

Figure 2.

The relationship between average branching order of plants (x-axis) and the expected average branching order of whorls visited by herbivores (y-axis) assuming random and equal probability of choosing each branching fork. Letters (a–f) are individual stems with one to three branching orders (Fig. 1); triangles are other examples of ‘plants’ that were generated with stems having one to three branching orders and equal visitation probability for each stem; the square is the empirical observation (as an overall ‘population’ average) by Alonso & Herrera (1996) with Daphne laureola[note that I start counting branch orders from the first fork, not from the base of stem as Alonso & Herrera (1996)].

Figure 3.

An example of a plant with main stem and branches at nodes (node number in the left margin); the probability of an insect larva (randomly) selecting a specific branch is proportional to the size (diameter) of the branch and is shown above the leaf whorl. The expected average branching order (number of nodes passed) of visited leaf whorls in this case is 1.91; the average value for all available leaf whorls is 1.67.

Acknowledgements

I thank Conchita Alonso, Lindsay Haddon, Antti Kause, Arja Ojala, Kalle Ruokolainen, Janne Suomela, Hanna Tuomisto, Karen Wiebe, Timo Vuorisalo and an anonymous referee for constructive comments on the manuscript. Jussi Neuvonen kindly helped with the figures.

Received 13 July 1998; revision accepted 5 November 1998

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