Instantaneous intake rate of herbivores as function of forage quality and mass: Effects on facilitative and competitive interactions

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Abstract

The functional response as the link between the consumer and its resource is a central issue in herbivore–vegetation interactions. Vegetation often consists of low and high quality tissue due to nutritional or structural differences. It has been observed that the instantaneous intake rate of herbivores decreases with decreasing forage quality. However, so far variation in forage quality is not explicitly considered when modeling this instantaneous intake rate. In this paper, we derive a model for the instantaneous intake rate depending on forage quality, i.e., the proportion of high quality tissue in the vegetation. In the model, a downward deflection of the functional response curve is caused by a reduction of the maximum consumption rate at high proportions of low quality tissue. The model gives a mechanistic explanation for decreasing intake rate with decreasing forage quality. Compared to a conventional functional response model with constant maximum consumption rate, a herbivore–grass model with the forage quality-dependent functional response leads to discontinuous changes in the vegetation and herbivore density. The effects hinge on the positive feedback between herbivore density and the proportion of high quality forage. Our analyses show that this positive feedback can explain the maintenance of lawn grass where a high herbivore density can maintain high quality forage. The model results indicate that depending on the coefficients of trophic conversion from resource to consumer, co-existence, facilitation and competitive exclusion between differently sized herbivore species can emerge.

Introduction

The functional response as the link between the consumer and its resource is a central issue in herbivore–vegetation interactions. Many theoretical studies have explored the consequences of different shapes of the functional response on herbivores and their resources (Spalinger and Hobbs, 1992, Gross et al., 1993, Van de Koppel et al., 1996, Bos et al., 2004, Fortin, 2006). Also, much is known about the effects of forage quality on passage (Allen, 1996), patch selection (Wilmshurst et al., 1995, Coppedge and Shaw, 1998, Wallis DeVries et al., 1999, Van der Wal et al., 2000, Fortin, 2002, Person et al., 2003), herbivore community assembly (Illius and Gordon, 1992, Belovsky, 1997, Mysterud, 2000), and daily intake (Wilmshurst et al., 1995, Wilmshurst et al., 1999, Van der Wal et al., 1998). However, few studies have considered forage quality as an explicit parameter affecting the functional response (Fryxell, 1991, Benvenutti et al., 2006, Drescher et al., 2006).

At daily time scales, decreasing forage intake by herbivores from growing and maturing forage resources has been attributed to decreasing forage quality and consequent digestion constraints (Fryxell, 1991, Illius and Gordon, 1991, Hutchings and Gordon, 2001). For example, the high intake at intermediate forage mass is seen as the maximizing solution under ingestion and digestion constraints that can explain patch selection by red deer Cervus elaphus (Langvatn and Hanley, 1993, Wilmshurst et al., 1995). These studies do not, however, explicitly consider the effects of forage quality on the instantaneous intake rate, but mostly substitute forage mass for forage quality. Indeed, forage mass and forage quality can be related, but they are not always interchangeable, for example when considering the potentially negative effects of grazing on forage quality (Hamilton et al., 1973, Ayantunde et al., 1999, Orr et al., 2004, Animut et al., 2005). Since it has been observed that intake rate during short time spans can respond independently from forage mass to changing forage quality (Benvenutti et al., 2006, Drescher et al., 2006), the development of a model for the instantaneous intake rate as an explicit function of both forage quality and forage mass would be an important contribution to our understanding of the factors controlling intake behaviour.

As grass grows and matures, commonly its quality as forage for grazers decreases (Fryxell, 1991, Wilmshurst et al., 1995, Wilmshurst et al., 1999, Prins and Olff, 1998, Van der Wal et al., 1998, Hassall et al., 2001), which is mainly due to changes in the proportions of various plant parts and their nutrient contents. This can be illustrated by the decreasing proportion of leaves and the average nitrogen content in the plants (both indicating high forage quality) with increasing grass mass in a South African savanna (Fig. 1). Changes in forage quality can be the result of differential investment in stems or leaves due to competition for light when vegetation becomes more dense (Stobbs, 1973) or of selective grazing (Hamilton et al., 1973, Ayantunde et al., 1999, Orr et al., 2004, Animut et al., 2005). However, the mechanism by which decreasing forage quality affects the instantaneous intake rate at the scale of the grass sward has previously received little attention. A recent study on forage intake by large grazers demonstrated that the instantaneous intake rate depends both on the density and the proportion of high and low quality tissue in the vegetation, i.e., grass leaves and stems (Drescher et al., 2006, Fig. 2). The positive effect of density and proportion of leaves on bite rate and bite size leads to a higher instantaneous intake rate, while the effort to gather a fixed quantity of leaves depends on the density of stems in the sward. Thus, for a given total forage mass on offer, an increase in the proportion of low quality tissue depresses the instantaneous intake rate, which in turn leads to a decreased maximum consumption rate for that patch.

By formalizing the intake-depressing effect of increasing proportion of low quality forage in the grass sward, we derived a function for the herbivore instantaneous intake rate that explicitly depends on both forage quality and mass. Forage quality is defined here as the proportion of green leaf tissue, though nutritional differences are implicitly contained in this definition since green leaves tend to contain more available nutrients than stem tissue (Stobbs, 1973). We studied the effects of this functional response on large scale herbivore–grass dynamics using a simple model and compared it with a conventional functional response model. We included the forage quality-dependent functional response in a herbivore–grass model with two herbivore species sharing a common forage resource and used this model to investigate herbivore species interactions.

Section snippets

The conventional functional response

The instantaneous rate of consumption by grazing herbivores is often described as a monotonically saturating function (type II curve, Holling, 1959), denoted as:c(P)=cmPP+k1where c(P) is the instantaneous consumption rate as a function of grass density P, cm is the maximum per capita consumption rate, and k1 is the half saturation constant, i.e., the grass density where the consumption rate is half of its maximum (Table 1). In this formulation, limited processing capacity causes the

Non-linearity in herbivore dynamics: the effect of the maximum specific growth rate of low quality forage (rLm)

In the case of the conventional functional response (Eq. (1)), the rate of change in herbivore density is a unimodal curve where herbivore density is following logistic growth (Fig. 5a–c). Equilibria of the herbivore density are found where the rate of change in herbivore density meets the x-axis (dN/dt = 0). Increasing the maximum specific growth rate of low quality forage (rLm) causes the change of the stable equilibrium of herbivore density from lower to higher values of herbivore density

Discussion

We derived an equation for the herbivore instantaneous intake rate depending on forage quality, i.e., the proportion of high quality tissue. Different from previous studies (Fryxell, 1991, Van de Koppel et al., 1996, Bos et al., 2004) we did not a priori assume a depressed consumption rate due to some negative effect of increasing forage mass on forage quality, for example due to digestive constraints (Fryxell et al., 2004). Instead, we are explicit that the instantaneous intake rate depends on

Acknowledgments

We are grateful to Fred de Boer, Sip van Wieren, Johan van de Koppel, Norman Owen-Smith and John Fryxell for comments on an earlier version of this manuscript. We are indebted to John Wilmshurst for many valuable suggestions. MD was financially supported by the Netherlands Foundation for Tropical Research (WOTRO) residing under the Netherlands Organisation for Scientific Research (NWO).

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