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The biomechanics of browsing and grazing¹

School of Biological Sciences, Monash University, Victoria 3800, Australia

Received for publication March 15, 2006. Accepted for publication July 21, 2006.

ABSTRACT

Terrestrial plant leaves are complex structures of composite materials. Resistance to fracture is achieved by a number of mechanisms, which operate at the molecular, cell, tissue, and structural levels. Leaves of dicots have different venation patterns and cell wall volume fractions from those of grasses, and consequently, they potentially resist fracture in different ways. Animals mechanically process plants in order to rupture the cell wall in preparation for enzymic hydrolysis, for which the imperative is to maximize new surface area and/or to expedite access to cell contents, ideally by promoting elastic fracture. The two different plant types are fed on by two different groups of organisms of very different sizes, digestive physiologies, mechanical processing abilities and properties, and nutritional requirements. Small insects can feed in or on parts of leaves, while larger mammals generally have to feed on the whole leaf. The scale of feeding also differs for the two groups of herbivores, but how this interacts with the scale of the mechanical properties of the leaf is not well understood. Plant leaves are attacked at all scales and probably can only produce generalized responses to specialized herbivores. In addition, the opportunities that these different scales of interactions open for the different herbivores remain unexplored.

Key Words: browsing • chewing • fracture biomechanics • grazing • leaf biomechanics • leaf toughness

An enduring paradox in ecology is the concept of the "green desert." In spite of our agricultural and domestic experiences with plant pests, it is manifest that plants are abundant and are not overwhelmed with herbivores, which attests to some real difficulty for animals in utilizing plants as a food resource. It is commonly assumed that plants resist herbivory because they are sufficiently protected by chemical toxins and antifeedants or that the plant tissue is not nourishing enough for herbivores. The mechanical factors inherent in plant design and construction that might limit or even effectively prevent herbivory have not received equivalent attention. It is now well known that plants in general are poor nutritional resources for animals, being relatively low in nitrogen and readily accessible energy. Animals that are obligate consumers of plants have very special adaptations. They generally have sophisticated digestive systems and complex mechanical processing mechanisms in the form of teeth or mandibles. This sophistication indicates that the physical structure of plant tissue is not easily managed.

Arguably one of the smallest differences in chemical structure, the difference between - and ß-glucose, has one of the most profound influences in biology. Linking energy-rich glucose molecules with -1,4 linkages produces readily mobilizable and digestible storage compounds such as starch and amylose. The molecules are flexible, and they have exposed OH groups, rendering them soluble and easily broken down into glucose monomers that are rapidly available for powering metabolic processes. On the other hand, linking the glucose molecules by ß-1,4 glycosidic bonds produces cellulose chains, a major component of plant cell walls. When the chains are bound together by hydrogen bonds, they form crystals, and combined with pectins, hemicelluloses, and lignin, they produce a very tough, stiff, and indigestible material (Wainwright et al., 1976 ). Cellulose contributes significantly to the bulk of the biomass on earth (Duchesne and Larson, 1989 ). Paradoxically, very few organisms can directly utilize this abundant energy source; these include bacteria, fungi, some nematodes, gastropods, and a very few specialized insects. No vertebrate can digest the cell wall unassisted; the familiar, large herbivorous mammals succeed in living off structural components of plant cells only by forming symbiotic relationships with bacteria or nematodes (Stevens and Hume, 1995 ). Some arthropods form similar relationships with bacteria to digest plant cell wall (Cazemier et al., 1997 ). Many herbivores only process plant tissue by some kind of mechanical disruption in order to access the relatively easily digestible cell contents and then void the cell wall. Access to contents requires chewing. Why more animals have not evolved cellulases but rely on microbial symbionts remains unclear. Whatever the reason, mechanical disruption is necessary for efficient digestion.

Combined with lignin, cellulose is extraordinarily resistant to processing into digestible units. The primary plant cell wall is composed mostly of hemicellulose, which is readily hydrolyzable, provided the molecules are not protected from digestive enzymes by lignin. As the cell ceases expansion and lays down secondary cell wall, the proportion of cellulose to hemicellulose almost reverses. The cell wall may become lignified through the S1 and S2 layers, providing further barriers to water and enzymes (Duchesne and Larson, 1989 ).

In time, bacteria by themselves can break down these materials, but animals do not have enough time. Animals such as mammals with high and constant metabolic rates are particularly constrained, especially the smaller mammals. Mammals are so constrained by their metabolic rate that the smallest herbivores that utilize bacteria to ferment cell wall as an energy source are c. 700 g in some marsupials and 35 g in rodents (Foley and Cork, 1992 ), 10 times larger than a locust and 1000 times larger than a leaf miner. Small mammals must expedite access to the cell contents for their own digestive enzymes or to the cell contents and cell wall for the bacterial enzymes by mechanically fracturing and disrupting the cell wall. Chewing achieves this, but chewing plant tissue requires special hardened masticatory or occlusal structures and only a few groups of animals have these.

The consequences are that the largest mammals are bulk feeders, ingesting whole leaves, many at a time. In large browsers, the mouthful may contain heavily lignified petioles and stems. In grazers, less lignified tissue may be ingested in a mouthful, but that will depend on whether the animal feeds on long or short grass. The smallest herbivorous mammals are forced to select more concentrated plant tissue relatively rich in cell contents with little dilution by the refractory cell wall.

Conversely, the smallest leaf miners (living within a leaf) ingest individual cells or even parts of cells. The plant mechanical defenses that are effective against either extreme of size might be expected to operate at very different scales and be of very different types. For the largest, thorns and spines deter access to the leaves. These are ineffective against the smallest, although hairs on the leaf surface can be a significant barrier (Hoffman and McEvoy, 1986 ). With respect to chewing, the resistance of a mouthful of leaves might operate at the structural, tissue, or cellular level depending on how the chewing parts interact with each other and the food. In a microscopic herbivore, resistance can operate only at the smaller scale.

Plant structural tissue, including stems, roots, and leaves, are composite materials. They are fundamentally extremely small repeating units of highly digestible cytosol, each in a package of relatively indigestible cell wall, with dimensions of tens of micrometers. At an even smaller scale, the cell wall itself is a composite at the nanometer scale. The structural organization and material properties at all levels of the system individually have powerful effects on the biomechanical properties of the whole. The proportion of cytosol to cell wall not only affects the fracture properties, but also has an important effect on the nutritional rewards gained by chewing the structure. A leaf cannot be compared to a cardboard box containing many cornflakes, rather it is a shrink-wrapped crate of many small boxes each containing just one cornflake. Large animals do not have the time or equipment to open each box. They crush and break the entire crate. Many of the boxes escape this initial process intact with their contents still sequestered. Small animals on the other hand have less bulk demands and a few cells' contents might contribute significantly to their daily nutritional needs. If the animal is small enough, it might be worth opening a few individual boxes and only consuming the contents.

The capacity to mechanically crush and fracture cells requires special tissues in animals, and these are associated with terrestrial life. Only a few animal phyla have successfully adapted to living on the surface of the earth, and these are predominantly the arthropods and vertebrates but also include the land snails. Vertebrates and invertebrates have adapted to the problems of exposure to gravity and dry conditions in fundamentally different ways. A stiff, light skeleton is required to move freely on the surface as distinct from living within a material, be that water, soil, or some other organism. Some kind of stiff (hard) skeleton is arguably essential for grinding and breaking up terrestrial plant matter. The hydrostatic skeleton found in most lower animals is not functional in this respect. Land snails that essentially have a hydrostatic skeleton have evolved chitinous mandibles and have usually retained the ancestral hardened radula. Arthropods have evolved a chitinous exoskeleton that has many similarities to lignified cellulose in that it is a sugar polymer, nominally N-acetyl-d-glucosamine molecules also linked by ß-1,4 glycosidic bonds (Wainwright et al., 1976 ). An exoskeleton provides protection for such small and therefore vulnerable animals. However, in order to grow, arthropods must molt and rebuild a slightly larger skeleton. This is both costly and risky because the animal is helpless while the new skeleton is hardening and becoming sufficiently stiff for the muscles to work against. On the other hand, every molt provides a new, unworn set of chewing mouthparts and, unlike mammals, there is evidence that this may allow rapid and qualitative shifts in diet (Wetterer, 1994 ; Lancaster et al., 2005 ).

Terrestrial vertebrates have an internal skeleton composed of mineralized tissues, which has the enormous advantage of being light compared to the relative bulk of an exoskeleton. Endoskeletons can grow continually but provide little or no protection. Partly as a result of the kind of skeleton and the breathing mechanism (which also differs fundamentally in the two groups), vertebrates grow into much larger organisms than terrestrial insects, usually orders of magnitude larger. The capacity to grow mineralized tissues that have been modified into effective chewing teeth gives the vertebrates the most effective hard-wearing set of chewing mouthparts known. Some vertebrates have evolved mechanisms such as having high tooth crowns or continually growing teeth that replace the crown as it is worn away to increase the tooth lifespan if the diet is particularly abrasive for at least part of the animal's life. These abilities are usually presumed to enable longer lifespans, although there is little evidence to actually confirm that.

Insect mandibles and vertebrate teeth are composed of very different materials with different properties (Wainwright et al., 1976 ) that operate at different scales. The chewing apparatus, whether made of a chitin–protein composite or enamel, must be stiffer and harder than the diet, or the apparatus itself will deform or even break rather than fracture the diet. It must also be tougher or else will wear too quickly, become ineffective, and reduce lifespan. These two properties of hardness and toughness in isotropic materials are usually mutually incompatible. However, composite materials can provide hardness and toughness together, but never more than that of any of the individual components (Atkins and Mai, 1985 ).

While plants are attacked by many other groups of organisms, this paper focuses on the two dominant but very different terrestrial herbivore groups—small to tiny insects with mouthparts having properties relatively similar to the plant cell wall and large vertebrates with extremely durable mouthparts. Insects can be small enough to live inside plant tissue and can usually select parts of plants, while vertebrates are often so large that they are forced to consume the entire organ, the leaf in most cases. We should expect that the impact of these herbivores on plants at a coarse scale is likely to be bimodal. While there are now a few studies identifying successful defense strategies against the smaller insects, it is not clear that there is any way to immediately deter the largest herbivores. Low nutrient levels, digestibility reducers, and tough materials that protect much of the cell contents may simply stimulate a large bulk feeder to consume more material to compensate for the low return. Their size provides processing power, and their hard teeth overcome virtually all plant tissues. Large animals are less likely to be limited by the mechanical properties at the organ level than by the abundance and distribution in space and time of the plant diet.

For the small insect, the content of the individual box is a valuable prize. However, the box itself is a relatively substantial barrier. For the much larger mammal, the contents of individual boxes are irrelevant, they must bulk process thousands of boxes at once, and in this case the biomechanical properties of the individual box may also be largely irrelevant. The animal probably has surplus power to fracture an individual cell or group of cells. The problem instead is that the teeth must meet more precisely to fracture as many of the individual boxes as possible. Anything that disturbs the accuracy of the tooth contacts will be deleterious. Wear, usually considered to be deleterious, might actually improve occlusal efficiency if it involves whetting the surfaces to produce a better fit (Palamara et al., 1984 ). However, mandibular wear for an insect, operating at such a different scale relative to the distribution and properties of the diet, is likely to be a very different matter.

This review focuses on the mechanics of chewing in the broader context of interacting with browse and grass, two dominant terrestrial plant forms with different structures. The broad differences between dicotyledonous browse (including tree, shrub, and forb leaves) and monocotyledonous grass leaves are manifest in any botany text. The predominant differences are in the pattern of venation, the degree of lignification, and possibly water content, all of which can affect fracture properties. In addition, browse and grass respond differently to being eaten, partly because browse generally has apical meristems and the grass has basal meristems (Wolfson and Tainton, 1999 ). With some notable exceptions, the focus of attention in most studies has been on one group of herbivores with one or two groups of plants. Rarely have studies involving mechanical properties compared contrasting plant types, more rarely among animal types, and extremely rarely across contrasting types of both plants and animals. Particular attention is given to the properties of plant structural material and the process of fracture engendered by quasistatic and dynamic processes (Atkins and Mai, 1985 ) of chewing mouthparts in the form of mammal teeth or insect mandibles and its consequences for browsers and grazers. Fruits and seeds are not discussed here, mostly because Lucas (2004) has given this detailed attention. I briefly consider the process of cropping or ingesting food, which has recently been extensively reviewed by Griffiths (2006) , because the amount of food ingested in a mouthful is relevant to the efficiency of post-acquisition processing.

BIOMATERIALS: PROPERTIES, COMPOSITION, AND SCALE

The properties of biomaterials are increasingly well known, partly as a result of the rapid development of fibrous composites that are now used in so many facets of our lives. As Jeronimidis and Atkins (1995) elegantly point out, knowing the properties of materials and how they interact allows us to tailor materials for specific purposes, more than by just randomly altering proportions of different materials in composite materials, such as the familiar fiberglass with different proportions of glass fibers in an epoxy matrix. In more sophisticated applications, it is precisely how the materials are laid down in alternating layers that contributes to specific properties.

Materials have many properties, as clearly described by Gordon (1968 , 1978 ), Wainwright et al. (1976) and more recently Vogel (2003) . More technical and definitive treatments are provided by Atkins and Mai (1985) , extended by French (1988) , Lucas and his colleagues (e.g., Lucas et al., 1991 ; Choong, 1996 ; Lucas 2004 ) and the insightful and eclectic work of Vincent (e.g., 1991 ). At one level, the principles are comparatively straightforward. Vincent (1992a – c ), Lucas (2004 and papers cited therein), and Sanson et al. (2001) provide relatively simple and repeatable methods that enable biologists with little experience to investigate relevant properties of biological materials. However, different approaches and techniques are advocated depending on the question being addressed although there is not always consensus on the best approach for a particular question. There are a variety of test types, including variations of punch, shearing or tearing tests, depending on whether the focus is on the properties of the leaf or how the herbivore processes the leaf and the method by which it does so. Even if we fully understood how mouth parts work in fracturing leaves it is not always clear whether the structural properties of the leaf (the product of the leaf material and its thickness) rather than simply the material properties of the leaf (properties of the leaf expressed per unit leaf thickness) are the most appropriate way of characterizing the fracture properties of leaves in a way that is relevant to understanding food acquisition and processing by the herbivore.

With respect to the kinds of tests available, Vincent (1992c) has expressed concerns about punch tests, which are commonly used in ecology because they are simple and easy to use and have the great advantage of being able to target small regions of a leaf. Resistance to a punch being driven through a leaf is a combination of shear and compressive strength, toughness, and the shape, size, and constitution of the leaf tissues. Some work is put into plastic deformation before fracture occurs, and this is difficult to discriminate from the intrinsic toughness or elastic work of fracture. It has limitations as a test to discriminate and identify specific biomechanical properties. However, it has its merits for an ecologist interested in a more global measure of leaf mechanical properties in relation to herbivory (Sanson et al., 2001 ). Careful consideration needs to be given to the question in hand, and different interests have led to the advocacy of different approaches.

The domain of materials science is a difficult and often bewildering field for biologists. Materials can be combined in different ways and proportions, and few are more complex than biological materials. The subtitle of Atkins and Mai's (1985) classic text "Elastic and Plastic Fracture" is "Metals, Polymers, Ceramics, Composites, Biological Materials." This list covers a wide range of materials, and they are not mutually exclusive. We commonly think of crystalline materials as inorganic, but cellulose chains are crystalline in the sense of regular, long range structures, and though different from metal crystals (Haslach and Armstrong, 2004 ), they have the properties of crystalline materials. Atkins and Mai (1985) characterize fibrous composites as having continuous or discontinuous filaments (or microfibrils of cellulose) in a matrix and laminated composites as having layers of various solids. They argue that biological materials are cellular, composite structures formed of fibrous or plate-like components. The components may be made of relatively few chemicals, often as polymers of amino acids (proteins) and sugars (polysaccharides). The variety of combinations is substantial, and there is a hierarchical structure from the basic macromolecules, microfibrils, fibrils, and structured fibers to the final "material." Daniel and Ishai (2006) analyzed the mechanics of composite materials at the different scales of micromechanics and macromechanics. Vogel (2003) divided the general subject of solid biomechanics into materials, structures, and structural systems and questioned whether bone is a structure or a composite material, recognizing there is no particular validity for either answer. The semantic aspect of the subject should not detract from appreciating the potential complexity of the interactions among the levels. The boundaries between the levels of organization are not clear cut (Spatz et al., 1999 ).

While there are relationships among the many material properties, resistance to fracture and stiffness are particularly important to this discussion. Toughness is explained as both a material and structural property and has been defined as the work done to produce a unit area of crack. Toughness is about the work or energy that must be put in to fracture a material. Tougher materials resist fracture better because, for various reasons, they require more energy to form a crack surface and have mechanisms that resist crack growth or propagation. Atkins and Mai (1985) describe the micromechanisms of fracture at the molecular level of polymers through the processes operating in fibrous or particulate composites, including fracture in the reinforcing fibers and the matrix, and finally to fracture in structures. Anything that stops or hinders a crack from growing contributes to toughness.

When a crack running through a material intercepts a strong element (e.g., a glass fiber or a cellulose chain), the energy necessary for the continued crack growth is dissipated by the atomic bonds of the strong element in the path of the crack. In addition, or separately, the crack may be deflected along the boundary between two surfaces and the energy progressively absorbed, slowing and eventually stopping the crack growth. Therefore, voids or small defects in the material can stop crack growth and paradoxically increase toughness. Interfaces between materials can do the same. In biological materials, as distinct from welded or riveted steel structures, presumably there is some form of bonding at the interfaces that must be broken for the crack to continue to grow. Another well-known example is the toughness contributed by fiber-pullout in composite materials (Atkins and Mai, 1985 ), and this is readily observed on the fracture surfaces of torn or chewed leaves. However, the energetic requirement for the formation of a new surface still applies. In addition, the cost of generating the surface or crack includes the cost of any physical deformation and disruption around the crack. For completely brittle elastic fracture, there is very little deformation around the crack, so little that the broken pieces can be fit back together almost perfectly. Permanent deformation around the crack means that some of the energy fed into the crack has been irreversibly consumed in plastic deformation, which prevents perfect reassembly of the broken pieces. This is plastic fracture (Atkins and Mai, 1985 ). Elastic fracture tends to produce cleaner fracture surfaces, and the damage is confined to the surface of the material. It follows that if organisms can promote brittle fracture less energy is required. However, the force required to complete fracture might be higher, and it is not known whether animals are limited by bite force or the capacity to provide the energy required when they feed on leaves.

This discussion implies that toughness manifests itself differently at different scales. Lucas (2004) gives a powerful analysis of this effect. He derives the intrinsic toughness of cell wall as 3.45 kJ · m^–2, but notes that this is a very low figure for a composite material. Natural wood is 10 times tougher than the estimate for cell wall, and the toughness of some composites manufactured by copying natural products can be 100 times as much. The reason for this apparently enhanced toughness relates to the energy absorbed as the wood cells begin to buckle and collapse and "elevates the toughness of woody tissues well above the cell wall toughness levels" (Lucas 2004 , p. 121). This statement illustrates that different mechanisms providing toughness, even though they are all energetic processes, operate at different levels within the structural hierarchy.

The scale of the structure has other implications. Flaws or deformations on the surface, that might initiate cracks, occur at a statistically higher rate in larger bodies, and this reduces the stress at which cracks are initiated. Atkins and Mai (1985) emphasize the importance of the cube/square law scaling in cracked bodies. This law produces an apparently anomalous situation, so that at a constant fracture toughness the stresses required to initiate a fracture become smaller as the size of the cracked body increases. The energy available to feed cracks increases as the cube of a characteristic length of a crack. However, the work required to overcome toughness depends on the area of the crack, which increases as the square of the length. Plastic fracture also does not scale geometrically. As a consequence, larger bodies have less plastic deformation than smaller bodies and thus tend to fracture in a more brittle fashion. The influence of scaling on fracture in biomaterials is poorly understood.

Minimizing energy expenditure to promote fracture may not be the only consideration. Some herbivores may need to increase the area available for enzyme degradation and may be prepared to pay the higher energetic cost to maximize the fractured surface area produced by chewing. In other words, it might be in their interests to promote plastic fracture, which increases toughness, because more damage is done. This is acceptable or tolerable only if the animal can supply and sustain the required forces. If the purpose is just to fracture the food into smaller particles, then promoting brittle elastic fracture is more desirable because less, if any, energy is "wasted" in plastically deforming the food before it fractures. The kind of digestive system the animal has and whether it is adapted to extracting cell content or cell wall components (or a combination of both) as a nutritional resource, will place different demands on the mechanical processing apparatus. Understanding tooth or mandible function in relation to the mechanical properties of the diet is only part of the story. Studies of tooth and mandible function often seem to be separated from the rest of the digestive system by the "oesophageal barrier" (Sanson, 1985 ). Few workers have crossed the barrier from either direction even though Fortelius (1990) considered that the digestive system is a major determinant of dental morphology. Exceptions are Hume's (1999) review of nutrition in marsupials, Owen-Smith's (1988 , 1999 ) treatment of southern African herbivores, and a few other specific studies (e.g., Freudenburger and Hume, 1992 ; Gross et al., 1996 ; Bezzobs and Sanson, 1997 ) that relate mastication to digestibility. The digestive system and the kinds or proportions of nutrients that the animal seeks to supply to its gut must influence the mechanical processing strategy employed. The process is highly dynamic in terms of the scale and rate of teeth and mandibles interacting with the food in the mouth. In the realm of nutritional ecology, a higher dynamic interaction overlays the oral process because the properties and abundance of the diet change in space and time. Long-lived animals, such as mammals, must adapt to seasonal changes in their diet or migrate. Short-lived animals, such as insects, have different imperatives and can specialize on parts of a plant that might exist for only a short time.

FRACTURE IN BIOMATERIALS

Biting and chewing are largely about fracture. Mammals bite plants for ingestion. Large carnivores chew their food to reduce it to a size that can be swallowed, while herbivorous mammals chew their food into much finer particles. Omnivorous mammals are an ill-defined group, but in general they appear to be limited to very low-fiber plant materials that fracture relatively easily; they are not considered in detail here. Specialized herbivores that consume high-fiber plant tissue primarily chew plants to gain access to the cytosol and/or to expose more surface area of the cell wall for more rapid enzymatic hydrolysis in the gut. Information on how and why materials fracture and on the measurement of properties associated with fracture in plants that might be useful for biologists are largely derived from the experience of engineers. The value of following well-established engineering principles has often been extolled. Conversely, understanding how natural biomaterials behave can give important insights to engineers and materials scientists and underpins the burgeoning field of biomimetics (Jeronimidis and Atkins, 1995), as discussed further by Milwich (2006) in this issue.

A source of great value in understanding the process of fracture, particularly in polymers, composites, and biological materials, is the classic text by Atkins and Mai (1985) . Fracture generates new surfaces. If the new surface projects all the way through the material, there is complete fracture and separation of the original particle into two or more particles. Resistance to fracture is derived from two processes: the resistance to crack initiation in the material and the resistance to the continued propagation of the crack through the material. In the fracture of a structure composed of different materials, cracks have to be repeatedly initiated when new unbroken materials are encountered as the crack grows through the structure. The maximum force recorded during a fracture test, commonly standardized for the area over which the force is applied, is sometimes reported as the force to fracture or the strength of the test piece. Strength is about the resistance to crack initiation or when the material changes from elastic deformation to plastic deformation. The first is the fracture stress and the last the yield strength (Atkins and Mai, 1985 ; Lucas, 2004 ) and are properties most easily related to materials. When a structure of different materials, such as a leaf, starts to break, parts of it are elastically deforming, parts have exceeded their yield strength, and parts are already fractured as cracks have initiated and started to grow. In this context, the strength of a structure is problematic. Strictly, it is not the force at which the material completely fractures. The force usually peaks well before the material finally fractures into separate pieces, particularly for structures made from composite materials. For these reasons, Lucas (2004) argues that strength as a property has been misunderstood, is rarely measured appropriately, and is potentially misleading at best. However, within the context of a standardized testing regime, the maximum force required to push a rod through a leaf is not without value. It is a truism that an animal must be able to generate the force needed to start and continue the fracture process to completion. The problem is not so much with the comparative data among different species but with the meaning of the individual measure.

Toughness, or the specific resistance to fracture, is the accumulated resistance to fracture divided by the increase in crack area and is a measure of the energy required to fracture the material. Because work is the product of force and distance, this is the work of fracture. Work can be measured only if the simultaneous force and displacement of that force is measured, which is why most simple penetrometers only measure force, not toughness. An increasing number of researchers in ecology are using simple penetrometers in a limited or even arguably inappropriate way. Techniques that do not take into account the area of the punch end or that incrementally load the punch by dropping weights into a container are examples that should be avoided. This is because either the results cannot be compared among studies or the time to load the punch can be so long that uncontrolled factors will affect the results.

Recently, some studies (Read and Sanson, 2003 ; Read et al., 2005 ) have reported that toughness and strength (defined as the maximum force to fracture standardized for the cross-sectional area of the punch, or the maximum resistance to the applied force [Wainwright et al., 1976 ]) are highly correlated across species, but often there are outliers in both directions. The correlation should not be a surprise because work that is measured in a test on a leaf is the summation of the instantaneous forces applied over the full displacement required to propagate cracks completely through the material. Thus, the average force measured in, for example, a cutting test with a blade, will exactly equal the specific work to fracture (work standardized for cross-sectional area of the fracture). Consequently, there is a temptation to conclude that it is adequate, and simpler, to measure the maximum force using a simple penetrometer. However, toughness and strength of leaves are not always correlated (Read and Sanson, 2003 ; Read et al., 2005 ), possibly because of differences in the way the structure is constituted. The work to fracture and the strength are likely to be less correlated when the "crack-stopping" or energy-absorbing properties of a structure are not uniformly distributed through the tissue. Simple penetrometers will miss this layer of complexity. In mechanics, yield strength and toughness are not simply related, but in fracture tests of leaves the yield strength is difficult if not impossible to identify.

The graininess of toughness in leaves will have stronger influences on small animals feeding within a leaf compared to animals consuming the whole leaf. This influence is easy to observe in the feeding patterns of insects of various guilds on leaves. One of the few studies to relate feeding location to the localized toughness of the leaf clearly showed this effect for caterpillars (Choong, 1996 ). A more complex pattern relating adaxial and abaxial toughness (measured by a penetrometer) and tissue distribution to feeding location and body size of two species of larvae feeding on oak leaves was demonstrated by Casher (1996) . The distribution in space and time of insect feeding guilds on a range of plant species has been related to mechanical, anatomical, and nutritional properties (Peeters, 2002a , b ; Peeters et al., in press ). There are many examples relating leaf toughness to feeding and ecology (Read and Stokes, 2006 , in this issue).

Even the larger folivorous ringtail possums (Pseudocheirus peregrinus) may respond to the heterogeneity of leaf structure. They consume whole leaves of less-tough species of eucalypts, but they avoid the veins of tougher eucalypt species that are completely consumed by the even larger koala (Phascolarctos cinereus) (J. Flynn and G. Sanson, Monash University, unpublished data). This pattern is unlikely to be explained by the distribution of chemical defenses in the leaf because no gradient in chemical defenses was detected (S. Caine, P. Heraud, and G. Sanson, Monash University, unpublished data).

The intrinsic strength or toughness of leaves is measured by straining the test piece very slowly, c. 0.1 mm · s^–1, using stiff machines. An advantage of very slow fracture tests is that the surface area generated by the fracture process is constrained and can be more accurately estimated by measuring the width and thickness of the leaf and deriving the product. There is insufficient energy supplied to the test piece to enable the crack to propagate ahead of the force being applied and allow it to deviate substantially along planes of less resistance, although crack path deviation into weak planes can occur (Atkins and Mai, 1985 ). In addition, a slow fracture test reduces inaccuracies due to elastic storage of strain energy in the bulk of the material that cannot be dissipated in the propagation of a crack before the material fails. Engineers tend to be interested in material properties in fracture tests and use this information to predict properties of larger bodies that include the material in their structure. Consequently, and for good reason, engineers divide the work of fracture by the surface area generated by the fracture, which standardizes the property for width and thickness of the piece. When dealing with isotropic materials such as metals, the surface area of the crack is by convention measured as the product of the width and thickness of the block of material tested. In reality, the fracture surface is probably never a perfectly clean plane except in the most brittle materials. It is easily demonstrated that a fracture surface can be easily twice the estimated surface or more. The issue of measuring the surface area produced by a fracture process is not trivial and has no resolution. The surface area measured will be sensitive to the resolution of the measurement, a classic fractal problem. We have no reason to believe that fracture surfaces are self-similar or fractal. Therefore, in most cases when the measured force or work is divided by the area of the new surface, the toughness or strength of the material is likely to be overestimated. Standardizing for all the dimensions of the leaf allows comparison of material properties between leaves. However, for an animal that has to bite or chew through the full thickness of the leaf, there is value in standardizing just for leaf width. Thicker leaves will require proportionately more energy to fracture. Both material properties and the structural properties that include thickness as a component may be relevant to herbivores.

Composite materials are combinations of materials each of which has characteristic properties. At the constituent level the scale of analysis is at the size of the reinforcing fiber diameter, particle size, or dimensions of the matrix interstices between the reinforcing components and has been referred to as micromechanics, the study of the interactions of the constituents (Daniel and Ishai, 2006 ). Micromechanics deals with deformation and stress in the constituents and local failure, which includes fiber failure, matrix failure, and interface/interphase failure. The last two modes are referred to as interfiber failure. Daniel and Ishai (2006) argue that micromechanics is particularly important in the study of failure mechanisms and strength, fracture toughness, and fatigue life, which may be less important in biological systems. These processes are strongly influenced by local characteristics that cannot be integrated or averaged. They further argue that micromechanics also allows for the prediction of average behavior at the laminar level as a function of the constituent properties and local conditions. However, presumably there are limitations on the predictions because of the former caveat. At the laminar level it is usually more expeditious to treat the material as homogeneous, recognizing it is an anisotropic material, and to use average properties in analysis, which is macromechanics (Daniel and Ishai, 2006 ). Failure criteria are expressed as average stresses and overall laminar strengths without reference to any particular failure mechanisms. They recommend this approach for analyzing the overall elastic or viscoelastic behavior of composite laminates and structures, and in practice this is what we do.

HOW TEETH AND MANDIBLES WORK

The conventional approaches just introduced are widely used for understanding plant fracture mechanics, but how applicable are they to understanding the mechanics of chewing in herbivores? Lucas (2004) presents a comprehensive treatment of tooth form and function in relation to the mechanics of diet, and there is little value in summarizing that work here. Lucas draws the important conclusion that the mechanical properties of foods, primarily toughness and hardness, are the major influence on tooth shape. This point is well supported for carnivores and for seed, fruit, and soft-leaf eaters. However, I suggest that for herbivores, particularly those consuming low nutrient, tough, fibrous foods in bulk, other factors are involved. The biomechanical properties of the materials constituting the structure, the hierarchy of the structure, and the requirement for continuous processing need to be fully integrated.

If the purpose of chewing is to produce a crack as cheaply as possible, then energy spent in producing plastic deformation is "wasted" and it is better to promote elastic fracture. However, for some herbivores plastic fracture that maximizes damage to the cell wall may be more important. Leaves are generally thinner than the thickness at which cracks will freely propagate, and for this reason an important, perhaps critical, factor that shapes teeth is the toughness of the diet (Lucas 2004 ). That is, the most efficient tooth shape is the one that continually propagates cracks, and bladed teeth best achieve this.

Foods with very low cell wall volumes have little crack resistance so that cracks, once initiated, will run more freely, and cusps on teeth may be the appropriate or adequate form to deliver the required stresses. However, foods like leaves, which have more crack-stopping mechanisms, require sharp blades (Lucas, 2004 ). Cutting across fibers that act as crack stoppers is necessary where the fibers run in the same direction, such as in grasses (Vogel, 2003 ). For these reasons, we should expect a different tooth form in animals adapted for feeding on grasses than those feeding on leaves with a reticulated pattern of veins.

A sharp blade controls the crack path and does not allow it to deviate. If the crack is allowed to deviate, it will absorb energy and allow the plant's toughening defenses to operate (Lucas, 2004 ). Therefore, sharpness of the functioning tooth blade does help suppress toughening mechanisms even though sharpness per se is not critical for crack propagation. However, because sharpness is usually a small-scale effect, at or close to the tip, it is not clear how sharpness is efficiently and locally applied when tough foods are processed in bulk. It implies that sharpness will only affect those particles directly engaged by the tip of the blade, but we do not know what happens to all the plant tissue trapped between opposing teeth in a browser or grazer. For the smaller herbivorous insects that attack single leaves, mandible sharpness may be a more important factor.

Young's modulus, which is a measure of the stiffness or rigidity of a material, also shapes the evolution of tooth form (Lucas, 2004 ). Young's modulus for a Hookean elastic material is simply the initial straight-line slope of a stress–strain curve when the material is loaded. Plant materials, unlike many if not most other biological materials, have relatively linear stress–strain curves, although heating affects the shape of the curve (Lucas, 2004 ). Teeth or mandibles must be stiffer than the food they are processing.

Principles of plant fracture can explain much about tooth or mandible form (Lucas, 2004 ), but some differences in tooth shape may depend on other factors, including food flow management and resistance to the varying regimes of wear. The evolution of grazers and grasses is a classic paradigm of evolutionary adaptation. The climate change of the Miocene brought about the expansion of grasslands and the rise of grazing mammals and almost certainly equivalent guilds of insects. A long-standing belief about this interaction is that grasses defend themselves with high silica and fiber levels in the cell walls and tolerate grazing via basal meristems. Grazing mammals evolved tooth characteristics to manage the increased abrasion and toughness of grasses compared to a typical browsing diet of soft dicotyledonous leaves. Features of the teeth such as high crowns, continuous growth, and elaborate enamel ridges are traditionally interpreted in this way. The evolution of browsing into grazing is seen as a major shift requiring special adaptations that are substantially related to the physical properties of the diet (Sanson, 1989 ). Generally, the transition from browser to grazer is rapid, and intermediate forms do not persist. Many mammals include both browse and grass in the diet, but when they do, these intermediate feeders generally have teeth adapted for grazing, suggesting that the requirements to chew grass are the critical function.

A ubiquitous factor in the evolution of mammalian herbivore molars is the incorporation of series of enamel ridges, which appear to act as cutting edges or blades and these are particularly well developed in teeth of grazers (Archer and Sanson, 2002 ). In the majority of herbivores that predominantly consume foliage, there is a substantial lateral excursion of the lower jaw across the upper jaw, which sequentially opposes the repeating enamel ridges on the upper and lower teeth during an occlusal stroke and disrupts the food trapped between them. This characteristic occlusal action has been described as the evolution of enhanced "shearing" compared to the "grinding" ancestral mode. Lucas (2004) questions the use of the term "shearing" because the ways teeth interact have little if anything to do with the development of true shear in the material being chewed. His discussion is in the context of modes of fracture, where Mode I (crack opening) is distinguished from Mode II (in plane shear) and Mode III (out of plane shear). Lucas is probably correct in regard to the development of true shear and that the geometry of fracture may not be important in selecting for tooth form. It is more than likely that, in a tangled mass of tissue orientated in all directions between a pair of occluding teeth, geometry is of even less relevance. However, we sometimes call scissor-like tools "shears." It is a term that, perhaps crudely to the purist, exemplifies two opposing blades that operate by passing across each other. This distinguishes the tool from one where the opposing parts approach each other more or less orthogonally and do not overlap. The cutting carnassial teeth of carnivores may be seen as analogues of shears operating in a vertical plane; there is no intent in that label to invoke shear as a mode of fracture. In this context, how can we most usefully characterize the action of the teeth of browsers and grazers? Most workers recognize that the terms crushing, grinding, and shearing are limited and perhaps limiting. Shearing applies to the teeth and need have no implication for the mode of fracture at a material level. In dropping the use of shearing for describing herbivore teeth, it would be unfortunate to lose sight of the fact that for some reason it appears to be advantageous for one tooth to pass over the other with substantial translation even though we do not have a good understanding of that process or why it has evolved so many times.

The enamel in a tooth of a browsing goat or a grazing sheep is harder and more resistant to wear than the supporting dentine. Consequently, the enamel is raised above the dentine, often forming extensive sinuous ridges. The ridges are variously termed lophs, cutting edges, blades, or shearing blades, but we have a very poor understanding of how these ridges function and whether their profiles are important. The ridges rarely exceed a few millimeters in depth, even in the teeth of the largest mammalian herbivores. Postmortem investigation of herbivore teeth of animals that have recently fed often indicate that the valleys between the ridges are packed with macerated plant material. It is not known how they function in this state, but most likely the packed food is squeezed down the valleys in pulses driven by repeated occlusal strokes as new food is forced into the front of each set of valleys. As the food is concentrated into ever narrower valleys, some of it is caught between opposing ridges and cut. If the ridges are reduced by natural or artificial wear (Gipps and Sanson, 1984 ; Lanyon and Sanson, 1986 ), they cease to function. Therefore, it is presumed that the ridges function by some process even when packed with food. It is possible that they only function when they are fully packed, but this requires further investigation.

Molars of large mammalian herbivores process bulk amounts of poor quality food. Numerous studies have noted the parallel venation and high cell wall volume promoting high toughness that is characteristic of grasses (Wright and Vincent, 1996 ). Such patterns are expected to require blades to cut across the fiber bundles of the veins (Vogel, 2003 ), and animals that consume grass have particularly well-developed blades. However, generation of fracture may not be the only factor influencing tooth shape. Organizing and directing food flow across the molar surface and onto a sequential set of cutting blades is likely to be important but has received little attention. The form of an herbivore tooth is probably not just a response to the toughness of the food, but likely includes flow paths and subtle arrangements of the enamel ridges that maximize the contacts in order to limit food escape.

We do not have a comparable fossil history of insects, but they too have evolved different mandibular adaptations, both among browsers (Bernays and Janzen, 1988 ) and between browsers and grazers, which have been broadly compared to mammalian teeth (Bernays, 1986 ). However, insects cannot easily produce cutting edges that translate across each other because of their exoskeletal structure. Every joint of an exoskeletal system has two hinge points constraining the adjacent segments into moving with respect to each other in a single plane, which is why a crab's leg requires so many joints and yet still does not have the full freedom of an endoskeletal limb. The significance of this limitation is that an insect's mandible is virtually constrained to moving in an arc around the two hinge points of each mandible. While there is a little flexibility in the hinge, there is little comparison with the translational movement that a mammal can generate, which further emphasizes the difference between insect herbivory and mammal herbivory.

Generally, only mammals have been able to develop jaw joints that allow considerable translation of one part over the other. Although many birds have highly kinetic skulls and jaws, they do not have teeth and are not a very meaningful exception. Some ornithopod dinosaurs developed mechanisms whereby some translation could occur by allowing the maxillary bones holding the upper teeth to move apart during a "chewing" stroke.

The apparent importance of translational movement in fracturing bulk plant material is illustrated by the giant panda (Ailuropoda melanoleuca). Pandas have a typical carnivore jaw joint and a large temporalis muscle, which tends to pull the lower jaw into the upper condyle. The typical cylindrical shape of the upper and lower condyles, which fit snugly into each other, prevents any forward or backward movement of the lower jaw. Many herbivores generate lateral movement of the teeth by rotating the mandible around one condyle, and the others move the whole mandible backward and forward. The only possibility for the panda is a full lateral movement of the jaw in both condyles at once, but even this movement is prevented by the interlocking canines. During chewing of bamboo leaves, pandas have virtually no lateral excursion (D. Andrew and G. Sanson, Monash University, unpublished data), meaning that the hypertrophied last molars are brought together in a simple and direct compressional mode (sensu lato). Vincent (1982) showed that grasses are very resistant to bruising, and this was confirmed by loading bamboo leaves under straight compression between surfaces that replicated panda molars (D. Andrew and G. Sanson, Monash University, unpublished data). We recorded slightly more damage as more leaves were stacked together and observed pandas collecting up to 20 to 30 leaves in a mouthful before chewing them. However, pandas have a peculiar method of rolling bunches of bamboo leaves into a cigar-like bunch and then crushing them. The very act of tightly rolling the leaves causes damage in the form of splitting of the leaves and some tearing. Crushing a rolled bunch of leaves substantially increases the cell rupture, but it is very inefficient compared to what might be expected from a horse or cow. This might easily explain the notoriously inefficient digestion of the panda (less than 20% of dry matter is digested; Dierenfeld et al., 1982 ).

There have been few studies examining the mechanical processes operating during ingestion in insects. There is some shearing generated during ingestion. The mandibles of herbivorous insects have a cutting edge, termed the "incisor region," and when two mandibles oppose each other one passes inside the other, analogous to a set of shears. The outer edge slides and scrapes past the inside edge of the other. Behind the incisal edge is a raised, roughened platform termed the "molar region," by analogy with mammalian teeth. It is presumed that some form of crushing takes place when the two mandibles, having sheared off a small particle, continue past each other and the molar regions meet. However, the action of the mandibular muscles pulling the whole mandible into the hinges, analogous to the panda, and the additional constraint of the interaction of the incisal regions probably completely prevents any translational grinding component between the molar regions, but this requires further investigation. Translation of molars during chewing seems to be important in mammals, but we do not know if it is important or how it works at the insect scale.

The effect of grinding or milling the food by machine into fine particles is an important indicator of the influence of plant structure on chewing capability. Studies using milled foods have usually been initiated in an attempt to separate the effect of plant tannins or other defense compounds from the potential toughness effect of the food. In cases where diets have been milled and presented to insects (Feeny, 1970 ; Clissold et al., 2006 ) or gastropod snails (Pennings and Paul, 1992 ) the animal performed better on the prepared food or showed no preference between milled foods when before they did for natural foods. The effect of milling the food on digestibility is well known in mammalian ruminant herbivores (e.g., Belyea et al., 1985 ). In this case, milling the food reduces digestibility because the fine particles flow through a size filter in the stomach and are not retained long enough for bacterial fermentation to be effective. This is a special case and highlights the paradoxical fact that for ruminants the teeth and at least the initial chewing process must not be too efficient. Bezzobs and Sanson (1997) were unable to maintain small herbivorous rodents on a high fiber diet; the animals lost weight. However, when the food was milled and rehydrated the animals still lost weight, but at a lower rate. On lower fiber diets, milling enabled the animals to maintain weight. Of even more significance was the finding that on an extremely low fiber diet the animals put on weight, but on the milled diet animals put on significantly more weight. Therefore, even for very low fiber diets, lower than the animal consistently encounters in the field or is apparently adapted to, plant structure affects the efficiency of chewing.

These results are empirical. We do not know how the teeth interact with a mouthful of plant tissue or how the necessary forces are applied to generate sufficient fracture of the kind to which the digestive system has adapted. A major challenge is to apply the principles of plant fracture to what happens in an animal's mouth as distinct from the processes observed under controlled mechanical test conditions.

IMPLICATIONS OF ANIMAL DIGESTIVE SYSTEMS AND INGESTIVE BEHAVIOR

Three basic digestive "strategies" occur in virtually all mammalian herbivores (Stevens and Hume, 1995 ). Because digestion in the gut operates on the particles delivered to the gut from the teeth, the kind of digestive system has the potential to place different demands on the teeth. The three digestive systems are the hindgut fermenters (HGFs) with relatively fast and variable gut passage rates and the foregut fermenters (FGFs), which are of two types: (1) the ruminants, with relatively controlled gut passage rates, which by regurgitating the food allow voluntary repetitive chewing of ingested food and (2) the non-ruminants, which can only chew the food at ingestion.

HGFs only have one opportunity to mechanically process the ingesta, and their cheek teeth are well developed with molarized premolars and relatively complex enamel patterns that must perform a vital function—the mechanical rupture of plant cells for maximum release of cell contents for digestion in the small intestine. In small HGFs, which include many rodents and folivorous marsupials, there is selective retention of small particles in a part of the gut, the caecum, where fermentation of the cell wall by bacteria takes place. There is no detectable reduction in particle size in the gut. Chewing produces the small particles and, as already noted, particle size distribution is affected by tooth wear (Lanyon and Sanson, 1986 ), which might be more of a problem in this group. The by-products of bacterial fermentation are in the form of volatile fatty acids, which are absorbed and contribute to the animal's daily energy needs. However, bacterial growth is affected by the availability of the cell contents, much of which has been removed in the small intestine. Periodically, the caecal contents, rich in nitrogenous bacteria, are expelled, and the animal may consume the pellet and digest the bacteria in the small intestine. Larger animals, such as the horse, rhinoceros, and elephant, do not selectively retain small particles, and the entire contents are exposed to more limited bacterial fermentation in the hindgut. Fecal particles are not ingested.

FGFs are fundamentally different in that their energy needs are derived largely from volatile fatty acids produced by bacterial fermentation of plant cell walls in the stomach. The bacteria obtain their nitrogen requirements from the plant cell contents, which are essentially unavailable to the host mammal. The animal obtains its nitrogen requirements by digestion of bacteria in the small intestine. Therefore, it might be predicted that ruminant teeth are adapted to damage cell wall as much as possible to maximize bacterial fermentation rather than simply to rupture cells. However, there is no evidence for this. The ruminant FGF may ingest its food with little initial mastication but considerable subsequent rumination. Ruminants have a filter between two chambers of their stomach, and only particles below a certain size can pass through the filter. This is often called a rate-limiting step (Stevens and Hume, 1995 ), and it places a fundamental control on the feeding behavior and diet selection in these animals. Particles must be reduced to the necessary size to pass through the filter by rumination chewing. There is no detectable size reduction by bacterial fermentation. Rumination is the principal process of particle size reduction, giving the animal considerable control over gut passage rate (Perez-Barberia and Gordon, 1998) and consequently when it can take its next meal. The other important consequence of the filter is that it requires the animal to be a selective feeder, searching for foods within a range of physical and nutritional properties. If the food of a ruminant is milled, it passes too rapidly through the filter and escapes the bacteria, reducing the digestibility of the food (Belyea et al., 1985 ), which suggests that chewing processes in ruminants are finely tuned to avoid reducing the material too much on ingestion. However, they must also be capable of grinding the food when necessary into small enough particles that can escape the stomach and allow another meal to be taken. They have the flexibility to respond to foods of different initial size (Gross et al., 1995 ).

The demands on the dentition of FGFs should be different than those on the HGFs, but it is not known whether these different demands are best achieved by the same kind of tooth morphology. Fortelius (1985) predicted that HGFs would have a dental morphology that more tightly reflects their dietary adaptations compared with FGFs. This prediction was based on the presumption that immersion of the food in the rumen fluids prior to rumination homogenizes the physical properties of the food. However, immersion of food in rumen fluid does not homogenize physical properties (D Archer and G. Sanson, Monash University, unpublished data), which is probably why diverse bovids were shown to have diverse tooth forms in detailed three-dimensional measures. For example, in a study of 26 species of southern African antelope, Archer and Sanson (2002) showed that the tooth form closely reflects Hofmann's (1968) classification of feeding types based on gut structure and function. Recent challenges to the physiological basis of Hofmann's conclusions, suggesting that the relationship between tooth form and gut structure relates to body size (Perez-Barberia and Gordon, 2001 ), however, do not negate this relationship. There appear to be complex relationships between plant structure and tooth and digestive system form and function that may underpin coevolution between plants and their herbivores.

Carbohydrate and nitrogen digestion in non-ruminant FGFs (e.g., macropodid kangaroos) has similarities to those of ruminants, yet they do not regurgitate the food and so, like HGFs, have only one opportunity for chewing the food. Roughly speaking, non-ruminant FGFs have the efficiency advantages of the FGFs with the potential flexibility of the HGFs. Like the ruminant FGFs, the dental morphology of the kangaroos reflects their dietary adaptations (Sanson, 1989 ), which also correlates closely with gut structure and function (Hume, 1999 ).

Body size places important constraints on the kinds of plants mammals can eat. Smaller mammals have higher mass-specific metabolic rates than large mammals, but have the same relative gut volume to extract their energy needs (Kleiber, 1961 ; Parra, 1978 ; McNab, 1987 ). Consequently, there is a general pattern of larger mammals consuming nutritionally poorer food than small mammals, which are forced to consume higher quality foods (Demment and van Soest, 1985 ; McNab, 1987 ; Norbury et al., 1989 ). Poorer quality foods generally equate with fiber level, a general measure of amounts of cell wall. The smallest mammals are thought to be too small to be able to utilize cell walls by fermentation. They must satisfy energetic requirements quickly and so have fast gut passage rates, too fast for more than superficial processing of food (Batzli and Cole, 1979 ). Therefore, the smallest mammals are limited to obtaining their nutrients from cell contents that have been liberated by chewing. In addition, because of gut scaling effects, the caecum is unable to supply sufficient fermentation products (Justice and Smith, 1992 ). These factors have led to general conclusions about the minimum body size below which mammals cannot be exclusively herbivorous (Parra, 1978 ; Demment and van Soest, 1985 ; Foley and Cork, 1992 ). They cannot live on plant matter rich in cell walls. However, some small rodents do digest plant fiber (Batzli and Cole, 1979 ; Hammond and Wunder, 1991 ) by mechanisms that increase the exposure time of the food to bacteria (Bjornhag, 1987 ; Foley and Hume, 1987 ). These mechanisms all rely on at least part of the diet being reduced to very small fragments by the teeth. However, in many of the studies on digestibility of plant diets in small mammals, the food has been pelleted, that is, the food has been processed by mechanical mills. Such an experimental approach discounts the effect of plant structure and its fracture properties (Bezzobs and Sanson, 1997 ).

The function of the cheek teeth (the premolars and molars) and their capacity to mechanically process the ingested diet may have an important but largely neglected impact on ingestive behavior. Spalinger et al. (1986) suggest that ruminants should select forages based in part on cell wall thickness and that handling time, in the form of rumination, may have a significant effect on forage selection and intake. Diet selection and intake rate in large grazing mammals have also been related to the width of the incisors, the front teeth that bite off the plant tissue before it is chewed and swallowed (Gordon and Illius, 1988 ; reviewed by Griffiths, 2006 ). The opportunity to make decisions about the next mouthful is related to the time taken to chew a mouthful of food (Gross et al., 1993 ).

Diet selection in grazing herbivores can lead to changes in sward composition as less preferred species increase in relative or even absolute abundance (Cingolani et al., 2005 ), a well known feature in southern African veld management (Tainton et al., 1999 ). Large herbivores have been shown to affect trophic guild structure in smaller herbivores (Fritz et al., 2002 ). It is likely that they also affect the microherbivores. The extensive herbivore feeding literature reveals complex interactions, from the behavioral choice of foods dispersed in space and time, to the cropping and chewing processes, and to digestion in the gut.

Studies of scaling of intake rate, feeding style, and dental and oral morphology (Shipley et al., 1994 ; Perez-Barberia and Gordon, 2001 ) make some important assumptions that have yet to be fully tested. One assumption is that molar and premolar size is appropriately measured as the product of the maximum length and maximum width. This kind of measure takes little or no account of the functional size of the teeth. It usually overestimates the surface area because teeth are rarely rectangular. This overestimate may not matter if the functional area scales directly with gross area, but when it has been explored there is a poor relationship (Archer and Sanson, 2001 ). A second assumption (Shipley et al., 1994 ) is that the rate at which food is broken down is proportional to the mass or volume of food trapped between the molars, following Fortelius (1985 , 1990 ). We know very little about how different volumes of food fracture when trapped between opposing teeth. If Lucas (2004) is correct and sharp blades must be continuously applied to leaves, then as mouthful volume increases by a cube function, the area of functioning tooth surface might scale by only a square function. It is more likely, as discussed later, that the functioning surface (the edge length of the blades) increases by some dimension between 2 and 3, depending on the resolution at which it is measured.

In all these herbivores the teeth play a critical role in the overall nutrition of the animals. When the teeth wear down and become dysfunctional, mammalian herbivores die, because tooth wear in mammalian herbivores appears to limit lifespan (Lanyon and Sanson, 1986 ; McArthur and Sanson, 1988 ; Kojola et al., 1998 ; Logan and Sanson, 2002c ).

There is little equivalent information for insects that relates the biomechanical properties of the diet to mechanical processing systems, digestive system morphology, feeding rate, and diet choice. The substantial literature on feeding in insects focuses more on digestive physiology without considering the associated mandibular morphology and function. Isely (1944) first noticed that graminivorous acridid grasshoppers have chisel-like incisors and well-developed molar regions on their mandibles that mechanically rupture cells to liberate the contents, and this morphology was associated with a neutral gut pH. On the other hand, some graminivores bite off pieces of plant tissue and swallow it without maceration, relying on a highly alkaline gut pH to leach nutrients out of the plant cells. Plant structure may affect insect herbivores. For example, the bundle sheath cells of C₄ grasses impede digestibility by grasshoppers (Caswell and Reed, 1976 ). Some lepidopterous larvae bite off and swallow small pieces of leaf, while others crush the excised fragment between the "molar" regions of the mandibles before swallowing. However, there was no difference between these two feeding forms in carbohydrate digestibility, but less protein was extracted in C₄ compared to C₃ grasses, even though the differences were small (Barbehenn and Bernays, 1992 ). These findings indicate that nutrients can be extracted from relatively undamaged plant fragments, possibly through plasmodesmata, after cell membranes are digested (Barbehenn, 1992 ), presumably by diffusion gradients. A survey of the mandibular morphology of 202 species of lepidopterous larvae indicated that 82% had only incisor regions, indicating that biting off whole particles and not crushing them is a common mode of feeding (Barbehenn, 1992 ). It is an important finding that cell contents can diffuse across neighboring cells and become available for the herbivore. However, there are likely to be limitations on the effective release of cell contents from the innermost cells imposed by the size of the particle and consequently by the length of the diffusion path to the outside of the fragment. In general, the bigger the insect the longer the residence time in the gut will be and more cell contents will be extracted. Large insects tend to have large mandibles and may bite off larger particles, potentially reducing the proportion of cells that can release their contents. As already noted in the plague locust, smaller nymphs have higher digestibilities than do larger nymphs for the same grass (Clissold et al., 2006 ). This was attributed to the small nymphs biting off smaller particles, resulting in a higher proportion of damaged cells and with a higher proportion of these cells within a few cells of the fragment boundary. More information about the difficulty of macerating C₄ grasses compared to C₃ grasses, as originally claimed by Caswell and Reed (1976) in the context of cell content extraction, would be valuable.

Patterns have emerged between investment in the feeding apparatus and toughness of the diet in a number of studies. However, the link to digestibility, which is the ultimate purpose of processing the diet, has only rarely been pursued. Bernays and Hamai (1987) measured the resistance to a 2-mm leaf blade from over 300 species of woody plant leaves, herbaceous dicots, and C₃ and C₄ grasses. The hardness/toughness value of the woody plants was only slightly lower than that of the C₄ grasses but twice that of the C₃ grasses, which was twice that of the herbaceous dicots. Mandible mass was correlated with head mass and muscle mass for grasshoppers feeding on grass, a mixture of grass and forbs and forbs only, with the animals on the tougher diets having larger feeding apparatus. In leaf-cutting ants, mature leaves become too tough to cut, although they remain palatable to the insect (Waller, 1982 ). Leaf-cutting ants fed tough leaves were larger than ants fed soft leaves (Tonhasca and Braganca, 2000 ). However, leaf toughness was not correlated with the preferences of flea beetles (Pettis et al., 2004 ).

TOOTH FUNCTION AND MECHANICAL DEFENSES AGAINST HERBIVORY

If different kinds of plants require animals that eat them to have different kinds of teeth or mandibles, then there is a basis for the evolution of mechanical defenses. There are analogies to the putative effect of tannins or other digestibility reducers in foliage that may act as plant defenses. The long recognized weakness of this type of defense is that it may not be an immediate deterrent and may even stimulate the herbivore to consume more tissue. Plant structure varies and will have different effects on different guilds of herbivores. The interactions that operate between insect and vertebrate herbivores and plants can have ecological consequences (Read and Stokes, 2006 ). However, being sure that mechanical factors act as a defense rather than as a correlate of other defenses or nutrient levels is a major problem. It is important that we understand how to measure these variables in order to be able to investigate the issue.

In response to Gordon's (1968) comment that, in an engineering material, the worst sin is not lack of strength or stiffness, but toughness, Atkins and Mai (1985) argued that the history of engineering is almost the history of preventing cracks spreading. Ashby (1999) suggested that to prevent cracks spreading and leading to failure, some designs are load-limited, some are energy-limited, and others are deflection-limited. Engineers seek to prevent fracture by preventing surfaces from forming. Herbivorous animals seek to generate and possibly even maximize surfaces by promoting fracture; to do this they must overcome toughness. The corollary of this is that, because the components of work are force and displacement, herbivores can either be force-limited or displacement-limited (Lucas et al., 2000 ; Lucas, 2004 ). Displacement-limited defense means that if the herbivore cannot provide the amount of displacement required, the material would only stretch but not break. Alternatively, making a structure fail at a large displacement limits the amount of detachment achieved in a given time (Lucas et al., 2000 ). Introducing time is germane to animals that spend a considerable portion of their time feeding. For an old koala chewing 36 000 times a day (Logan and Sanson, 2002c ), any slight increase in the time for the chewing stroke compounds the cost to unsupportable levels. Molars of mammalian herbivores generally engage with high lateral translation, potentially providing substantial displacement. In insects, displacement is achieved only at the incisal region of the mandibles, not on the molar region. If the requirement for displacement can be reduced by increasing the load rate, the plant's toughness defense is subverted. Displacement limitation may be more of a problem for smaller herbivores with their teeth or mandibles moving around a fulcrum on shorter arcs. Force-limited defenses operate when an animal cannot provide sufficient stress to initiate a crack, and successful force-limited defense is achieved by high hardness, not surprisingly found in localized external tissues like spines, prickles, thorns, and even hairs (Lucas et al., 2000 ). Leaves tend to be pliant and not hard, and it follows that for tough but soft leaves, displacement-limited defense becomes more significant. However, leaves vary in their hardness and toughness and different animal responses might be expected.

Lucas (2004) has produced a comprehensive analysis of fracture mechanics and how vertebrate teeth work. It is an excellent basis for investigating the consequences that having to chew makes on an animal's life, dietary choices, and the potential impact on the plants it eats. In turn we can start to investigate what factors might be selected in plants to make them more resistant to chewing, if that is an advantage overall. We must be mindful that a plant's investment in being difficult to chew may incur a number of trade-offs, including growth (Read and Stokes, 2006 ), that might overwhelm the advantages of protection. The chances of a plant being eaten are not often examined. Plants may not be able to afford insurance against catastrophic but rare events. It is an actuarial decision. Investment in defense against low-level but ubiquitous insect attack may be necessary. However, there may be no point in investing against a swarm of insects that can defoliate the trees in the swarm's path or an elephant that might destroy the whole tree to get at some leaves. The cost may be so high that in economic terms it is worth taking the risk of not being noticed by the elephant or the insect swarm, because that is what the competitors might be doing. Investing in defense might mean such a slow growth rate that the plant is outcompeted for light and nutrients before the elephant even appears, if it ever does. Plants probably have access to a wealth of factors that provide toughness at the material, structural, and system levels to provide a tuned defense. The problem for plants is that they are attacked by guilds of specialists at all the different scales of their defenses.

TOOTH FUNCTION, VISCOELASTICITY, AND CHEWING RATE

If the need to overcome toughness is a primary influence on the form of the tooth, and by implication insect mandibles, are there other ways not specifically related to stress or strain limitations that might reduce toughness? One possible way is by increasing the strain rate, that is, the rate at which the load is applied. Most biological materials are viscoelastic, and leaves may have high viscoelasticity (Fukuhara et al., 2005 ), which means they are susceptible to the rate at which the strain or displacement is applied. Generally, the mechanical behavior of polymers, e.g., biological macromolecules, is time-dependent. The magnitude of the stress and the time during which it is applied, i.e., the rate at which the stress is applied, as well as the temperature, are important (Haslach and Armstrong, 2004 ). Ductile stress–strain curves transform to brittle curves at decreasing temperature or increasing strain rate for most materials, and the consequence of increasing brittleness is generally to increase strength and decrease toughness (Atkins and Mai, 1985 ). These interactions are complex and elastic, viscoelastic and plastic deformations can be distinguished under different loading conditions, blurring the distinction between materials and structures (Spatz et al., 1999 ). The viscoelastic properties of animal and plant cells have received considerable attention, including the time-dependence effects associated with plant cell expansion (Cosgrove, 1997 ) and other examples given by Lucas (2004) . The anatomy and static and dynamic fracture properties in leaves of New Zealand flax were examined by King and Vincent (1996) who concluded that rate effects are important in understanding grass leaf fracture during grazing, while noting that the interactions are complex. However, dynamic fracture at strain rates and temperatures found in biological systems, particularly during chewing, has received little attention.

During the occlusal stroke of a typical mammalian herbivore tooth, the lower tooth passes across the upper, and the ridges act as opposing horizontal blades with a sequence of successive contacts. The angle between the blades where they meet can be determined, and as the teeth cross each other, the angles continually change but can also be measured (G. Sanson, Monash University, unpublished data). This analysis is an extension of an insightful but overlooked occlusal model by Rensberger (1973) . It was expected that the orientation of the blades would optimize the mechanical advantage of the contact, but in the African buffalo only about 9% of the enamel ridge was oriented in such a way as to give good mechanical advantage. Upon further analysis, it was concluded that the opposing ridges were arranged in such a way that the velocity of the cutting point was amplified, arguably at the expense of mechanical advantage. It also appears that low angle contacts tend to limit the escape of food particles from converging blades. When scissors or shearing blades close at high approach angles, they tend to push the engaged material ahead of the point where the blades contact. At low angles, friction may be sufficient to prevent the food being pushed out ahead of the cutting point. I suggest that an advantage of increasing the velocity of the contact is to increase the strain rate and therefore brittleness. In the context of a tooth as complex as a buffalo tooth, this will be a local and transient effect where the significance is yet to be fully explored. Possible consequences of increasing brittleness are to reduce the size of the fracture zone and to reduce the tendency of the crack to deviate along paths of least resistance, which would increase the toughness of the food at that point. According to this discussion, allowing deviation of the crack surface increases toughness; thus, more energy must be supplied to propagate the crack. Very little is known about viscoelastic responses of plants in the dynamically loaded conditions of chewing.

G. Sanson and S. Kerr (Monash University, unpublished data) have measured work of fracture in relation to cutting speed in two species of grasses (Pennisetum clandestinum Hochst. ex Chiov. and Arundo donax L.). Pennisetum is a palatable grass, while Arundo is an unpalatable reed. Ten leaves of each species were cut at 0.01, 1, 5, 10, 20, 40, 70, and 100 mm · s^–1 with a guillotine, following the protocol of Sanson et al. (2001) . For Pennisetum, there was a rise in toughness, as absolute work (J), and then a decline with increased velocity of the cutting blade over this range (Fig. 1). There was a 30% difference between the minimum toughness at 0.01 mm · s^–1 to the maximum at 20 mm · s^–1. A slightly different pattern was observed in Arundo, where the maximum work was obtained at 1 mm · s^–1, and there was only a 10% difference between the minimum and maximum toughness (Fig. 1). The maximum velocity of any cutting edge found between buffalo teeth was estimated at 110 mm · s^–1 and the minimum at 70 mm · s^–1, which is within the range of velocities tested. These preliminary results indicate that strain or chewing rate may have biomechanical consequences that have the potential to influence tooth evolution and might also affect diet selection in a way not considered before because of the difference in processing effects.

View larger version (8K): [in this window] [in a new window]   Fig. 1. Toughness, measured as work to shear (J), as a function of cutting blade velocity (mm · s–1) for Pennisetum clandestinum (closed circles) and Arundo donax (open circles)

It is known that as an animal's teeth wear they change shape, but do they become more or less effective at fracturing and processing plant food? When teeth wear, they maintain contact with their opposing counterparts by over-erupting or by continual growth. We know that tooth wear, which subtly changes tooth shape, can reduce digestibility in ringtail possums (Pseudocheirus peregrinus) (Gipps and Sanson, 1984 ). In koalas (Phascolarctos cinereus), tooth wear increases food particle size in the gut (Lanyon and Sanson, 1986 ), the number of chews per leaf, and the feeding time (Logan and Sanson, 2002c ). The consequences for activity patterns (Logan and Sanson, 2002a ) and social behavior (Logan and Sanson, 2002b ) can be profound, with older koalas being forced to feed into the day and abandoning attempts to maintain home ranges and social status. As a koala's teeth wear, the modal particle size increases and particle size is critical for the selective retention of fine particles in the caecum where fermentative food breakdown by bacteria takes place (Cork and Sanson, 1991 ). Therefore, even though older koalas (with more worn teeth) chew each leaf more, chew more leaves, and spend more time feeding, they cannot compensate for the loss of tooth efficiency, and the particle size distribution in the gut continues to rise. The koala's behavioral response only partially compensates for the loss of tooth efficiency and only delays the decline in the animal's capacity to feed, and eventually they die.

Less work of this kind appears to have been undertaken on herbivorous insects, but there are significant studies that suggest similar patterns may operate. Tough leaves wear the mandibles of leaf beetles more than tender leaves, and beetles with worn jaws consume leaves more slowly (Raupp, 1985 ). An interesting compensation for feeding on tougher foods was observed in caterpillars; later instars fed on "hard" diets produced larger head masses, though the body mass remained the same (Bernays, 1986 ). Saturniid and sphingid caterpillars that feed respectively on tough leaves and soft leaves have different mandible shapes and relative head masses (Bernays and Janzen, 1988 ). This induced response suggests that, through molting, insects can respond to changes in their diet that are perhaps less easily accommodated by mammals. Clissold et al. (2006) argue that smaller plague locust nymphs have higher digestibility on their native grass diet than older nymphs because they have smaller mandibles. Each bite by smaller mandibles releases relatively more cell contents per bite than bites of larger nymphs. On the other hand, the very smallest nymphs either do not have sufficient gape to effectively attack the grass blade or cannot generate enough force. There are numerous studies of the effect of plant toughness on insect feeding (Read and Stokes, 2006 ).

The other conspicuous feature of molars adapted for grazing abrasive grasses is the high crown, termed hypsodonty. In some herbivores the tooth is continually growing for at least part of the animal's life, replacing enamel that is worn away. The classic example is the evolution of the horse dentition in relation to the expanding grasslands of the Miocene in North America. The common wombat (Vombatus ursinus) has molars that continually grow throughout life at 0.1 mm per day in captive animals fed lucerne hay, but can double their growth rate if abrasives are added to the diet (G. Sanson, unpublished data). These responses are due to the abrasives in or on the diet wearing the teeth. Abrasives are derived from two sources, exogenous grit and silica phytoliths in the grass tissue. Baker et al. (1959) measured the hardness of oat phytoliths using a microhardness indenter and reported that they are harder than sheep teeth. However, Sanson et al. (2006) measured silica phytolith hardness in four species of cosmopolitan grasses with a nanoindenter and found that no phytoliths were harder than any reported value for mammalian tooth enamel. Endogenous silica may not be an important abrasive for mammals, but the crystalline silica that settles on plant surfaces is harder than tooth enamel and does scratch it. The distribution and effect of dust on grasses and other plants accessible to herbivores in dusty environments needs to be examined.

Lucas (2004) suggested that sensitive feedback systems in tooth-supporting tissues can detect the presence of particles during chewing and reduce occlusal loads to prevent excessive damage. Mammalian teeth are composite tissues that must accommodate high stresses (Wainwright et al., 1976 ; Vincent, 1991 ; Vogel, 2003 ; Lucas, 2004 ). The enamel prisms can be arranged in many ways, producing characteristic Hunter–Schreger bands. The way the prisms are arranged affects their biomechanical properties and wear resistance, and these orientations have been related to diet and chewing stress (von Koenigswald et al., 1987 ; Rensberger, 1992 ; Rensberger and Pfretzschner, 1992 ), suggesting complex co-evolutionary interactions between plants and their herbivores.

However, endogenous plant silica is harder than insect mandibles, and this is another example of the differences between insect and mammal herbivores in their interactions with plants. Mandible wear has been recorded in some African grasshoppers and, while wear might affect feeding rate, experimental tests and field observations suggested that it was unlikely to be a significant factor causing mortality (Chapman, 1964 ). This finding is hard to explain, especially given the long adult life of some locusts, and deserves further investigation. Similar experiments with Australian plague locusts indicated that high levels of induced wear in larval instars affected feeding performance and induced earlier and extra molts (D. Hochuli, P. Melna and G. Sanson, Monash University, unpublished data). Insect mandibles can include zinc or manganese to harden the cutting edge of the mandible, but not that of the trailing faces (Chapman, 1995 ). In addition, hardness increases three-fold in leaf-cutting ants as the adults age and is correlated with zinc content (Schofield et al., 2002 ). However, the hardness is still significantly lower than mammal dentine or enamel.

CONCLUSION

Composite plant tissues fracture in different ways depending on the proportion and orientation of the constituents and the way they are assembled into structures such as leaves. Fracture occurs differently at micro- and macromechanical scales. Paradoxically, it is the largest herbivores, that in general metabolize the cellulose chains using microbial symbionts, which are likely to benefit from disrupting the cellulose chains by chewing. To achieve this, the teeth must operate very precisely at a microscale. However, large herbivore teeth also tend to operate at the macroscale because they manage whole leaves or even multiple leaves. The smallest herbivores, the insects, operate at an intermediate to lower end of the macroscale because they consume at the cell and tissue level. This implies that plants must defend at all scales. The implications of these observations for the evolution of plant structural defenses and the adaptations of animals that feed on plants are yet to be fully explored.

FOOTNOTES

¹

² Author for correspondence (gordon.sanson{at}sci.monash.edu.au )

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