---
title: "Plant Adaptations and Phenotypic Plasticity"
book: "University Biology — Year 2"
subject: biology
language: en
chapter: 15
exercises: 12
source: https://one-course.com/books/biology/4/en/chapter/15-plant-adaptations-and-phenotypic-plasticity
---

# Chapter 15 — Plant Adaptations and Phenotypic Plasticity

Two leaves from the same oak: the one from the top of the crown is small, thick and leathery, the one from the shaded interior three times as large and thin as paper. A seedling of the same oak under a closed canopy grows tall and spindly; its sibling in a clearing stays short and stout. Neither difference is genetic. A plant cannot walk to a better place, so it builds itself to fit the place it has: it senses light, gravity, touch, water, salt, cold, and it bends, thickens, elongates, closes its pores or hardens its cells accordingly. This chapter is about that plasticity — how a plant reads its surroundings and what it does about them — and about the heritable [adaptations](#def-b2-plant-plasticity-plasticity) by which lineages have fitted themselves to deserts, shade, salt and frost.

## 15.1 Plasticity and its limits

**Definition 15.1 (Phenotypic plasticity and the norm of reaction).**

*Phenotypic plasticity* is the capacity of one [genotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) to produce different [phenotypes](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) in different environments. The *norm of reaction* of a [genotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) is the curve of its [phenotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) against an environmental variable — leaf thickness against light, stem length against temperature; [genotypes](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) differ in their norms, and the differences are heritable even when the plasticity itself is not. *Acclimation* is the reversible, physiological form: a leaf that thickens its cuticle in a dry week, a cell that makes antifreeze in autumn. *Adaptation*, in the evolutionary sense, is the heritable fit of a lineage to its habitat, selected over generations; a cactus is adapted to drought, a bean acclimates to a dry spell. Plants are more plastic than animals because they are modular and indeterminate ([Chapter 13](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#ch-b2-plant-meristems)): the next leaf can be built differently from the last, and the sessile life makes plasticity the only way to move.

![Two norms of reaction. Each genotype makes thicker leaves in more light; the slope of the curve — the plasticity — is itself a heritable trait, and the two genotypes differ in it.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/fig-b5bbcb3a1b19.svg)

*Two norms of reaction. Each [genotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) makes thicker leaves in more light; the slope of the curve — the plasticity — is itself a heritable trait, and the two [genotypes](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) differ in it.*

**Proposition 15.2 (Sun leaves and shade leaves).**

A leaf developing in full sun is small, thick, with two or three layers of palisade cells, many stomata, a thick cuticle, a high concentration of the carbon-fixing enzyme and a high maximal rate of photosynthesis; a leaf of the same plant developing in shade is large, thin, with one palisade layer, more chlorophyll per unit mass, a low respiration rate and a low light-compensation point. The [shade leaf](#prop-b2-plant-plasticity-sunshade) is built to harvest every photon at minimal cost, the [sun leaf](#prop-b2-plant-plasticity-sunshade) to use a flood of them without overheating or wilting. The decision is made while the leaf is still a primordium, from the light — and in particular its colour — that reaches the bud; a mature leaf cannot rebuild itself, which is why a plant moved from shade to sun scorches until it has made new leaves.

![A sun leaf and a shade leaf from one oak: same genotype, different light, different leaves.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/img-fcba9e369da9.jpg)

*A [sun leaf](#prop-b2-plant-plasticity-sunshade) and a [shade leaf](#prop-b2-plant-plasticity-sunshade) from one oak: same [genotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary), different light, different leaves.*

## 15.2 Reading the light

**Theorem 15.3 (Phytochrome as a light-quality meter).**

Phytochrome exists in two forms: $P_r$, which absorbs red light ($660\,\mathrm{nm}$) and is converted to $P_{fr}$, and $P_{fr}$, which absorbs far-red ($730\,\mathrm{nm}$) and is converted back — and it is $P_{fr}$ that acts. In continuous light the two conversions balance at a *photoequilibrium* whose position depends only on the ratio of red to far-red in the light:

$$
\varphi = \frac{P_{fr}}{P_{r} + P_{fr}} = \frac{R}{R + a\,FR},
$$

where $R$ and $FR$ are the photon flux densities in the two bands and $a$ a constant of the pigment ($a \approx 0.77$). Sunlight has $R{:}FR \approx 1.15$, giving $\varphi \approx 0.6$; light filtered through leaves, which absorb red and transmit far-red, has $R{:}FR
\approx 0.2$ and $\varphi \approx 0.2$. A low $\varphi$ tells a plant it is under or beside other plants before it is actually shaded — far-red reflected from a neighbour is detected on the side facing it — and it responds with the *[shade avoidance](#thm-b2-plant-plasticity-phytochrome) syndrome*: faster stem elongation, longer petioles, leaves held upward, less branching, earlier flowering. A seedling in a closed canopy doubles its rate of elongation.

**Proof.** Let $k_1 R$ be the rate constant for $P_r \to P_{fr}$ (proportional to the red flux) and $k_2\,FR$ that for $P_{fr} \to P_r$. At equilibrium $k_1 R\,P_r = k_2\,FR\,P_{fr}$, so $P_{fr}/P_r = k_1 R/
(k_2 FR)$ and $\varphi = P_{fr}/(P_r + P_{fr}) = R/(R + a\,FR)$ with $a = k_2/k_1$. (Both forms absorb somewhat in both bands, which the constant $a$ absorbs; the form of the result is unchanged.) With $a = 0.77$: $1.15/(1.15 + 0.77) = 0.60$; $0.2/(0.2 + 0.77) = 0.21$. ∎

![The phytochrome photoequilibrium against the red-to-far-red ratio. Sunlight holds most of the pigment in the active form; leaf-filtered light holds it mostly inactive, and the plant reads the difference as neighbours.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/fig-ce409e2d0f0d.svg)

*The phytochrome photoequilibrium against the red-to-far-red ratio. Sunlight holds most of the pigment in the active form; leaf-filtered light holds it mostly inactive, and the plant reads the difference as neighbours.*

**Proposition 15.4 (Phototropism).**

A *tropism* is a growth movement oriented by a directional stimulus. In *phototropism* a shoot bends toward blue light: the light is sensed at the tip by a blue-light receptor (phototropin), the auxin descending from the tip is redirected toward the shaded side — its carriers move to the lateral membrane — and the shaded side, receiving more auxin, elongates faster than the lit side, so the shoot curves toward the light. The bending is differential growth, not a muscle: it occurs only in the [elongation zone](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#prop-b2-plant-meristems-ram), takes an hour or two, and is irreversible. Roots, in which the same auxin excess *inhibits* elongation, bend away.

**Evidence.** Darwin (1880) showed with grass coleoptiles that the tip perceives the light and the zone below it bends: covering the tip with an opaque cap abolished the bending, covering the base with a tube did not, and a transparent cap left it intact. Boysen-Jensen (1913) cut the tip off and replaced it with a block of gelatin between: bending persisted, so the signal was a diffusible substance; a sheet of mica inserted on the shaded side blocked it, on the lit side did not, so the substance travelled down the shaded side. Went (1928) collected the substance in agar from cut tips and found that a block placed off-centre on a decapitated coleoptile in the dark made it bend away from the block — by an angle proportional to the amount — and, collecting agar from the two halves of a unilaterally lit tip, found about two thirds of the auxin on the shaded side and one third on the lit side (Briggs, 1957, with better methods). The lateral redistribution of a growth hormone is the [Cholodny–Went hypothesis](#prop-b2-plant-plasticity-phototropism), and it has held. ∎

![The coleoptile experiments. Darwin: the tip senses the light and the region below bends; capping the tip stops it, shielding the base does not. Boysen-Jensen: the signal crosses a block of gelatin — it is a substance.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/fig-7d1d94bbb22b.svg)

*The coleoptile experiments. Darwin: the tip senses the light and the region below bends; capping the tip stops it, shielding the base does not. Boysen-Jensen: the signal crosses a block of gelatin — it is a substance.*

![Seedlings in a box with one window: all bend toward the light, by growing faster on the side away from it.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/img-9a4ffad335fe.jpg)

*Seedlings in a box with one window: all bend toward the light, by growing faster on the side away from it.*

**Theorem 15.5 (How much a stem bends).**

If the shaded side of a stem of diameter $d$ elongates by a relative amount $\varepsilon_s$ and the lit side by $\varepsilon_l$ over a growing zone of length $L$, the zone curves through an angle

$$
\theta = \frac{L\,(\varepsilon_s - \varepsilon_l)}{d}
$$

(in radians). A coleoptile growing at $5\,\%$ an hour over a zone of $10\,\mathrm{mm}$ and $1\,\mathrm{mm}$ across, with auxin split $65 : 35$ so that the two sides grow at $1.3$ and $0.7$ times the mean, bends in three hours by $\theta = 10\times(0.195 - 0.105)/1 =
0.9$ radians, about $50{}^{\circ}$. Bending needs no new mechanism: the ordinary growth of [Chapter 13](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#ch-b2-plant-meristems), made unequal on two sides, is enough.

**Proof.** The two sides of the zone become arcs of radii $\rho + d/2$ and $\rho - d/2$ subtending the same angle $\theta$, of lengths $L(1 +
\varepsilon_s)$ and $L(1 + \varepsilon_l)$; their difference is $\theta d$, so $\theta = L(\varepsilon_s - \varepsilon_l)/d$. Over three hours at $5\,\%$ an hour the mean extension is $0.15$; $1.3\times 0.15 = 0.195$ and $0.7\times 0.15 = 0.105$. ∎

**Proposition 15.6 (Gravitropism).**

A shoot laid on its side turns upward and a root downward within hours. The direction of gravity is sensed by *statoliths* — dense starch grains in specialised cells of the [root cap](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#prop-b2-plant-meristems-ram) and of the stem’s starch sheath — which settle to the lower side of the cell in seconds and, by pressing on the membrane or the endoplasmic reticulum, redirect the auxin carriers so that auxin accumulates on the lower side. In the shoot the lower side grows faster and the stem curves up; in the root the same auxin excess inhibits the lower side, the upper side grows faster, and the root curves down. Remove the [root cap](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#prop-b2-plant-meristems-ram) and the root grows straight in any direction; starch-free mutants sense gravity poorly; a root on a slowly rotating drum (a clinostat), which never lets the statoliths settle, grows without direction. The response is a second use of the Cholodny–Went mechanism, with a different sensor.

## 15.3 Water: closing the pores

**Proposition 15.7 (Stomatal control).**

The leaf’s pores, the *stomata*, are each bounded by two *[guard cells](#prop-b2-plant-plasticity-stomata)* whose walls are thickened unevenly, so that when they take up potassium and water and swell, they bow apart and open the pore, and when they lose them they close it. They open in the morning under blue light and low internal $\mathrm{CO_2}$, and close in the dark; they close within minutes when *[abscisic acid](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#def-b2-plant-flowering-dormancy)* arrives — made in roots that sense drying soil and carried up in the xylem, or made in the leaf itself as it loses turgor — and when the air is very dry. The *[stomatal conductance](#prop-b2-plant-plasticity-stomata)* $g_s$ sets both the water lost, $E = g_s\,(w_i - w_a)$ (the difference in water vapour mole fraction between the leaf interior, saturated, and the air), and the $\mathrm{CO_2}$ taken in, $A = g_s\,(c_a -
c_i)/1.6$ (the factor $1.6$ being the ratio of the diffusivities of water vapour and $\mathrm{CO_2}$). The leaf trades water for carbon through one valve, and its *water-use efficiency* is

$$
\frac{A}{E} = \frac{c_a - c_i}{1.6\,(w_i - w_a)},
$$

a few thousandths of a mole of carbon per mole of water: a typical C$_3$ leaf spends $400\text{ to }600\,\mathrm{g}$ of water per gram of carbon fixed, a C$_4$ leaf half that, a [CAM plant](#prop-b2-plant-plasticity-xerophytes) a fifth.

![Stomata on the underside of a leaf, some open and some closed: two guard cells around each pore, the valve through which the leaf trades water for carbon dioxide.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/img-75a0d4fb54e6.jpg)

*Stomata on the underside of a leaf, some open and some closed: two [guard cells](#prop-b2-plant-plasticity-stomata) around each pore, the valve through which the leaf trades water for carbon dioxide.*

**Example 15.8 (The cost of a day’s carbon).**

At midday a sunflower leaf with $g_s = 0.3\,\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$, $w_i - w_a = 0.02$ and $c_a - c_i = 120\,\text{µ}\mathrm{mol}/\mathrm{mol}$ transpires $E = 6\,\mathrm{mmol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$ and fixes $A =
0.3\times 120/1.6 = 22\,\text{µ}\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$: $A/E =
3.7 \times 10^{-3}\,$, i.e. 270 molecules of water for each carbon atom, $400\,\mathrm{g}$ of water per gram of carbon. A hectare of such leaves loses $40\,\mathrm{t}$ of water on a summer day to fix $100\,\mathrm{kg}$ of carbon. When the soil dries, [abscisic acid](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#def-b2-plant-flowering-dormancy) closes the stomata to a tenth of this conductance: $E$ falls tenfold, $A$ less than that (since $c_i$ falls too), and the plant survives on a starvation diet rather than dying of thirst.

**Proposition 15.9 (Adaptations to drought).**

Plants of dry places (*xerophytes*) combine heritable structures and strategies. Reduce the loss: thick cuticle, stomata sunk in pits or under hairs (which thicken the still air layer), leaves reduced to spines (cactus) or shed in the dry season, small thick leaves that roll. Store: succulent stems and leaves with water-holding mucilage. Reach: roots $50\,\mathrm{m}$ deep (mesquite) or spreading just under the surface to catch a shower. Shift: [CAM plants](#prop-b2-plant-plasticity-xerophytes) open their stomata at night, when $w_i - w_a$ is small, fix $\mathrm{CO_2}$ into malic acid, and refix it behind closed stomata by day — the same carbon at a fifth of the water. Escape: desert annuals live as [seeds](https://one-course.com/books/biology/4/en/chapter/6-sexual-reproduction-of-flowering-plants#def-b2-angiosperm-reproduction-seed) for years and complete a [life cycle](https://one-course.com/books/biology/4/en/chapter/5-life-cycles-and-reproduction-of-land-plants#def-b2-plant-life-cycles-cycles) in the weeks after rain. Tolerate: resurrection plants lose $95\,\%$ of their water and revive. Each strategy has a price — CAM is slow, succulence is heavy, spines cannot photosynthesise — and the plant that pays it is outgrown wherever water is plentiful.

![A barrel cactus: a succulent stem with a thick cuticle, ribs that let it swell after rain, leaves reduced to spines, and stomata that open only at night.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/img-097b4a5fddd4.jpg)

*A barrel cactus: a succulent stem with a thick cuticle, ribs that let it swell after rain, leaves reduced to spines, and stomata that open only at night.*

## 15.4 Cold, salt and the stress response

**Proposition 15.10 (Acclimation to stress).**

A week at $4\,{}^{\circ}\mathrm{C}$ lowers the temperature that kills a winter rye from $-5\,{}^{\circ}\mathrm{C}$ to $-25\,{}^{\circ}\mathrm{C}$: the cells have loaded sugars and proteins that lower the freezing point and protect membranes, changed their lipids to stay fluid, and made antifreeze proteins that stop ice crystals growing; the killing event is not the ice, which forms harmlessly between cells, but the dehydration of the cell as water leaves it to join the ice. A few hours at $40\,{}^{\circ}\mathrm{C}$ induce *[heat shock proteins](#prop-b2-plant-plasticity-stress)* that refold denatured proteins and protect the cell at $45\,{}^{\circ}\mathrm{C}$. Salt is met by exclusion at the root, compartmentation into the vacuole (with compatible solutes in the cytosol to balance it), and, in true *halophytes*, secretion through salt glands. Most of these responses pass through the same signalling: a sensor, a rise in cytosolic calcium, [abscisic acid](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#def-b2-plant-flowering-dormancy), and a set of [transcription factors](https://one-course.com/books/biology/4/en/chapter/12-cell-differentiation-the-skeletal-muscle-cell#prop-b2-cell-differentiation-transcriptional) that switch on hundreds of protective genes — a stress programme as general as the immune response of an animal, and, like it, costly: the acclimated plant grows slowly, and a plant that acclimates when it need not loses to one that does not.

**Evidence.** [Cold-acclimation](#def-b2-plant-plasticity-plasticity) experiments measure the temperature at which half the cells of a leaf die (the LT$_{50}$) before and after a period at low temperature; the shift, of ten to twenty degrees in a week, is reversed by a week of warmth. Mutants unable to switch on the cold programme (the CBF [transcription factors](https://one-course.com/books/biology/4/en/chapter/12-cell-differentiation-the-skeletal-muscle-cell#prop-b2-cell-differentiation-transcriptional)) acclimate poorly, and plants expressing those factors constitutively survive frost without [acclimation](#def-b2-plant-plasticity-plasticity) — but grow as dwarfs. ∎

![The common shape of a plant’s stress response: a sensor, a calcium and abscisic acid signal, transcription factors, and a programme of protective genes — paid for in growth.](https://one-course.com/images/onecourse/chapters/biology-4/b2-plant-plasticity/fig-74876bb7ab5d.svg)

*The common shape of a plant’s stress response: a sensor, a calcium and [abscisic acid](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#def-b2-plant-flowering-dormancy) signal, [transcription factors](https://one-course.com/books/biology/4/en/chapter/12-cell-differentiation-the-skeletal-muscle-cell#prop-b2-cell-differentiation-transcriptional), and a programme of protective genes — paid for in growth.*

**Example 15.11 (Cues that lie).**

Plasticity is only as good as the cue. A seedling under a neighbour’s far-red shade elongates — correctly, if the neighbour is a seedling it can overtop; fatally, if it is a tree, since the reserves spent on stem are lost to root and leaf. Crops planted densely shade each other, elongate, and lodge; breeders have selected wheats and rices that ignore the far-red signal. A warm week in February brings out leaves that a March frost kills; the plants that survive are those that also count the cold ([Chapter 14](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#ch-b2-plant-flowering)). Every plastic response is a bet on the cue’s honesty, and the [norm of reaction](#def-b2-plant-plasticity-plasticity) is shaped by how often, in the lineage’s past, the cue told the truth.

## 15.5 Exercises

**Exercise 15.1 ★.**

Define [phenotypic plasticity](#def-b2-plant-plasticity-plasticity), [norm of reaction](#def-b2-plant-plasticity-plasticity), [acclimation](#def-b2-plant-plasticity-plasticity) and [adaptation](#def-b2-plant-plasticity-plasticity), with a plant example of each.

**Solution of Exercise 15.1.**

Plasticity: one [genotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary), several [phenotypes](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) according to the environment (sun and shade leaves on one oak). [Norm of reaction](#def-b2-plant-plasticity-plasticity): the curve of a [genotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary)’s [phenotype](https://one-course.com/books/biology/4/en/chapter/4-meiosis-genetic-mixing-and-heredity#def-b2-meiosis-heredity-vocabulary) against an environmental variable (leaf thickness against light). [Acclimation](#def-b2-plant-plasticity-plasticity): a reversible physiological adjustment (frost hardening of rye in autumn). [Adaptation](#def-b2-plant-plasticity-plasticity): a heritable fit selected over generations (the CAM metabolism of a cactus).

**Exercise 15.2 ★.**

Describe Darwin’s four coleoptile treatments and what each showed.

**Solution of Exercise 15.2.**

Intact coleoptile lit from one side: bends toward the light. Tip covered with an opaque cap: no bending — the tip perceives the light. Tip covered with a transparent cap: bends — the cap itself is harmless. Base shielded by an opaque tube, tip exposed: bends — the perception is at the tip and the response below it.

**Exercise 15.3 ★.**

List five differences between a [sun leaf](#prop-b2-plant-plasticity-sunshade) and a [shade leaf](#prop-b2-plant-plasticity-sunshade), and say when in the leaf’s life the choice is made.

**Solution of Exercise 15.3.**

[Sun leaf](#prop-b2-plant-plasticity-sunshade): small, thick, two or three palisade layers, thick cuticle, many stomata, high maximal photosynthesis and high compensation point. [Shade leaf](#prop-b2-plant-plasticity-sunshade): large, thin, one palisade layer, more chlorophyll per gram, low respiration, low compensation point. The choice is made while the leaf is a primordium in the bud, from the light it receives; a mature leaf cannot change.

**Exercise 15.4 ★.**

How does a stoma open, what opens it in the morning, and what closes it in a drought?

**Solution of Exercise 15.4.**

The [guard cells](#prop-b2-plant-plasticity-stomata) take up potassium and water, swell, and, their inner walls being thicker, bow apart to open the pore. Blue light and low internal $\mathrm{CO_2}$ open them in the morning; [abscisic acid](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#def-b2-plant-flowering-dormancy), from roots in drying soil or from the leaf, closes them in a drought, as does very dry air.

**Exercise 15.5 ★★.**

Compute $\varphi$ for $R{:}FR = 1.15$ (sun), $0.7$ (a gap), $0.2$ (under a canopy) and $0.05$ (deep shade) with $a = 0.77$. Between which two of these does the plant switch on [shade avoidance](#thm-b2-plant-plasticity-phytochrome) if the threshold is $\varphi = 0.4$?

**Solution of Exercise 15.5.**

$\varphi = R/(R + 0.77\,FR)$ with $FR = 1$: $1.15$: $0.60$; $0.7$: $0.48$; $0.2$: $0.21$; $0.05$: $0.06$. The threshold $0.4$ falls between the gap ($0.48$) and the canopy ($0.21$): [shade avoidance](#thm-b2-plant-plasticity-phytochrome) switches on under the canopy.

**Exercise 15.6 ★★.**

A leaf has $g_s = 0.25\,\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$, $w_i - w_a = 0.025$, $c_a - c_i = 100\,\text{µ}\mathrm{mol}/\mathrm{mol}$. Compute $E$, $A$, the water-use efficiency in moles and in grams of water per gram of carbon, and the water lost per square metre in a 12-hour day.

**Solution of Exercise 15.6.**

$E = 0.25\times 0.025 = 6.25\,\mathrm{mmol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$; $A =
0.25\times 100/1.6 = 15.6\,\text{µ}\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$; $A/E =
2.5\times 10^{-3}$ mol of carbon per mol of water, i.e. 400 water molecules per carbon, $400\times 18/12 = 600\,\mathrm{g}$ of water per gram of carbon. In 12 hours: $6.25\times 10^{-3}\times 43200 =
270\,\mathrm{mol}/\mathrm{m}^{2}$, $4.9\,\mathrm{L}$ per square metre.

**Exercise 15.7 ★★.**

Recompute the previous exercise for a [CAM plant](#prop-b2-plant-plasticity-xerophytes) whose stomata open at night with $w_i - w_a = 0.005$ and the same conductance. By what factor is the water cost of carbon reduced?

**Solution of Exercise 15.7.**

$E = 0.25\times 0.005 = 1.25\,\mathrm{mmol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$, $A$ unchanged: $A/E = 0.0125$, 80 waters per carbon, $120\,\mathrm{g}/\mathrm{g}$ — a fifth of the daytime cost.

**Exercise 15.8 ★★.**

A statolith is a starch grain of radius $2\,\text{µ}\mathrm{m}$ and density $1500\,\mathrm{kg}/\mathrm{m}^{3}$ in cytoplasm of density $1100\,\mathrm{kg}/\mathrm{m}^{3}$ and viscosity $0.01\,\mathrm{Pa}\,\mathrm{s}$. Compute its settling speed (Stokes) and the time to cross a $10\,\text{µ}\mathrm{m}$ cell. Why does a clinostat turning once a minute abolish gravitropism?

**Solution of Exercise 15.8.**

$v = 2r^{2}\Delta\rho g/9\eta = 2\times 4\times 10^{-12}\times
400\times 9.81/0.09 = 3.5 \times 10^{-7}\,\mathrm{m}/\mathrm{s}$: $0.35\,\text{µ}\mathrm{m}/\mathrm{s}$, about $30\,\mathrm{s}$ to cross the cell. On a clinostat the direction of gravity relative to the cell changes every few seconds of settling, so the grains never accumulate on one side and the averaged stimulus over the plant’s integration time (minutes) is zero.

**Exercise 15.9 ★★.**

A stem $2\,\mathrm{mm}$ across grows $2\,\%$ an hour over a $20\,\mathrm{mm}$ zone. Light from one side splits the auxin $60 : 40$. Through what angle has it bent after two hours? After how long is it at $90{}^{\circ}$ to its original direction?

**Solution of Exercise 15.9.**

Mean extension in two hours $0.04$; sides $1.2\times 0.04 = 0.048$ and $0.8\times 0.04 = 0.032$; $\theta = 20\times 0.016/2 = 0.16$ rad, about $9{}^{\circ}$. Bending accumulates at $0.08$ rad per hour; $\pi/2$ takes about $20\,\mathrm{h}$.

**Exercise 15.10 ★★★.**

A seedling with $50\,\mathrm{mg}$ of reserves elongates at $2\,\mathrm{cm}$ a day in the open and $4\,\mathrm{cm}$ a day under a canopy, spending $1\,\mathrm{mg}$ of reserves per centimetre of stem beyond what its leaves supply. The canopy is $30\,\mathrm{cm}$ above it in a nettle bed and $10\,\mathrm{m}$ in a wood. In which case does [shade avoidance](#thm-b2-plant-plasticity-phytochrome) succeed, and what happens in the other?

**Solution of Exercise 15.10.**

Reserves allow $50\,\mathrm{cm}$ of stem. Nettle bed: $30\,\mathrm{cm}$ in 7.5 days for $30\,\mathrm{mg}$ — the seedling reaches light with reserves to spare. [Wood](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#def-b2-plant-meristems-wood): $10\,\mathrm{m}$ is out of reach; the seedling spends its $50\,\mathrm{mg}$ on half a metre of pale stem in twelve days and dies etiolated, whereas a shade-tolerant strategy — a few thin leaves, slow growth — might have kept it alive for years.

**Exercise 15.11 ★★★.**

Explain why freezing kills a cell by dehydration rather than by ice, what a week of cold does to prevent it, and why a plant that expresses the cold programme all year is a dwarf.

**Solution of Exercise 15.11.**

Ice forms first in the extracellular spaces, where the solution is more dilute; the vapour pressure over ice is lower than over the cell’s water, so water leaves the cell to join the ice and the cell dehydrates and its membranes collapse. A week of cold loads the cell with sugars and protective proteins that lower its freezing point and stabilise membranes, and makes antifreeze proteins that limit crystal growth. Keeping the programme on all year diverts carbon from growth to protection and slows division: a permanently hardened plant is a small one.

**Exercise 15.12 ★★★.**

“Plasticity is a bet on the honesty of a cue.” Discuss with the far-red signal, the warm week in February, and the breeding of crops that ignore their neighbours.

**Solution of Exercise 15.12.**

The far-red signal is honest when the neighbour can be overtopped and a lie when it is a tree; the warm week is honest in April and a lie in February; in a dense crop every plant’s neighbours are its equals, so the signal is honest in form but useless, and breeders select plants that ignore it. A [norm of reaction](#def-b2-plant-plasticity-plasticity) is the record of how often each cue has told the truth in the lineage’s past, and it fails whenever the present differs from that past.

## 15.6 Problem: A Seedling Under the Canopy

**Problem 15.1.**

Weekend problem — a seedling’s light climate, elongation, water budget and tropisms computed from the physics of its sensors, ending on its phytochrome state, its height after a fortnight, and its daily water use

A birch seedling germinates under a canopy that transmits $3\,\%$ of the sunlight and lowers $R{:}FR$ from $1.15$ to $0.2$ ($a = 0.77$). In full sun it would elongate at $1.5\,\mathrm{cm}$ a day; under the canopy its elongation rate is multiplied by $1 +
2(0.6 - \varphi)$. Its stem is $2\,\mathrm{mm}$ across with a $15\,\mathrm{mm}$ growing zone. Leaves: $20\,\mathrm{cm}^{2}$ in all; $g_s =
0.2\,\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$; $w_i - w_a = 0.015$ in the shade, $0.03$ in a gap; $c_a - c_i = 80\,\text{µ}\mathrm{mol}/\mathrm{mol}$; the day lasts $14\,\mathrm{h}$. Statoliths: radius $2.5\,\text{µ}\mathrm{m}$, density $1500\,\mathrm{kg}/\mathrm{m}^{3}$, in cytoplasm of $1100\,\mathrm{kg}/\mathrm{m}^{3}$ and $0.01\,\mathrm{Pa}\,\mathrm{s}$.

**Part I — The light.**

1. Compute $\varphi$ in the open and under the canopy.
2. What does the seedling conclude from $\varphi$ , and what would it conclude if the canopy transmitted $3\,\%$ of the light without changing its colour (a shade cloth)?
3. Compute the elongation rate under the canopy.
4. How tall is the seedling after 14 days there, against a sibling in the open?
5. A gap opens on one side, raising $R{:}FR$ on that side to $0.8$ . What two responses follow, and by which two photoreceptors?
6. Why are leaves developed under the canopy larger and thinner, and what happens to them if the canopy is felled?

**Part II — Bending toward the gap.**

7. Light from the gap splits the auxin $65 : 35$ across the stem. With the canopy elongation rate of question 3, compute the relative extension of each side of the growing zone in one hour.
8. Compute the angle of bending after one hour.
9. After how long does the stem point straight at the gap, if the gap is at $60{}^{\circ}$ from vertical?
10. The stem is now leaning. Compute the settling speed of a statolith and the time to cross a $12\,\text{µ}\mathrm{m}$ cell.
11. The shoot’s gravitropism and its phototropism now disagree. Which wins in a shade-avoiding plant, and why is that adaptive?
12. A root of the same seedling is tilted $45{}^{\circ}$ by a stone. Predict its response and explain why it is opposite to the shoot’s although the mechanism is the same.

**Part III — Water.**

13. Compute the transpiration rate per square metre in the shade, and the water lost by the seedling’s leaves in a day.
14. Compute the carbon fixed per square metre per second and per day, and the water-use efficiency in grams of water per gram of carbon.
15. What is the seedling’s whole daily carbon gain in the shade, in milligrams?
16. Recompute the water lost and the efficiency in the gap.
17. The soil dries and [abscisic acid](https://one-course.com/books/biology/4/en/chapter/14-reproductive-development-and-flowering-control#def-b2-plant-flowering-dormancy) reduces $g_s$ to $0.02\,\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$ . Recompute $E$ and $A$ (assume $c_a - c_i$ rises to $200\,\text{µ}\mathrm{mol}/\mathrm{mol}$ ). Which falls more, and why?
18. The seedling has $5\,\mathrm{g}$ of leaf tissue that is $85\,\%$ water and can lose a fifth of it before wilting. How long does it last in the gap with the stomata open if the roots supply nothing?
19. Explain why a CAM strategy would not suit a birch seedling under a canopy.

**Part IV — The bet.**

20. The seedling holds $100\,\mathrm{mg}$ of reserves and spends $2\,\mathrm{mg}$ per centimetre of stem beyond what its leaves supply in the shade. How much stem can it build on reserves alone?
21. The canopy is a nettle bed $40\,\mathrm{cm}$ above; then a wood $8\,\mathrm{m}$ above. Say in each case whether elongation reaches light before the reserves run out, and what the better response would have been in the wood.
22. A birch is a pioneer of open ground; a beech seedling can wait for decades in deep shade. Compare their expected norms of reaction to $\varphi$ .
23. A plant breeder wants a dense-planted crop that does not elongate. Which sensor or response would you disable, and what side effect must you check?
24. Explain in two sentences why a plant that cannot sense its neighbours and a plant that always believes them are both worse off than one that sometimes does.
25. State the result: $\varphi$ in sun and shade, the seedling’s height after 14 days, and its daily water use in the shade and in the gap.

**Solution of Problem 15.1.**

**1.** Open: $1.15/(1.15 + 0.77) = 0.60$; canopy: $0.2/(0.2 +
0.77) = 0.21$. **2.** Low $\varphi$: plants overhead — elongate. Under a shade cloth $\varphi$ stays $0.60$: a dark day, not a neighbour; no [shade avoidance](#thm-b2-plant-plasticity-phytochrome), only slower growth for want of light. **3.** $1 + 2(0.60 - 0.21) = 1.78$: $2.7\,\mathrm{cm}$ a day. **4.** $37\,\mathrm{cm}$ against $21\,\mathrm{cm}$. **5.** Bending toward the gap (phototropism, via the blue-light receptor phototropin) and faster elongation and leaf reorientation on the side with the higher $R{:}FR$ (via phytochrome). **6.** Shade leaves are built large and thin to catch scarce light cheaply; in full sun they overheat, photo-inhibit and scorch, and the plant must replace them with sun leaves. **7.** $2.7\,\mathrm{cm}$ a day over a $15\,\mathrm{mm}$ zone is $0.11\,\mathrm{cm}$ an hour, a relative extension of $0.074$ per hour; shaded side $1.3\times 0.074 = 0.096$, lit side $0.7\times 0.074 =
0.052$. **8.** $\theta = 15\times(0.096 - 0.052)/2 = 0.33$ rad, about $19{}^{\circ}$ in an hour. **9.** $60{}^{\circ}$ is $1.05$ rad: about three hours. **10.** $v = 2\times 6.25\times 10^{-12}\times 400\times
9.81/0.09 = 5.5 \times 10^{-7}\,\mathrm{m}/\mathrm{s}$, $0.55\,\text{µ}\mathrm{m}/\mathrm{s}$: $22\,\mathrm{s}$ to cross the cell. **11.** Phototropism, and [shade avoidance](#thm-b2-plant-plasticity-phytochrome) itself raises the angle at which the shoot is content to grow: light is the resource being fought for, and a stem that straightened against gravity would turn back into the shade. **12.** The root bends downward until it is vertical: statoliths settle to the lower side, auxin accumulates there, and in a root the extra auxin inhibits growth, so the upper side grows faster. Same redistribution, opposite sensitivity of the cells. **13.** $E = 0.2\times 0.015 = 3\,\mathrm{mmol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$; over $2\times 10^{-3}$ $\mathrm{m}^{2}$ and $50\,400\,\mathrm{s}$: $0.30\,\mathrm{mol}$, $5.4\,\mathrm{g}$ of water a day. **14.** $A = 0.2\times 80/1.6 = 10\,\text{µ}\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$; per day $0.50$ mol of carbon per square metre; $A/E = 3.3\times
10^{-3}$: 300 waters per carbon, $450\,\mathrm{g}/\mathrm{g}$. **15.** $0.50\times 2\times 10^{-3} = 1\,\mathrm{mmol}$: $12\,\mathrm{mg}$ of carbon a day. **16.** Gap: $E = 6\,\mathrm{mmol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$, $10.9\,\mathrm{g}$ a day; efficiency $900\,\mathrm{g}/\mathrm{g}$. **17.** $E = 0.02\times 0.03 = 0.6\,\mathrm{mmol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$ (tenfold down); $A = 0.02\times 200/1.6 = 2.5\,\text{µ}\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$ (fourfold down). Water falls more: as the leaf draws down its internal $\mathrm{CO_2}$ the gradient for carbon widens while that for water cannot. **18.** $4.25\,\mathrm{g}$ of water, $0.85\,\mathrm{g}$ to lose; at $10.9\,\mathrm{g}$ a day ($0.78$ g an hour) it wilts in about an hour. **19.** CAM is slow and needs succulent storage tissue; a seedling racing for light under a canopy, where water loss is small anyway, needs speed, not economy. **20.** $100/2 = 50\,\mathrm{cm}$. **21.** Nettle bed: $40\,\mathrm{cm}$ in 15 days for $80\,\mathrm{mg}$ — it reaches light. [Wood](https://one-course.com/books/biology/4/en/chapter/13-plant-vegetative-development-meristems-and-growth#def-b2-plant-meristems-wood): $8\,\mathrm{m}$ is unreachable; it spends its reserves on half a metre and dies. Better in the wood: stay short, make thin shade leaves and wait for a gap — the beech’s way. **22.** Birch: a steep norm, elongating strongly at low $\varphi$, since a pioneer’s neighbours are its own size. Beech: a flat norm, little elongation and much tolerance, since its neighbours are trees. **23.** Disable the shade-avoidance response — keep phytochrome B active or remove the [transcription factors](https://one-course.com/books/biology/4/en/chapter/12-cell-differentiation-the-skeletal-muscle-cell#prop-b2-cell-differentiation-transcriptional) it restrains — and check flowering time, germination and stem strength, which the same pathway controls. **24.** A plant that cannot sense neighbours is overtopped whenever it could have won; a plant that always believes the cue squanders itself under every tree. The winning norm bets on the cue in proportion to how often, in the lineage’s past, it was right. **25.** $\varphi = 0.60$ in the open and $0.21$ under the canopy; $37\,\mathrm{cm}$ after 14 days; $5.4\,\mathrm{g}$ of water a day in the shade, $10.9\,\mathrm{g}$ in the gap.