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Plants produce chemicals as methods against animal herbivory. Such chemical defenses are classified into two major categories: (i) quantitative defenses with massive production of indigestible substances; and (ii) qualitative defenses with production of poisonous substances. A mathematical model was developed that identified factors that favored the evolution of quantitative defenses. Selecting an annual plant for simplicity, the allocation of photosynthetic production between growth substances and defense substances was considered. If the plant invests more in defense substances, it can protect itself more efficiently from herbivory but with a reduced growth rate. If it invests more in growth substances, the contrary holds. Using Pontoryagin's maximum principle, the following results were obtained: (i) the plant should conduct quantitative defenses when the growth rate (G), reflecting resource-availability, is low and the growth period (T) is long as well; (ii) if the plant invests in quantitative defenses, the optimal proportion of defense substances (χ*) should be higher asG is smaller, but it is independent ofT; and (iii) the value of χ* is not monotone for the effectiveness of defense substance (A), but has a maximum at an intermediate value ofA. Predictions of the model partly supported both Feeny's apparency theory, claiming that apparent plants or their parts for herbivores should quantitatively defend themselves, and Coley's resource-availability theory, claiming that plants with rich resources should invest in growth rather than defense.  相似文献   
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Macrophytes play a key role in stabilizing clear‐water conditions in shallow freshwater ecosystems. Their populations are maintained by a balance between plant grazing and plant growth. As a freshwater snail commonly found in shallow lakes, Radix swinhoei can affect the growth of submerged macrophytes by removing epiphyton from the surface of aquatic plants and by grazing directly on macrophyte organs. Thus, we conducted a long‐term (11‐month) experiment to explore the effects of snail density on macrophytes with distinctive structures in an outdoor clear‐water mesocosm system (with relatively low total nitrogen (TN, 0.66 ± 0.27 mg/L) and total phosphorus (TP, 36 ± 20 μg/L) and a phytoplankton chlorophyll a (Chla) range of 14.8 ± 4.9 μg/L) based on two different snail densities (low and high) and four macrophyte species treatments (Myriophyllum spicatum, Potamogeton wrightii, P. crispus, and P. oxyphyllus). In the high‐density treatment, snail biomass and abundance (36.5 ± 16.5 g/m2 and 169 ± 92 ind/m2, respectively) were approximately twice that observed in the low‐density treatment, resulting in lower total and aboveground biomass and ramet number in the macrophytes. In addition, plant height and plant volume inhabited (PVI) showed species‐specific responses to snail densities, that is, the height of P. oxyphyllus and PVI of M. spicatum were both higher under low‐density treatment. Thus, compared with low‐density treatment, the inhibitory effects of long‐term high snail density on macrophytes by direct feeding may be greater than the positive effects resulting from epiphyton clearance when under clear‐water conditions with low epiphyton biomass. Thus, under clear‐water conditions, the growth and community composition of submerged macrophytes could be potentially modified by the manual addition of invertebrates (i.e., snails) to lakes if the inhibitory effects from predatory fish are minor.  相似文献   
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