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Abstract. The role of plant defensive compounds has often been studied within the purview of consumer diet choice. However, consumers are often confronted with foods distributed within depletable patches. To investigate the complication of resource depletion, I merged a consumer--resource model of nutritional relationships between foods with the technique of giving-up densities for measuring foraging behavior in depletable food patches. Theory predicts that foods containing plant defenses that act as digestibility reducers (e.g., lignins and tannins) will be relatively less depleted under higher predation risk than will foods without defenses. In contrast, foods containing defensive toxins (e.g., alkaloids) that affect fitness directly, and not through diminished physiological uptake of energy, will be depleted without bias to predation risk or other foraging costs. I tested the theory using fox squirrels (Sciurus niger) feeding on sunflower seeds that were impregnated with either tannic or oxalic acid. Squi rrels had their highest giving-up densities on oxalate-treated seeds and their lowest on water-treated (control) seeds. GUDs were also higher when patches were placed in riskier microhabitats. Moreover, risky microhabitats increased tannin GUDs relative to control GUDs but had no effect on oxalate GUDs. The former observation is consistent with defenses that act as digestibility reducers, and the latter is consistent with defensive toxins. These results indicate that the effects of plant defensive compounds on foraging behavior are complicated and require consideration of not only the potential effects of the compound, but also the environment to which the forager is exposed. Tannins influence squirrel foraging behavior, but the effects may not be seen or realized unless the forager is in a sufficiently risky environment.

Key words: defensive toxins; diet choice; digestibility reducers; fox squirrel; oxalic acid; plant--animal interactions; predation risk; resource depletion, Sciurus niger; secondary compounds, tannins.


Foraging on foods containing chemical plant defenses or beneficial nutrients has been the subject of numerous theoretical (Pulliam 1975, Stephens and Krebs 1986, Belovsky and Schmitz 1994, Hirakawa 1995, Schmidt et al. 1998) and empirical studies (mammalian examples include Belovsky 1981, Smallwood and Peters 1986, Bryant et al. 1991, McArthur et al. 1993, Schmidt et al. 1998). These studies have focused on questions related to diet choice, often under conditions in which the forager consumes food ad libitum (e.g., Smallwood and Peters 1986, Schmitz et al. 1992, McArthur et al. 1993; but see Schmidt et al. 1998). Yet, typically, foragers are confronted with food distributed in depletable resource patches. A largely separate, but related (Brown and Mitchell 1989, Steele and Weigl 1992), body of theory has developed around the question of how much time to expend in a depletable resource patch (Iwasa et al. 1981, Stephens and Krebs 1986, Brown 1992). Patch use theory has not been expanded to explore patch use b ehavior when food items contain chemical defenses. That is the focus of the present study: how does the chemical composition of foods influence patch use behavior?

In particular, I focus on the role of plant secondary or defensive compounds. Plant defensive compounds have two general modes of action (Howe and Westley 1988). Toxins (e.g., alkaloids, cyanogenic glycosides) act by repressing specific biochemical reactions. In contrast, other compounds such as lignins and tannins are thought to interfere with the physiological uptake of carbohydrates and protein, respectively (Hagerman and Butler 1992). For instance, tannins exhibit an ability to precipitate proteins and reduce the activity of digestive enzymes in vitro (reviewed in Bernays et al. 1989) and to reduce protein digestibility in vivo (e.g., Chung-Maccoubrey et al. 1997). However, plant consumers may possess physiological mechanisms that counteract the effects of tannins (Mehansho et al. 1987, Mole and Waterman 1987, Robbins et al. 1987, 1991), albeit the detoxification mechanisms will probably entail a cost to the consumer. Might this difference in the mode of action among defensive compounds yield qualitative differences in the way foragers exploit resource patches? Specifically, do defensive compounds interact with metabolic or predation costs, and if so, does the interaction depend on the compound's mode of action? Because energy and safety from predators are complementary inputs to fitness (Brown 1992), we might expect interactions among patch exploitation, predation risk, and toxicity of food items.

Here, I develop a theoretical framework for modeling the consumption of foods containing chemical plant defenses (or nutrients) that are distributed within depletable resource patches. Furthermore, I combine this modeling approach with an experimental protocol that uses giving-up densities (Brown 1988) in artificial food patches to assay the qualitative physiological effect of the toxic compounds, tannic, and oxalic acids. I apply these techniques to a free-ranging population of fox squirrels (Sciurus niger) feeding on sunflower seeds impregnated with either tannic or oxalic acid. Tannins may make up significant portions of the diets of squirrels that consume acorn mast (0.5-10% tannins; Ofcarcik and Burns 1971). Oxalates are ingested through the consumption of leaves and fungus, which are rich in oxalates and may make a significant part of the fox squirrel diet in spring and summer (Nixdn et al. 1968).

Patch use theory when food contain toxins

In this section, I follow the procedure used by Brown (1992) for determining the optimal time allocation for a forager that has T time units that it can partition among n activities, where [t.sub.i] is the amount of time devoted to the ith activity. For convenience, assume that activities 1 and 2 denote foraging in food patches 1 and 2, respectively; all others, n - 2, denote alternative activities. Activities 1 and 2 contribute to the forager's expected number of offspring, F, via the acquisition energy and through incurring predation risk. The expected number of offspring is an increasing function of net energy, which is, in turn, an increasing function of time spent foraging in a food patch as long as harvest exceeds the energetic cost of exploitation. The rate of energy acquisition, e, is the difference between the forager's harvest rate, [f.sub.i], and the energetic cost of exploitation, [c.sub.i]:

[partial]e/[partial][t.sub.i] = [f.sub.i] - [c.sub.i]. (1a)

Furthermore, assume that patches are depletable, and thus,

[partial][f.sub.i]/[partial][t.sub.i] [less than] 0. (1b)

Predation risk is likewise an increasing function of time spent in a patch, and is related to survivorship, p, by the expression

P = exp(-[sigma][[micro].sub.i][t.sub.i]) (1c)

where [[micro].sub.i] is the instantaneous risk of predation while engaging in the ith activity.

The forager's fitness function will be related to both its acquisition of energy (which contributes to the production of offspring) and its probability of surviving to reproduce. Brown (1992) discusses a number of models that incorporate these two components. I restrict the current discussion to Brown's model 4, which best applies to organisms that realize fitness after some finite amount of time, T, has elapsed, rather than through instantaneous conversion of energy into offspring. Fitness is given as the product of the number of surviving descendants (F + 1 for an iteroperous species) in the absence of predation and the probability of surviving to realize its fitness:

Max G = p(F+ 1), subject to [sigma] [t.sub.i] = T.

Incorporating food chemistry: toxins.--To incorporate the additional effect of chemical defenses (or nutrients) on patch use behavior, further assume that foods contain a chemical substance, X, whose consumption is an increasing function of time spent in a food patch, [partial]X/[partial][t.sub.i] [greater than] 0, and that X contributes negatively (or positively for a nutrient) to the expected number of offspring. In neither case does the chemical interact with energy uptake. Thus, the chemical may be a nutrient, such as calcium, that provides fitness benefits through a greater expected number of offspring produced, e.g., stronger eggshells. Alternatively, the chemical may be a toxin that acts by repressing a specific biochemical reaction and negatively affects future offspring production. The fitness function becomes

max G = p([t.sub.i])[F(e([t.sub.i]), X([t.sub.i]))], subject to [sigma] [t.sub.i] = T.

Digestibility reducers.--Another class of plant defenses acts as digestibility reducers (DR), interfering with the physiological uptake of proteins (in the case of tannins) or carbohydrates (in the case of lignins). Under this scenario, energy is an increasing (but reduced relative to plant foods without defenses) function of the amount of food consumed, R, and food consumption is an increasing function of time spent in a patch. The fitness function becomes

max G = p([t.sub.i])[F(e(R([t.sub.i])))] subject to [sigma] [t.sub.i] = T.

It is important to realize that the effects of secondary compounds enter into the models in different fashions. Foods containing toxins yield the fitness benefit of energy plus the additive, negative fitness consequences of the toxin, [partial]F/[partial]X [less than] 0. Consumption of the toxin is related to energy intake by [partial]X/[partial]t = [alpha][f.sub.i], where [alpha] is the proportionality constant, or a measure of the toxin's concentration. The exploitation cost, [c.sub.i], is left out of the equation because it is subsumed within [partial]e/[partial]t (see Eq. la).

In contrast, foods containing digestibility reducers yield the fitness benefits of energy only, but consumption of energy is reduced through the negative effects of the digestibility reducer, ([partial]F/[partial]e)( [partial]e/[partial]R), where 0 [less than] [partial]e/[partial]R [less than] 1 to denote the reduction in energy relative to the same food without plant defenses (where [partial]e/[partial]R = 1). Furthermore, [[partial].sup.2]e/[partial][R.sup.2] may be negative if additional consumption further inhibits assimilation of energy, but this effect will not be considered here. Consumption of energy is related to food intake via [partial]R/[partial][t.sub.j] = ([f.sub.j] - [c.sub.j]).

To determine the optimal allocation of time among activities, I use the technique of Lagrange multipliers (e.g., Brown 1992). The Lagrangian function for either model is

L = p(F + 1) + [[phi].sub.t](T - [sigma] [t.sub.i]). (2)

The Lagrange multiplier, [[phi].sub.t], gives the marginal fitness associated with relaxing the constraint, in this case, time. The necessary conditions for optimal time allocation are


[partial]L/[partial][t.sub.i] = (F + 1)([partial]p/[partial][t.sub.i]) + p[([partial]F/[partial]e)([partial]e/[partial][t.sub.i]) + ([partial]F/[partial]X)([partial]X/[partial][t.sub.i])] - [[phi].sub.t] = 0 (3a)


[partial]L/[partial][t.sub.i] = (F + 1)([partial]p/[partial][t.sub.i]) + p([partial]F/[partial]e) X ([partial]e/[partial]R)([partial]R/[partial][t.sub.i]) - [[phi].sub.t] = 0 (3b)

To determine when a forager should leave food patch j = 1, 2, substitute the following relationships: [partial]e/[partial][t.sub.j] = [f.sub.j] - [c.sub.j], [partial]p/[partial][t.sub.j] = - [[micro].sub.j]p, [partial]X/[partial][t.sub.j] = [alpha][f.sub.j], and [partial]R/[partial][t.sub.j] = ([f.sub.j] - [c.sub.j]). Solving Eqs. (3a,b) for the quitting harvest rate, [f.sub.j], gives


[f.sub.j] = [[[micro].sub.j](F + 1) + [[phi].sub.t]/p + [c.sub.j]([partial]F/[partial]e)]/([partial]F/[partial]e) + [alpha]([partial]F/[partial]X) (4a)


[f.sub.j] = [[[micro].sub.j](F + 1) + [[phi].sub.t]/p + [c.sub.j]([partial]F/[partial]e)([partial]e/[partial]R)]/([partial]F/ [partial]e)([partial]e/[partial]R). (4b)

The terms in the numerator correspond to foraging costs associated with predation risk, missed opportunities, and metabolism, respectively (Brown 1988, 1992), and are identical to those in Brown (1992). However, these costs are further modified by the terms in the denominator that denote the marginal value of energy, [partial]F/[partial]e, adjusted for the additional negative, marginal effect of a toxin, [alpha]([partial]F/[partial]X), or the reduction in energy uptake through the effects of a digestibility reducer, ([partial]e/[partial]R).

Toxins vs. digestibility reducers.--The modus operandi of a plant defense can be investigated by considering the marginal rate of substitution (MRS) of two food patches (Schmidt et al. 1998). The MRS of two food patches is simply the ratio of their marginal values. The marginal value of a food patch is equivalent to its quitting harvest rate, i.e., the amount of energy obtained per unit time spent in a patch at the point at which the forager ceased exploiting the patch. The ratio of quitting harvest rates from two separate patches exploited by the same forager indicates the exchange rate of time spent in one patch for time spent in the second patch. Consider the MRS for two patches identical in all respects ([[micro].sub.1] = [[micro].sub.2], [p.sub.1] = [p.sub.2], [c.sub.1] = [c.sub.2]) except that food in patch 1 contains a qualitative toxin, whereas patch 2 contains nontoxic food. The equation for the quitting harvest rates of the latter patch is the same as for the former, but without the additional term in the denominator that accounts for the negative value of a toxin:

[MRS.sub.2,1] = [f.sub.1]/[f.sub.2] = ([[[micro].sub.1](F + 1) + [[phi].sub.t]/p + [c.sub.1]([partial]F/[partial]e)]/([partial]F/[partial]e) + [alpha]([partial]F/[partial]X)) X (([partial]F/[partial]e)/[[[micro].sub.2](F + 1) + [[phi].sub.t]/p + [c.sub.2]([partial]F/[partial]e)])

which simplifies to

([partial]F/[partial]e)/([partial]F/[partial]e) + [alpha]([partial]F/[partial]X). (5)

The MRS is independent of the foraging costs and is dependent only on the marginal value of energy, [partial]F/[partial]e, the marginal value of toxin, [partial]F/[partial]X, and the toxin's concentration, [alpha]. Increasing a toxin's concentration or its fitness consequence decreases the value of a food patch.

Contrast this with the MRS when the food in patch 1 contains a digestibility reducer:

[f.sub.1]/[f.sub.2] = [[[micro].sub.1](F + 1) + [[phi].sub.t]/p + [c.sub.1]([partial]F/[partial]e)([partial]e/[partial]R)]/([partial]F/ [partial]e)([partial]e/[partial]R) X ([partial]F/[partial]e)/[[[micro].sub.2](F + 1) + [[phi].sub.t]/p + [c.sub.2]([partial]F/[partial]e)].

That, given [[micro].sub.1] = [[micro].sub.2], [p.sub.1] = [p.sub.2], and [c.sub.1] = [c.sub.2], simplifies to

1/[partial]e/[partial]R ([[micro](F + 1) + [[phi].sub.t]/p + c([partial]F/[partial]e)([partial]e/[partial]R)]/[[micro](F + 1) + [[phi].sub.t]/p c([partial]F/[partial]e)]). (6)

The MRS of the two patches is a function all three foraging costs. Increasing predation or missed opportunities increases the MRS (DRs are relatively less preferred in risky habitats), whereas increasing the metabolic cost decreases the MRS. Thus, the differential use of depletable resource patches provides an assay for detecting a qualitative difference in the physiological effects of a chemical defensive compound. If the MRS remains constant under different foraging costs, the defense is a qualitative toxin. If the MRS varies under different levels of predation risk, missed opportunity, or metabolic costs, the toxin functions as a digestibility reducer.

Why is the rate of substitution between food patches containing DRs, but not toxins, a function of the foraging costs? This surprising result is based on the relationship between the components of fitness: energy, time, and safety. A reduction in fitness attributed to the effects of toxins is experienced directly and not through the relationship between energy and the other fitness components. In contrast, DRs influence the fitness benefit of the consumed food. The additional inputs to fitness, safety and time, are not perfect substitutes for food or energy consumption, but rather are complementary. The lower the value of food (i.e., energy), the greater the value placed on safety from predators and alternative activities, and vice versa; the forager actually experiences a higher predation cost when foraging on a low-quality food. Moreover, this relationship is not restricted to foods containing DRs, but applies to any two foods that differ in their per unit energy content. For the metabolic cost, the relatio nship is reversed, because increasing the metabolic cost, which is experienced similarly between the two patch types, dilutes the effect of higher predation and missed opportunity costs in the patch containing DRs.

To test the predictions of the models, I used giving-up densities (GUDs) in experimental food patches to detect changes in the MRS (see Schmidt et al. 1998). Patches are created by mixing a measured amount of food into a volume of substrate. Foragers experience diminishing returns in feeding effort as their harvest rate declines with time spent foraging in the patch (assumption 1b); they cease foraging on the patch when the harvest rate no longer compensates for foraging costs. Because the harvest rate in the tray is a function of the remaining density of seeds (Kotler and Brown 1990), GUDs provide a surrogate for the forager's quitting harvest rate (Brown 1988), and thus for the marginal value of that patch.


I studied free-living fox squirrels feeding from experimental food patches (see Plate 1) at The Morton Arboretum in Lisle, Illinois, 35 km west of Chicago, USA. The arboretum has [sim]600 ha of deciduous forests, coniferous woods, meadows, and prairie grasslands. The deciduous woods and associated meadows support an abundant population of fox squirrels. I selected two study sites located along woodland-meadow boundaries and separated by [greater than] 1 km. Sites were further subdivided into three stations (separated by [greater than] 100 m), each containing four artificial food patches (i.e., seed trays).

I measured foraging behavior in food patches (seed trays) consisting of plastic trays (30 X 16 X 10 cm) filled with 2 L of sand into which 10 g of sunflower seeds were thoroughly mixed. Food consisted of "oiler's" husked sunflower seeds soaked for 2.5 h in a 10% (mass : volume) solution of tannic acid, oxalic acid, or distilled water (see Schmidt et al. 1998). Treated seeds were oven-dried for [sim]1.5 h at 90[degrees]C, followed by air-drying for several days before use. These procedures yielded an estimated tannin concentration of 1.74% (range: 1.19-2.01% by tissue mass) and an oxalic acid concentration of 5.3% (Schmidt et al. 1998). Seed trays were available to squirrels from early in the morning to late afternoon, when I sifted their contents to remove any uneaten seeds (squirrels consume seeds at the tray and do not cache them), and weighed the seeds to measure the patch's giving-up density (GUD). The experiment was preceded by a "pre-baiting" period of two days in which food was placed in the trays, bu t GUDs were not collected.

At each station, two seed trays were placed near the forest-field edge (safe microhabitat) and two trays were placed several meters (5-8) into the field (risky microhabitat) to manipulate predation risk (Thorson et al. 1998). One control tray within each pair of trays at a microhabitat contained water-soaked seeds; the other treated tray contained either tannin- or oxalatesoaked seeds (the same compound was used at both microsites within a station). I collected GUDs for eight days between 28 December 1995 and 6 February 1996, rotating the treatments among stations so that the same type of toxin was not present at a station for two consecutive days. For each day, I randomly determined the placement of the treated tray relative to the water tray.

Statistical methods

To test for the effect of treating sunflower seeds with tannic acid, oxalic acid, or water, I used ANOVA with food (tannin, oxalate, water) as the independent variable; day, site, station, and microhabitat (safe, risky) as the block variables; and the interaction between microhabitat and food. I used the logarithm of GUD as the dependent variable. Logarithmically transformed GUDs normalize the data by removing heteroscedasticity, and provide a more linear relationship between quitting harvest rates and GUDs (Kotler and Brown 1990).

Next, I attempted to separate the foraging costs (predation, missed opportunity, and metabolic) and examined the effect of increasing each on the marginal rate of substitution. Specifically, Eq. 5 predicts that the MRS of toxin-treated for water-treated seeds: (1) does not change with increases in predation, missed-opportunity, or metabolic costs. Equation 6 predicts that the MRS of digestibility reducers for water-soaked seeds: (2) increases with increased predation cost; (3) increases with increased missed-opportunity cost; and (4) decreases with increasing metabolic costs.

To test for the effect of predation risk (placing trays into riskier microhabitats) on the MRS, I used ANCOVA with the tannin or oxalate GUD (tested separately) as the dependent variable; microhabitat, day, and station as the group variables; and water GUD as the covariate. In addition, I included the interaction term between the covariate and microhabitat. If the MRS changes between microhabitats, for a fixed GUD in the water tray, the GUD in the treated tray should increase in the risky microhabitat relative to the safe microhabitat. This can be seen as either a higher slope (significant interaction between microhabitat, and the covariate) or higher intercept (significant effect of microhabitat) in the ANCOVA.

To test prediction 2, I used linear regression with the logarithm of the ratio of treated: water GUDs in the risky microhabitat, log([T.sub.r]/[W.sub.r]), as the dependent variable. Recall that the ratio of quitting harvest rates (represented through GUDs) is the MRS between two

patches. The ratio was logarithmically transformed to remove variance problems associated with creating a ratio of two random variables. It is difficult to separate the foraging costs into independent variables, because missed-opportunity costs are experienced over all trays at a station, whereas predation costs are more heavily experienced in the open (riskier) trays (hence, the use of the ANCOVA, which treats the water GUD as a covariate). As such, the missed-opportunity costs, independent of the added predation risk, can be estimated from the water GUD in the safe microhabitat ([W.sub.s]). As GUDs increase (overall), DRs should become relatively less preferred, with a predicted positive slope in the regression. Preference should n ot change for foods containing qualitative toxins.

To test prediction 3, I regressed the logarithm of the ratio of treated : water GUDs in the safe microhabitat, log ([T.sub.s]/[W.sub.s]), against a metabolic cost variable. I used the ratio of GUDs in the safe microhabitat as the dependent variable, rather than [T.sub.r]/[W.sub.r], because predation costs might have otherwise swamped the metabolic costs (Brown et al. 1994) and obscured the relationship. To estimate metabolic costs, I used a composite variable that incorporated temperature, wind velocity, and cloud cover. Temperature was entered directly in degrees Celsius. Wind velocity and cloud cover were scored as 1, 2, or 3 (wind: 1, light winds, [less than]3 on the Beaufort scale; 2 [greater than]3 on the Beaufort scale; cloud cover: 1, overcast; 2, partly cloudy; 3, sunny) and were added to the temperature score. This metric is admittedly a poor surrogate for the factors influencing metabolic costs, but it nonetheless provides an opportunity to explore the predicted relationships between metabolic cost and the marginal rate of substitution, [T.sub.s]/[W.sub.s]. As the metabolic cost increases, DRs should become relatively more preferred, with a predicted negative slope in the regression. Preference should not change for foods containing qualitative toxins.


Effect of adding chemical defenses

Food ([F.sub.2,144] = 34.33, P [less than] 0.001), day ([F.sub.7,144] = 11.97, P [less than] 0.001), and microhabitat ([F.sub.1,144] = 24.37) all significantly influenced GUDs. Water-treated seeds had the lowest GUD, followed by tannin- and oxalate-treated seeds (Fig. 1), although only the latter differed significantly from the former two (Fig. 1). GUDs were also significantly higher in the risky microhabitat than in the safe microhabitat (Fig. 1).

MSR under higher predation risk

Oxalates.--For the oxalate-treated seeds, the interaction between the covariate and microhabitat was non-significant ([F.sub.1,28] = 0.116, P [greater than] 0.70), and was subsequently dropped from the analysis. The covariate and day were both significant (Table 1a). More importantly, microhabitat had no influence on the MRS, the expected outcome for qualitative toxins.

Tannins.--For the tannin-treated seeds, the covariate was highly significant (Table 1b). In contrast to oxalatetreated seeds, the interaction between the covariate and microhabitat was significant (Table 1b). The slope of the regression equation was significantly higher for the risky microhabitat than the safe microhabitat, a result consistent with the prediction for digestibility reducers.

MSR under higher MOC and metabolic costs

Oxalates.--[T.sub.r]/[W.sub.r] was negatively, but not significantly, related to the missed-opportunity cost (MOC) indexed by [W.sub.s] (slope = -0.185; P = 0.07; Fig. 2a). [T.sub.s]/[W.sub.s] was not significantly related to the metabolic cost (slope = 0.036; P [greater than] 0.40; Fig. 2b).

Tannins.--[T.sub.r]/[W.sub.r] was positively related to the missed-opportunity cost (slope = 0.395; P [less than] 0.01; Fig. 3a). [T.sub.s]/[W.sub.s] was negatively related to the metabolic cost (slope = -0.047; P = 0.06; Fig. 3b).


Incorporating the consumption of foods containing plant defensive compounds into the framework of patch use theory significantly extends the paradigm of plant--animal interactions beyond the simple canons of diet choice models. The present study only begins to explore these ramifications and highlights the non-intuitive prediction that predation risk and plant defensive compounds interact to determine patterns of herbivory. Furthermore, this interaction is influence by the physiological mechanism whereby defensive compounds render food undesirable. Foods containing plant defenses that act as digestibility reducers (e.g., lignins and tannins) will be relatively less depleted under higher predation risk than will foods without defenses. In contrast, foods containing defensive toxins (e.g., alkaloids) that affect fitness directly, and not through diminished physiological uptake of energy, will be depleted without bias to predation risk or foraging costs. These differential effects on herbivory mediated through defensive compounds are based on the complementary relationship between safety from predators and energy consumption. Such a relationship has been noted before (Brown 1992, Brown et al. 1992, Morgan et al. 1997). F or example, Brown et al. (1992) demonstrated that patch exploitation decreased more in risky habitats than in safe habitats as landscapes were augmented with food in order to decrease the unit value of energy. The present study expands these results to show that such effects occur between patch types that differ in the value of their food items, and do not require changes at the landscape level.

The ecological consequences of plant defensive compounds on consumer behavior extend beyond their influence on diet selectivity (Belovsky and Schmitz 1994, Schmidt et al. 1998). Food resources are often distributed in depletable patches and, in turn, these patches are distributed across a landscape that differs in foraging costs such as predation risk. The theory developed herein predicts that patch exploitation for foods containing digestibility-reducing toxins will be biased (relative to undefended foods) toward safe habitats. The model's predictions have been couched in terms of quitting harvest rates and giving-up densities that provide an empirical means of determining the qualitative physiological effects of plant defensive compounds. Thus, the technique provides one potential method to explore both qualitatively and quantitatively the ecological influences of plant chemistry in the field.

The results obtained are consistent with those of previous studies on the effects of plant defenses and predation risk on squirrel foraging behavior. First, as in Schmidt et al. (1998), oxalates, but not tannins, significantly increased GUDs relative to control seeds (Fig. 1). Second, placing food patches several meters into the field increased squirrels' perceived predation risk, as indicated by the rise in GUDs (Brown et al. 1992, Thorson et al. 1998; Fig. 1).

The results are also consistent with the known biochemical functions of the two plant defenses. Oxalates are absorbed through the gut wall into the blood stream, where they bind to calcium and may compromise blood coagulation and cause renal damage (Blackwell 1990). Oxalates, therefore, function as toxins rather than as digestibility reducers. Consistent with the known physiological effects of oxalates, squirrels consumed oxalate-treated seeds at a constant MRS as expected for toxic plant defenses. Increased foraging costs did not influence the MRS of oxalate for water-treated seeds. Under higher missed-opportunity cost, the MRS, in fact, tended to decrease (Fig. 2a), which is inconsistent with either type of chemical defense. However, this is probably an artifact, because as overall GUDs increased with missed opportunity (the independent variable in Fig. 2a), GUDs in the risky habitat (the dependent variable in Fig. 2a) could not increase further than the initial amount of food. The effect of this ceiling i s that both water and oxalate GUDs converged as GUDs increased, so that their ratio approached 1 (or zero when logarithmically transformed; Fig. 2a).

Tannins, on the other hand, were consumed in a manner consistent with digestibility-reducing compounds. The value of consuming tannins was reduced in risky habitats relative to safe habitats and under higher missed-opportunity costs, but increased under higher metabolic costs. Although some studies suggest that tannins may function primarily as toxins (Bryant et al. 1991, 1992), others have demonstrated a reduction of energy assimilation and an absence of toxic effects for a variety of mammalian species (Schmitz et al. 1992, McArthur et al. 1993), including gray squirrels, Sciurus carolinensis (Chung-Maccoubrey et al. 1997). The present results argue for the latter interpretation of tannias as digestibility-reducing compounds.

The effects of plant defensive compounds on foraging behavior are complicated and require a consideration of not only the potential effects of putative defensive compounds, but also the environment to which the forager is exposed (Belovsky and Schmitz 1994). Tannins influence squirrel foraging behavior, but the effects may not be seen or realized unless the forager is in a sufficiently risky environment. As such, the contradictory effects of tannins observed in studies of squirrel foraging behavior (e.g., Schmidt et al. 1998) may be due to differences in methodology that reduce predation risk, or do not incorporate resource depletion.

One further note on methodology is in order. The predictions drawn from Eq. 6 are necessarily qualitative because of the difficulty of accurately measuring the parameters of the model. Moreover, the numerator and denominator of the right-hand side of Eq. 6 will be similar given that ([partial]e/[partial]R) is close to unity, or the metabolic cost is relatively weak. Thus, the relevance of its predictions to natural systems or the ease with which they can be demonstrated is perhaps contingent upon these necessary circumstances. For organisms in which the predation cost dominates the metabolic cost (e.g., desert granivores; Brown et al. 1994), or under less metabolically demanding conditions, the influence of defensive compounds on the MRS may not be detected in GUD measurements.

Finally, this study provides a further illustration of tri-trophic-level interactions. Although multiple-trophic-level interactions are becoming more commonplace in the literature (e.g., Spiller and Schoener 1990, Marquis and Whelan 1994), this study shows that trophic cascades can also be mediated through behavioral decisions of the consumer species, as influenced by higher trophic levels (Fryxell and Lundberg 1997, Schmitz et al. 1997). As such, they represent nonlethal interactions (Lima 1998) between predator and prey that culminate in different foraging patterns on plant species. In turn, if it is sufficient to influence overall plant fitness, disproportionate herbivory may change the species composition of plant communities (Huntly 1991, Nolet et al. 1994) by favoring species containing digestibility-reducing compounds. The world not only should be greener when predators limit or constrain herbivory (Hairston et al. 1960, Oksanen et al. 1981), but also should be harder to digest.


I would like to thank Hank Howe for spurring my initial interest in plant--animal interactions, and Joel Brown for many insightful comments and discussions on the subject of foraging theory. I am grateful to Christopher Dunn (research director) and The Morton Arboretum staff for facilitating this research.

(1.) E-mail:


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         Results of ANCOVA testing for the effect of microhabitat
          (predation risk) on the relationship between giving-up
        densities (GUD) on food treated with oxalate or tannin vs.
                     the control, water-treated food.
Variable                       df   MS   F ratio
a) Oxalate ([r.sup.2] = 0.580)
Water GUD                       1 16.243  4.350 [*]
Microhabitat                    1  8.083  2.164
Day                             7  9.448  2.530 [*]
Station                         1 12.653  3.388
Error                          29  3.734
b) Tannin ([r.sup.2] = 0.799)
Water GUD                       1 16.077 15.168 [***]
Microhabitat                    1  2.546  2.402
Day                             7  2.059  1.943
Station                         1  0.042  0.039
Microhabitat X water            1  4.692  4.426 [*]
Error                          28  1.060
Notes: In each analysis, water GUD was the covariate;
microhabitat, day, and station were the group variables.
The interaction term between microhabitat and the covariate
was retained in the model if significant (P [less than]
0.10). (*.)P [less than] 0.05;
(***.)P = 0.001.
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