Behavioral Ecology Vol. 15 No. 1: 94-101
© 2004 International Society for Behavioral Ecology
Factors affecting soldier allocation in clonal aphids: a life-history model and test
a Department of Zoology, University of British Columbia, 6270 University Blvd., Vancouver, British Columbia V6T 1Z4, Canada b Behavioural Ecology Research Group, Department of Biological Sciences, Simon Fraser University, Burnaby, British Columbia V5A 1S6, Canada
Address correspondence to J.G. Tyerman. E-mail: tyerman{at}zoology.ubc.ca.
Received 17 August 2001; revised 2 January 2003; accepted 11 February 2003.
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ABSTRACT |
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Aphid species using a defensive soldier caste offer us the opportunity to study allocation decisions by eusocial groups, without the hindrance of genetic dissimilarity between colony members, which often impair studies involving Hymenopteran or Isopteran systems. When the entire aphid clone is considered the adaptive unit of organization, understanding soldier allocation strategies is tantamount to understanding the outcome of the tradeoff between clonal growth (i.e., asexual reproduction) and clonal defense. Under this framework, we present the results of a dynamic programming effort aimed at determining the optimal ontogeny of defensive allocation strategies by eusocial clonal organisms. We consider the allocation decision for clones with both obligately and facultatively sterile soldiers, under various levels of predation, and favorable and unfavorable ecological conditions. We test predictions of the model with the eusocial aphid, Pemphigus spyrothecae. Our model predicts that defensive investment should be dependent on the time of the season, with clones discounting defense nearer the end of season. Defensive investment should also vary inversely with clonal productivity and be sensitive to the current state (e.g., level of defense) of the clone. Census data collected in Burnaby, British Columbia, Canada, conform to patterns of clonal composition derived from allocation decisions generated in the model. Finally, qualitative predictions about patterns of clonal organization under "good" and "poor" ecological conditions were upheld by comparing clones in preferred and less-preferred galling sites.
Key words: colony defense, dynamic programming model, eusocial aphids, Pemphigus spyrothecae, soldier allocation strategies, tradeoffs.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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A central tenet of life-history theory is that tradeoffs constrain the evolution of allocation decisions (Daan and Tinbergen, 1997
). For example, allocation of resources to defense necessarily requires a compensatory decrease in allocation to growth. Less certain is our knowledge about the evolution of allocation decisions by eusocial groups. Traditionally, studies have used sexually reproducing taxa (e.g., Hymenoptera and Isoptera; for review, see Choe and Crespi, 1997) and have been complicated by the fact that genetic conflicts of interest between colony members may distort allocation strategies away from that which would be expected if overall group performance were to be considered (Seger, 1991; Trivers and Hare, 1976). Eusocial species that reproduce asexually, however, simplify the study of group-level allocation and organization as these genetic conflicts are no longer present (Stern and Foster, 1996, 1997). Here we present a theoretical exploration of soldier investment by clonally reproducing eusocial aphid species, as well as a test of the model with the species Pemphigus spyrothecae.
Eusocial aphids have an altruistic soldier caste that defends colonies from natural enemies (Stern and Foster, 1996, 1997). Aphids reproduce parthenogenetically, creating a common genetic interest for all individuals derived from the same stem mother. This simplifies the underlying allocation theory, as we can now consider investment decisions at the level of the clone (Stern and Foster, 1996, 1997). We acknowledge that dissent between individuals of different clones may arise, however, and if clonal mixing in nature is common, this may complicate the issue, calling for a frequency dependent modeling approach (see Abbot et al., 2001; Stern and Foster, 1996; Tyerman, 2001). Nonetheless, a state-dependent, yet frequency-independent approach, provides an important point of comparison for future studies that include higher levels of complexity.
Aphid species with obligately sterile soldiers face a tradeoff between clonal defense (i.e., soldier production) and clonal growth (i.e., reproductive production). Though less severe, aphid species with facultatively sterile soldiers face a similar tradeoff: clones that invest in defense delay their investment in growth, which will reduce the overall productivity of the clone. In both cases, the resolution of the tradeoff will likely depend on the state of the aphid colony. For example, small aphid clones may make different defensive allocations than do larger clones, or clones of similar size but with different compositions of soldiers and reproductives may favor different allocation strategies.
Our theoretical consideration takes the form of a dynamic state variable model (Clark, 1993; Clark and Mangel, 2000) and extends preliminary work conducted by Akimoto (1996) and Stern and Foster (1996). Akimoto considered the evolution of optimal duration for first-instar soldiers under different ecological contexts, for a generalized system in which soldiers could mature into reproductive adults after the conclusion of their juvenile tours of duty. Stern and Foster considered optimal soldier ratios under a game theoretic framework, in which clonal mixing could lead to the exploitation of the defensive efforts of soldier producing clones by nonsoldier producing (i.e., "cheater") clones. Thus, our contribution will add to the slowly growing, but much needed (Stern and Foster, 1997), theory underlying our understanding of the evolution and ecology of defensive allocation in eusocial aphids. Although our model was motivated by our field studies of P. spyrothecae, it should be applicable to clonal species other than aphids (e.g., anemones, slime molds). Furthermore, this model is similar in spirit to models of allocation in other systems (i.e., plants; see Bazazz et al., 1985; Herms and Mattson, 1992) that face analogous resource partitioning dilemmas. One advantage of using clonal organisms over suites of traits within an organism (i.e., traditional studies) to investigate allocation decisions is accounting procedures become simplified (numbers of individuals rather than proportions of tissue).
As a first step, we assume that the optimal solution to the question of soldier production is flexible, such that aphid clones can adjust their allocation as circumstance dictates. Second, we assume that each soldier allocation strategy is independent of the other allocation strategies in the population, a circumstance likely to be species and context specific (Stern and Foster, 1997). We examine a range of values for ecological and functional parameters that may be likely to influence the allocation decisions of aphid clones, and we compare allocation strategies for clones with obligately and facultatively sterile soldiers. Finally, we compare predictions from the model to census data from a field population of P. spyrothecae in Burnaby, British Columbia, Canada.
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METHODS |
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Natural history
In mid to late spring, a female P. spyrothecae hatches from an over-wintering egg, initiates a spiral gall on the emerging leaf petiole of a poplar tree (Populus nigra var italica), and commences to reproduce asexually. This female is referred to as the fundatrix or stem-mother. During this phase, first instar nymphs act as soldiers (Aoki and Kurosu, 1986
) and develop into apterous adults, which produce facultatively sterile soldiers or nonsoldier nymphs. At the end of the summer, apterous adults produce sexuals, which depart from galls once they desiccate and crack open. Mating occurs outside the gall, and females lay over-wintering eggs on the bark of the host tree (for further details of life history, see Aoki and Kurosu, 1986; Chan and Forbes, 1975; Foster and Northcott, 1994). Little is known about the predators of P. spyrothecae in British Columbia, Canada, although we have directly observed lacewing larvae inside galls. In its native habitat (Europe), P. spyrothecae are depredated by anthocorid bugs (Foster, 1990).
The model: overview
Because the optimal allocation decision by an aphid clone is likely to depend on the size and composition of the clone (e.g., number of soldiers) we decided that a state-dependent model would be an appropriate tool for our investigation. The model takes the form of a stochastic dynamic program (Clark, 1993; Clark and Mangel, 2000) and forward simulation (for list of variables and parameters, see Table 1). The model assumes that allocation to soldier and nonsoldier castes in aphid clones is flexible (i.e., phenotypically plastic) and is dependent on the size and composition (i.e., internal state) of the clone, and that the presence or absence of a predator in the gall (i.e., external environment). The decision to be modeled is the number of newborn nymphs to allocate to soldiers and nonsoldier nymphs throughout the season, which is analogous to an individual (in the traditional sense) partitioning resources between defense and growth, throughout development. The optimal solution will be that allocation strategy that maximizes the expected lifetime reproductive success of the clone. Time is discretized into days, and encompasses the asexual phase of the life cycle of P. spyrothecae (from the middle of May to the end of August, or about 100 days). Our fitness surrogate (i.e., terminal fitness) is a function of the number of adults present in the clone at the end of the parthenogenetic phase (modified from Stern and Foster, 1996).
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State variables
The four state variables encompass three aphid-caste classes and an information state. The three aphid-caste classes, or internal states of the clone, are numbers of soldiers, s(t); numbers of nonsoldier nymphs, n(t); and numbers of apterous adults, a(t). Soldiers defend the clone against predators, whereas nonsoldier nymphs mature into apterous adults (which then reproduce asexually, contributing to clonal growth). Our first version of the model assumes soldiers are obligately sterile, whereas our second version assumes facultative sterility, with soldiers maturing into adults at a fixed rate. As mentioned, apterous adults produce both soldiers and nonsoldier nymphs. To model the maturation from nymph to adult, we condensed all the possible nymph ages into a single class and allowed a fixed proportion—n(t)/Mn and s(t)/Ms for nonsoldier and soldier nymphs, respectively—to mature each day. Finally, the information state variable, or external state, p(t), describes whether a predator is present or absent in the gall. This assumes that aphid clones have perfect knowledge about predators in their immediate environment.
State dynamics
The state values can change at several substages in each time period, as detailed below. At the outset of each day, the clone assesses whether a predator is present in the gall (from the previous time period). If a predator is absent, a new predator may arrive with probability µ, or not, with probability 1 - µ. We assume that predation is rare (i.e., no more than one predator enters a gall per day), and that predators do not leave galls unless evicted or killed by soldiers. If a predator is present, then p(t) = 1. If absent, then p(t) = 0. Clonal growth (i.e., the absolute number of nymphs produced), G, is modeled with the logistic function, as follows:
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If instead, a predator is present in the gall (i.e., p[t] = 1), then it may be killed or evicted from the gall by the soldiers with probability E(s), where
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Eeff). If the predator is evicted or killed, then the state dynamics are as follows:
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; Arakaki, 1989). If soldiers are absent or the clone fails to evict a predator from the gall, then casualties to other castes accrue.
Terminal fitness
In the final time period, when t = T, the fitness of an aphid clone, theta (
), is a function of the number of adults that are present in the colony (after the method of Akimoto, 1996; Stern and Foster, 1996), multiplied by a fitness conversion constant W, such that
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Dynamic programming equation
The dynamic programming equation (DPE) to determine the optimal allocation of growth to soldiers (and nonsoldiers) is given by F; when p(t) = 1,
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The dynamic model was solved via backward induction (Clark and Mangel, 2000). The solutions for different combinations of state variables and times were placed into a decision matrix for implementation in forward simulations (see below). Computational limitation required us to determine optimal allocation strategies for internal states (i.e., s[t], n[t], and a[t]) in increments of five aphids, and to use linear interpolation across the aphid-caste state variables in the forward iterations of the simulation.
Forward simulation
To analyze the results of this model, we ran forward simulations, using the decision matrix generated by the DPE, and predation rates drawn randomly from a uniform distribution to guide cohorts of a thousand aphid clones through hypothetical seasons. Differences in the distributions of clones generated by the model when different parameter values were used, furnished us with expectations that could be compared with census data (see below). This was necessary as it has proved difficult to directly assess the allocation decision of aphid clones, although relatively easy to determine the resulting pattern of clonal organization that has arisen from earlier allocation decisions.
Census data
Ontogeny of clonal composition
Galls were collected from May–August from a field site in Burnaby, British Columbia, Canada, on a weekly basis. Approximately 25 galls were chosen each week from five trees. Galls were selected randomly from branches from heights of 0–2 m. The presence of a fundatrix, the numbers of soldiers, nonsoldier nymphs, apterous adults (all instars), and alates (i.e., winged individuals) were recorded. Soldiers appear darker than do nonsoldier nymphs, owing to a higher degree of sclerotization, and have larger hind-legs then do nonsoldiers (Foster, 1990). Data were recorded as mean number of aphids in each class (±1 SE).
Double gall survey
Occasionally, when galling densities are high (Whitham, 1979), two (or more) aphid fundatrices may successfully initiate galls on the same leaf petiole, hereafter referred to as double galls. Assuming double galls are initiated at the same time but that growing conditions differ between clones occupying basal and distal positions in the double gall, then we are provided with a natural experiment to test predictions generated by the model.
Several observations suggest that double galls are initiated at the same time in the season. First, Whitham (1992) noted that 83% of Pemphigus aphid stem mothers arrived at the developing leaves within a 3-day period (see also Faith, 1979). Second, as gall initiation involves manipulating the natural growth of leaf petioles, fundatrices would have to select petioles at an appropriate stage of development, leaving a narrow window of opportunity for gall initiation to be successful. In addition, Akimoto (1998) noted that sessile insects such as gall formers, scale insects, and leafminers may be particularly susceptible to individual heterogeneity in bud burst by their host plants, and Komatsu and Akimoto (1995) found in another species of nonmigratory galling aphid, Keltenbachiella japonica, that intraspecific variation for egg-hatch date was synchronized for the bud-burst date on the hosts on which stem mothers were found.
Basal and distal positions in a double gall do differ qualitatively as well: in a related species of Pemphigid aphid, fundatrices compete for and defend gall sites, preferring basal to distal positions (Whitham, 1979). Territorial disputes between aphid stem mothers have been noted to last for several days (Whitham, 1979), and as such may be costly, if not deadly (Akimoto, 1988; Aoki and Makino, 1982). Territoriality is unlikely to have evolved if the disputed resource being contested, namely, gall initiation position, was not of some intrinsic value. Insect galls are likely to be resource sinks, drawing nutrients from other tissues of the host plant in addition to its own leaf (Larson and Whitham, 1991). Thus, gall positions nearer the source (i.e., basal) may be preferable to galling insects, especially early in the season when leaves have not fully developed. Our assumption is that stem mother preference for galling position reveals a fundamental difference in fitness, with the basal gall position yielding enhanced fitness to aphid clones, relative to the distal position (Larson and Whitham, 1991).
In addition to the weekly census data, double galls were surveyed early in July, with the intention of comparing them to simulated aphid clones that developed under favorable and unfavorable ecological conditions generated in the model (factors are summarized in Table 2). Differences in the mean size of clone and mean soldier ratio between basal and distal groups were analyzed with paired t tests.
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RESULTS |
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Decision matrix
To simplify the interpretation of the decision matrix, we determined the regions of state-space that were insensitive to time (i.e., where the model had achieved stationarity; Clark and Mangel, 2000
). Here, we operationally define stationarity as regions of state-space where consecutive (with respect to time) allocation strategies have greater than 98% congruence (Figure 1). Stationarity was maintained until the final 25 and 15 time intervals, for obligate and facultative sterility versions of the model, respectively.
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We examined the clonal productivity and the optimal soldier allocation strategy (Figure 2) in a region of stationarity (i.e., t = 50) for three aphid clone sizes (i.e., total number of aphids: N = 30, N = 90, and N = 150), under various clonal compositions (i.e., combinations of soldiers, nonsoldier nymphs, and apterous adults), with and without a predator present in the gall. The productivity of a clone was highest at the intermediate clone size (N = 90). Productivity was lower when clonal size was low (N = 30), because there were fewer adults contributing to the production of new aphid nymphs. Similarly, productivity was lower for large clones (N = 150), owing to the density-dependent constraints of a clone growing near its carrying capacity (i.e., K = 200). For both obligately and facultatively sterile soldier versions of the model, soldier allocation varied inversely with clone productivity. When productivity was relatively low, allocation to defense was relatively high. Conversely, when productivity was relatively high, allocation to defense was relatively low.
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Interestingly, soldier allocation was lower when a predator was present in the gall (p[t] = 1) compared with when a predator was absent (p[t] = 0). This may be attributed to high intrinsic growth rates, suggesting that an alternative way for aphid clones to defend themselves against predators is to simply outgrow the appetite of their predators. When clonal size was low (N = 30), the composition of the clone had little effect on the soldier allocation decision of the clone. At intermediate and large clonal sizes, however, the composition of the clone greatly affected the allocation policy of the clone. At intermediate sizes, if there were soldiers in the clone, then allocation to soldiers was low. The exception to this trend at intermediate size occurred when the clone was composed of many soldiers and nonsoldier nymphs (and therefore few adults), resulting in low clonal productivity. Qualitatively, the results were similar when we assumed facultative sterility in soldiers, although at intermediate densities (e.g., N = 90), allocation to soldiers was greater than allocation in the obligate sterility model.
Forward simulations and census data
The typical number of aphids comprising a clone over the asexual phase of the life cycle, generated by the simulation, is shown in Figure 3a. If soldiers were facultatively sterile, clone size increased exponentially (until the carrying capacity was met). If soldiers were obligately sterile, clone size increased logarithmically. Mean clone size from field populations of P. spyrothecae increased exponentially over the sampling period (Figure 3b).
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The soldier ratio was calculated as the proportion of soldiers to total number of aphids comprising a clone. Typical soldier ratios generated by forward simulation are shown in Figure 3c (both obligately and facultatively sterile soldier versions of the model), and the ratio of soldiers obtained from census data is illustrated in Figure 3d. The qualitative pattern of the field data and the predictions generated by the forward simulations were similar. Soldier ratios increased sharply during early time periods and then decreased for the remaining time periods. When soldiers were obligately sterile, the initial decline in soldier ratio was not as severe as the decline, if soldiers were assumed to be facultatively sterile. Furthermore, facultative sterility caused the soldier ratio to decline steadily for the remaining time periods.
Double galls
Forward simulations were conducted with different parameter settings to determine how changing ecological circumstance would affect overall patterns of clonal organization. When ecological circumstances were relatively favorable (or "good"; see Table 2), average clone sizes were larger, and average soldier ratios were lower.
These expectations were tested in double galls, in which it was suspected that ecological circumstance also varied between galls occupying basal and distal positions (see Methods). Double gall survey data are summarized in Figure 4. Clones occupying galls in the basal position were significantly larger and had significantly lower soldier ratios than did clones in galls occupying the distal position. These results conform to the expectations generated in the model, although we cannot rule out other hypotheses that also predict these patterns (see below).
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
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Because the tactics of defense and growth may be mutually exclusive, investment in one comes at the expense of investment in the other and may be state dependent. Here, we have provided a general theoretical framework for understanding such an allocation problem, and applied it to a specific example of the eusocial aphid, P. spyrothecae.
From our analysis of stationarity, it appears that we can break the problem up into two phases. The first phase covered the interval of time from the outset of parthenogenetic colony growth until three fourths of the way through the season. During this phase, optimal allocation decisions appeared to be largely insensitive to time. The second phase covered the remaining interval of time, and here, the allocation decision became sensitive to time: with the end in sight, our theory states that optimal aphid clones should invest less in defense than do comparable clones making decisions earlier in the season. This outcome is largely dependent on the terminal fitness function, which rewarded clones for the numbers of adults (which are capable of producing sexual morphs) present at the end of the season, and gave no weight to the number of soldiers at the end of the season. If risk of predation were to increase at the end of the season—perhaps because aphid clones were larger, concomitant with an increasing functional response by predators; or clones were more exposed to predators due to gall desiccation—then no discounting of defense would occur.
In addition to time, the size and composition of the aphid clone greatly affected its allocation decision. Clonal productivity was highest at intermediate sizes—a pattern that was driven by a balance between numbers of adults present in the clone and the constraints of the carrying capacity (K). Intermediate-sized clones invested little in defense, because they were able to outgrow the appetites of unevicted predators. Both small and large clones had limited productivity, because of the low numbers of adults in the former, and clones being constrained by K in the latter. As such, allocation to defense was high.
Several patterns generated by forward simulation were qualitatively similar to census data. In particular, the version of the model that assumed facultative sterility captured the patterns seen in P. spyrothecae. Our model predictions about soldier allocation (assessed via clonal composition) were upheld in tests of aphid clones occupying adjacent galls in naturally occurring double galls. Confounds to these results may arise if double galls were formed at different times of the season, or if there was a difference in predation risk between basal and distal gall positions. As discussed above, galls are likely to be initiated at similar times in the season, and we have no data to address the question of differential predation at the two gall positions.
Early in the season, there is likely to be a net flow of resources into developing leaves, so clones occupying more distal positions may be resource limited by clones occupying more basal positions (Inbar et al., 1995; Larson and Whitham, 1991). It would be interesting to see if the relative productivity of the clones changed as the season progressed and as leaves became net sources rather than net sinks for plant nutrients.
We assumed that aphid clones could adjust their soldier production schedules to changes in the environments (both internal and external), if such a response were optimal. Akimoto (1996), on the other hand, assumed that variation in defensive effort was genetically mediated, rather than facultative. We did not constrain our model to generate phenotypically fixed (i.e., nonplastic) responses, and although such strategies were possible, they were suboptimal. On examination of the fitness functions for alternative soldier allocation strategies across any given environmental regime, we can detect where selection would act against strategies that deviated from the optimal soldier allocation strategy. For example, when the daily probability of predation, µ, was low, deviations from the optimal strategy had severe consequences to fitness. However, when µ was high, deviations from the optimal strategy were of little consequence (Figure 5).
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Other empirical evidence for plasticity in soldier allocation by Pemphigus aphids is lacking, although we would argue it almost certainly exists. The fact that aphids display adaptive flexibility in many other facets of their biology (e.g., pea aphids can produce alate and sexual morphs late in the season [for review see Dixon, 1985
] and can increase the proportion of alate individuals in predators are present [Dixon and Agarwala, 1999; Weisser et al., 1999]), at least suggests that we should not rule out such flexibility for degree of soldier allocation from the outset. We have conducted preliminary studies (Tyerman JG, unpublished data) in which leaf quality was experimentally manipulated, and colony size and composition were affected, suggesting that such flexibility in P. spyrothecae is possible in response to changes in environmental factors. Shibao (1999) studied Pseudoregma bambucicola, a free-living aphid in Japan and found that soldier proportion (in terms of production) was positively correlated to the size of the colony that the aphid stem mothers came from. Our model suggests that there should be a negative correlation between soldier proportion and colony size. We speculate that these differences may be attributed to whether the aphid species is gall- or free-living. Free-living aphid species may attract more predators as their colonies expand (i.e., a positive functional response), favoring an increase in defensive effort as size increases. Gall-living aphids, however, may not be subjected to this increasing functional response, as their numbers may be concealed by the galls they inhabit. In addition, Shibao (1999) failed to detect a difference in soldier proportion when a predator was present or absent with the producing aphid stem mothers (no indication of statistical power was made). Interestingly, his data, although not significant, suggested that soldier proportion was lower in the presence of predators than in the absence of predators, a result in agreement with our model.
Here, we have illustrated the importance of state-dependence in questions of investment to growth and defense by aphid clones of P. spyrothecae; yet, we hope our findings are applicable to other systems facing analogous allocation dilemmas (involving continual investment, e.g., in plants; Herms and Mattson, 1992). We found that investment strategies were dependent on the size and composition of the clone making the decision, and that under some circumstances (i.e., high productivity), investment in growth may be the favored response to predation.
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ACKNOWLEDGEMENTS |
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We would like to express thanks to members of the Roitberg lab and the Behavioural Ecology Research Group at Simon Fraser University for helpful discussions on this subject. In particular, C. Clark and R. Ydenberg commented on early versions of the model, and F. Breden, B. Crespi, E. Mondor, and two anonymous reviewers provided invaluable editorial comments on early drafts of the manuscript. The Natural Sciences and Engineering Research Council provided financial support to B.D.R.
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