teristic variation of these fluxes with temperature (Fig. 9.9, top). Both increase with temperature, until at some critical temperature they level out and peak. At temperatures warmer than the critical, the rates drop rather abruptly. This pattern has a straightforward explanation. In most chemical reactions, whether they occur in cells or in a beaker, rates of reaction roughly double with every 10oC increase of temperature. This is what drives the increase of both CO2 consumption and CO2 production over the cooler range of leaf temperatures. Most chemical reactions in cells, however, are mediated by protein catalysts called enzymes. Enzymes are rather delicate machines, and high temperature may disrupt their functioning or the ways they interact with other enzymes. A degradation of their function is the result.
In many leaves, the consumption and production rates for CO2 respond differently to temperature: CO2 production rates commonly peak at higher leaf temperatures than do the rates of gross photosynthesis. One interesting consequence of this mismatch is that the leaf's maximum net photosynthesis occurs at a cooler leaf temperature than the temperature of maximum gross photosynthesis. We shall call this the optimum temperature for photosynthesis, or T.
Corporate decisions on costs and allocations are subject to the discipline of the market. If the corporation does not make wise decisions, its competitive strength will diminish, and it will be in danger of making little profit or going into bankruptcy. Natural selection provides a similar disciplinary environment; poor allocation "decisions" trees make with respect to their leaves are penalized with reduced fitness, perhaps even extinction. One would therefore expect to see a convergence between leaves' optimum temperatures for photosynthesis and the temperatures they commonly experience. In other words, natural selection should force plants toward the rule:
where Tleaf represents the average leaf temperature in a particular environment. The basic evolutionary prob lem for plants, then, is to somehow match these two temperatures. There are essentially two ways plants can do this.
One way is for Mohammed to go to the mountain: push the leaf's T$ toward Tleaf. This involves modifying the complement of enzymes that control metabolism and photosynthesis in the leaf so that they function best at the temperature leaves are most likely to experience. In fact, many plants do just this: leaves of desert plants, for example, tend to have higher optimum temperatures for photosynthesis than do arctic plants. No surprises there, since deserts are commonly hot places. Plants also must cope with more acute variations of temperature: even deserts can be cold during some parts of the year. When faced with these occasional extremes, plants sometimes maintain optimum photosynthesis by keeping multiple sets of enzymes for photosynthesis and metabolism (called isoenzymes, or simply isozymes), each set to operate at different temperatures. If temperatures in the desert get very cold, for example, the plant could shut down its complement of "hot environment" isoenzymes (that is, those that result in a high T$) and activate its "cold environment" isoenzymes (the ones that result in a lower T$).
Such metabolic adaptations are not without cost. Having a strictly determined T leaves the plant at the mercy of a fickle and changeable environment. The benefits that accrue to extending T with isozymes also is limited, because each set of isozymes adds to the plant's genetic "overhead." Each set of isoenzymes requires the cell to maintain multiple sets of genes for the same reactions, which means more energy invested in overhead. Nevertheless, the fact that many plants do tune their biochemistry to prevailing temperature indicates this has been a good strategy for them.
Many plants do the opposite, though. Forcing Tleaf toward T$, they move the mountain to Mohammed. This seems odd, because it is difficult to see how a leaf's temperature could be anything but what the environment imposes on it. Nevertheless, the physical environment is a rich mosaic of various kinds of energy, and leaves can actually play these different sources of energy against one another to attain some degree of control over their temperatures. Leaves most commonly do this through variation in their shape. So, if an environment is too cold for its leaves to function efficiently, a tree could elevate its leaf temperatures to some extent simply by altering their shapes.
To understand how plants do this, and how leaf galls might disrupt it, we must understand how heat flows between a leaf and its surroundings. The temperature of any object, leaves included, is a measure of the quantity of thermal energy, or heat, contained in it. Heat content is, in turn, determined by the balance between the heat coming in (qin, expressed in watts per square meter) and the heat going out (qout, also in W m-2). Usually, there will be some temperature at which these flows of heat balance, or come into equilibrium, so that the net flux of heat is zero:
We can estimate the temperature of a leaf at equilibrium if we can account for all the flows of heat into and out of the leaf and their dependence upon leaf temperature. For most leaves, these flows fall into three categories. First, solar radiation can warm a leaf that absorbs light. Second, evaporation can remove heat from the leaf. Third, wind blowing past the leaf can either warm the leaf or cool it, depending upon whether the air is warmer or cooler.
All these fluxes of heat combine into the leaf's heat balance equation. For a leaf at steady temperature, all the inflows and outflows of heat cancel and add to zero (equation 9.2). So, for a leaf exchanging heat with the environment by radiation (qr), evaporation (qe), and convection (qc), the heat balance equation is:
where each quantity q represents a flux rate of heat.
Each of these flux rates depends upon the leaf temperature. Convective heat exchange, for example, is a simple function of the difference in temperature between the leaf and air. Therefore, it is, in principle, possible to rewrite each of the heat flows as a function of leaf temperature. Doing so should, again in principle, make it possible to solve for the temperature at which the heat flows all add up to zero. This will be the temperature of the leaf in a particular environmental regime of sunlight, humidity, and air temperature.
The rub lies, as it so often does, in those deceptively simple words "in principle." In fact, the equations for each of the heat fluxes can be hellishly complicated. For example, radiative heat flux includes the leaf's temperature all right, but it must be the absolute temperature (in kelvins) raised to the fourth power. The equation also must include terms for orientation of the leaf with respect to the sun, position of the sun in the sky, scattering of sunlight by the atmosphere and particulate debris, and proximity and temperatures of other sources of radiation heat exchange, like reflection from nearby leaves or from the ground. The equation for evaporative heat flux is simpler, but scarcely so: evaporative heat flux is influenced by the vapor pressure of the leaf's water, which is dependent upon leaf temperature, and also by the humidity and the water's heat of vaporization, themselves complex functions of temperature. So one can write the heat balance equation all right, but it will very likely occupy the better part of a page.
So, as my daughter would have put it when she was ten, do you have to be "like, really smart" to be able to get a leaf temperature out of the heat balance equation? If you want an accurate temperature, the answer to this question, I am afraid, is "yes." Fortunately, the equation can be made much simpler and still yield reasonable approximations for a leaf's temperature. The first step is to realize that part of the solution is hard (radiation and evaporation), and part of it is simple (convection). We then try to do the simple bit as best as we can and fall back on approximating the hard bits.
Turning first to the relatively simple process of con vection, qc can be easily rewritten as a function of leaf temperature and air temperature (Tair):
where hc is a quantity known as the convection coefficient (W oC-1 m-2). Equation 9.4 is easy to solve because it expresses convective heat loss as a simple linear function of the difference between leaf temperature and air temperature. We now substitute the quantity hc(Tair - Tleaf) for qc in the heat balance equation, so that it looks like this:
We next simplify the terms for radiation and evaporation by combining them into a single term, qnet, which is simply the sum of the radiative and evaporative heat fluxes. Expressing it this way enables us to put in reasonable numbers for net heat flux rather than solving for them directly. For example, if qnet = 0, this simply means that any radiative heating of the leaf is offset by an equal rate of evaporative cooling. Similarly, if qnet > 0, radiative heating exceeds evaporative cooling, and there is a net heating of the leaf. Typical net fluxes will vary between +300 and - 300 W m-2. A little simple algebra then lets us solve this equation for leaf temperature:
Equation 9.7 allows us to estimate leaf temperature from three simple quantities: air temperature, the leaf's convection coefficient, and the net heat flux. It also expresses some convenient rules of thumb for how leaf temperature behaves and how a plant could control it. There are four:
1. Leaf temperature is a simple linear function of air temperature plus some temperature increment that is equivalent to the ratio of the leaf's net heat flux and the leaf's convection coefficient.
2. Temperature increment is not determined by the absolute magnitude of any of the leaf's fluxes of heat, but by how these fluxes vary in proportion to one another. For example, if qnet = 600 W m-2 and hc = 60 W oC-1 m-2, the temperature increment would be 10oC. The same temperature increment would result if qnet = 200 W m-2 and hc = 20 W oC-1 m-2.
3. Temperature increment is magnified by increasing net flux with respect to the leaf's convection coefficient. Similarly, temperature increment is reduced by increasing the convection coefficient with respect to the leaf's net heat flux.
4. Temperature increment can be either positive, indicating an elevation of leaf temperature above air temperature, or negative, meaning that the leaf will be cooler than air temperature. Whether temperature increment is positive or negative depends upon which term in the net heat flux predominates. If evaporative cooling is more intense than radiative heating, the leaf will be cooled. If radiative heating is more intense, the leaf will be warmed.
Optimizing Leaf Temperature through Variations of Leaf Shape
The key to controlling leaf temperature, then, is manipulating the temperature increment. Suppose, for example, a plant lives in a hot sunny environment, where air temperature is high. The plant could keep its leaf from getting too hot if it could keep the leaf's temperature increment low. The terms of the temperature increment, qnet/hc, suggest some strategies a plant might pursue. It could, for example, adjust the absorption of radiation to keep qnet as small as possible. Many desert plants indeed do just this: their leaves are covered with silvery hairs or whitish waxy coatings that reflect light away from the leaf. In a pinch, by increasing evaporation from the leaf, the plant might even drive qnet below zero (although this might be problematic in a desert, where water is scarce).
The temperature increment could also be lowered by elevating the convection coefficient, hc. The convection coefficient is mainly a function of the boundary layers that limit heat exchange by convection. In general, thinner boundary layers make for steeper temperature gradients between the leaf surface and air. Increasing the temperature gradient boosts heat flow, irrespective of what the temperature difference might be. In other words, anything that thins a leaf's boundary layer will elevate the convection coefficient and reduce the temperature increment.
The boundary layer is the connection between leaf temperature and leaf shape. Consider what happens when wind encounters a flat surface like a leaf. At the leaf's leading edge, the boundary layer will be very thin, and its thickness will grow as the air moves along the leaf's surface. It follows that the boundary layer will be thinner over a narrow leaf than it would be over a broad leaf—narrow leaves give the boundary layer less distance along the leaf to grow. Plants in hot sunny environments, therefore, should have leaves that are smaller or narrower than plants in cooler or shadier environments. Indeed, that is generally the case. Desert trees like mesquite or acacia usually have tiny leaves, compared with those of related species that live in more temperate climes. The massive leaves of rhubarb, found only in shady conditions, further underscore this point.
Even within a single plant, though, leaves experience a wide range of environmental conditions. In the crown of a maple or oak tree, for example, leaves that are located at the crown's outer margins will experience sunnier and hotter conditions than leaves in the shadier interior of the crown. If a maple leaf has a standard size and shape, leaves that are inside the crown should therefore be cooler than leaves at the sunnier margins. If maple leaves have a particular optimum temperature for photosynthesis, the tree runs the risk that, at any particular time of the day, a considerable fraction of its leaves will not be functioning at their optimum temperatures. Some simple variations of leaf shape or size can ameliorate this problem. For example, leaves in the shady interior of the crown tend to be larger and smoother in outline, while leaves in the crown's sunnier margins tend to be smaller and "pointier," divided more along the margins. Consequently, "shade leaves" will have thicker boundary layers over them, reducing convection heat loss and increasing the leaves' temperature increment. "Sun leaves" have thinner boundary layers, and their "pointiness" acts further to disrupt the boundary layers. These features enhance convective heat loss, reducing temperature increment. The end result is a relative uniformity of leaf temperature throughout the crown, despite the substantial variation of radiative heat reaching the different leaves.
Leaf Galls and Convective Heat Loss from Leaves We are now (finally!) ready to return to the matter of leaf galls. Let us review three things we have learned so far. First, affliction by leaf galls produces dramatic changes of leaf shape. Second, leaf temperature is an important factor in the efficiency of leaf function. Finally, leaf shape is an important component in a tree's ability to manipulate the temperature of its leaves. Putting these thoughts together, may we conclude that insects that induce galls are somehow manipulating leaf shape to alter the leaf's temperature, and so bias the leaf's metabolism, presumably to the inducer's benefit?
This is a pretty tall order, admittedly, but I'm going to explore it anyway. I warn you in advance that my argument is very speculative. You may, in the end, find yourself agreeing with Mark Twain when he famously disparaged scientists who make "such wholesale returns of conjecture out of such a trifling investment of fact." Nevertheless, the principle of Goldberg's lever suggests that my attempt may pay off, so here goes.
If galls affect leaf temperature at all, it is likely they will do so through an effect on the leaf's convective heat exchange. For example, galls that protrude above the leaf surface, like the hackberry gall or the needle galls of maple, could alter the boundary layers at the leaf surface. This in itself is not remarkable: many plants use protuberances like spines or hairs to alter the convective environment of their leaves. Just how plants use these spines is not always consistent, however. Many desert plants have spines or tufts of hair to promote turbulence in the boundary layers that gather at their leaves, and this turbulence thins boundary layers and enhances convective heat flux. On the other hand, some plants use these protruding structures to thicken boundary layers and produce an insulating layer of relatively still air that reduces convection fluxes. So it is not possible to say in advance what effect galls might have on an infested leaf's temperature. The presence of galls could either increase or reduce a leaf's temperature increment. And, of course, there is always the possibility that galls will have no effect whatsoever on the leaf's temperature.
Fortunately, this is a question that can be fairly easily settled by experiment. It is simple to construct a model leaf out of aluminum sheet and to heat it with a heating coil. The heat dissipated by the coil is calculated from the electrical current passing through it, and dividing this loss of heat by the model leaf's surface area gives the qnet. Leaf temperature and air temperature are also easily measured, which gives Tleaf and Tair. The convection coefficient is then calculated by rearranging equation 9.6:
I have made some measurements in my laboratory of model leaves with two types of galls. I simulated "needle galls" by gluing small lengths of monofilament upright on the leaf surface, about the length and diameter of the real thing. For hackberry galls, which are more or less spherical, I glued small beads of expanded polystyrene onto the model leaf. I then placed the entire apparatus into a wind tunnel and made measurements of the model leaf's convection coefficient at various wind speeds. The result is clear: the presence of "galls" on a model leaf reduces the leaf's average
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