Limiting factors and primary productivity

One factor at a time

A process made of many steps runs at the pace its slowest step allows. Photosynthesis needs light energy, carbon dioxide as raw material and a workable temperature for its enzymes, and at any moment one of the three is holding the rate back. That one is the limiting factor: the factor in shortest supply, and the only one whose increase would speed things up.

Describe the drawing

A graph of the rate of photosynthesis against light intensity carrying three curves. All three rise together from the origin along the same steep straight line while the light is low, then peel apart and flatten off at three different heights: lowest at the low carbon dioxide concentration, higher when the carbon dioxide is raised, and higher still when the temperature is raised as well. Annotations mark the shared gradient at low light and the levelling off at high light, and a key names the conditions for each curve.

That overlap on the left is the whole argument. Where the curves coincide the rate depends only on how much light there is, so light is limiting and the extra carbon dioxide is doing nothing, because there is not enough energy to use what is already there. Where the curves flatten and separate, more light no longer helps, and whatever is different between the curves is what is now limiting.

Read a plateau carefully. A plateau does not mean the plant has hit some absolute maximum; it means the factor on the x-axis has stopped being the one that matters. Raise something else and the plateau moves up. If raising carbon dioxide lifts the plateau, carbon dioxide was limiting there; if raising the temperature lifts it further, temperature was limiting after that.

Temperature behaves differently from the other two. Light intensity and carbon dioxide concentration feed the reaction; temperature affects the enzymes catalysing it. So a temperature graph rises to an optimum and then falls, because beyond roughly 40 °C the enzymes of the Calvin cycle, rubisco among them, begin to denature. Across the range used in these experiments the light and carbon dioxide curves flatten out rather than falling, although photoinhibition can reduce the rate at very high irradiance.

Limiting factor

The factor, of all those a process requires, whose shortage is holding the rate back at that moment.

Plateau

The region of a rate graph where increasing the factor on the horizontal axis no longer increases the rate, because something else has become limiting.

Measuring the rate in a whole plant

Curves like these come from experiments, and on a school bench the experiment uses an aquatic plant or algae. What is measured is the gas the plant exchanges with the water around it: oxygen given off, or carbon dioxide taken up. Either way it is the net rate, photosynthesis minus the plant's own respiration, because the plant respires throughout. Cambridge International asks for investigations with whole plants, aquatic plants included; OCR asks for practical investigations of the factors affecting the rate; AQA suggests aquatic plants, algae or immobilised algal beads; and Pearson Edexcel's Biology B core practical 10, on wavelength, can use the same apparatus.

A sprig of pondweed such as Elodea or Cabomba is placed, cut end uppermost, in a boiling tube of dilute sodium hydrogencarbonate solution. The hydrogencarbonate ions supply carbon dioxide, so carbon dioxide does not limit the rate unless it is the variable being changed. The tube stands in a water bath to hold its temperature, and the plant is left for a few minutes in each new condition before a reading is taken, so that the rate has settled.

Counting bubbles is quick and imprecise: bubbles differ in size, and a fast stream cannot be counted. A photosynthometer collects the gas instead. The mouth of its capillary tube sits just above the cut end, gas gathers there for a fixed time, and a syringe then draws the bubble along the capillary beside a scale. The bubble's length and the capillary's radius give its volume, V = πr²l, and volume divided by time is the rate.

Describe the drawing

Apparatus for measuring the rate of photosynthesis of pondweed. A lamp on the left is a measured distance d from a boiling tube standing in a water bath with a thermometer. The tube holds hydrogencarbonate solution and a sprig of pondweed with its cut end at the top, giving off bubbles. The mouth of a capillary tube sits just above the cut; the capillary rises out of the tube and runs sideways along a scale to a syringe, which draws the collected gas bubble along the scale so its length can be read. A note gives light intensity as proportional to one over d squared.

The gas collected is mostly oxygen, though not all of it. Nitrogen dissolved in the water comes out with it, some of the oxygen dissolves instead of collecting, and the plant uses some in respiration. Rates measured the same way can still be compared with each other; a volume of gas is not an exact measure of the oxygen produced.

Light intensity. Move the lamp. Light from a small lamp spreads out as it travels, so its intensity is proportional to 1/d², where d is the distance from lamp to plant: the inverse square law. Halve the distance and the intensity is four times as great. Plot the rate against 1/d², or against a light-meter reading, rather than against d. Work in a darkened room so the lamp is the only light, and stop the lamp warming the water, with an LED or a beaker of water as a heat shield, reading the thermometer to show the temperature stayed the same.

Carbon dioxide concentration. Use a range of sodium hydrogencarbonate concentrations, with the lamp at a fixed distance and the water bath at a fixed temperature.

Temperature. Set the water bath to each temperature in turn and let the tube reach it before timing. Keep the light bright and the hydrogencarbonate concentration fixed, so that temperature is the factor that limits.

Wavelength. Put coloured filters between the lamp and the plant, or use coloured LEDs. Filters of different colours also pass different amounts of light, so the intensity reaching the plant has to be measured with a light meter and matched; otherwise the experiment compares brightness rather than colour. Red and blue light give the highest rates and green the lowest, as the action spectrum predicts.

Algal beads. A single-celled alga such as Chlorella, trapped in beads of sodium alginate, gives many near-identical replicates. Equal numbers of beads go into tubes of hydrogencarbonate indicator, whose colour depends on the carbon dioxide concentration through pH. As the algae remove carbon dioxide the indicator moves from orange-red towards purple; where respiration outpaces photosynthesis it moves towards yellow. The colour after a fixed time, or the absorbance read in a colorimeter, measures the net rate. A tube wrapped in foil, where the algae can only respire, is the control showing that the change in the lit tubes was caused by photosynthesis.

Lamps and water are used together here, so keep the electrics away from the water bath and let lamps cool before handling them. Check the CLEAPSS guidance and your school's risk assessment for the indicator and the alginate method.

Photosynthometer

Apparatus that collects the gas given off by an aquatic plant at the mouth of a capillary tube, so its volume can be measured against a scale.

Inverse square law

Light intensity from a small source is proportional to 1/d², where d is the distance from the source.

Hydrogencarbonate indicator

A pH indicator that shows carbon dioxide concentration: yellow when it is raised, orange-red in equilibrium with air, purple when it is lowered.

Immobilised algae

Algal cells trapped in beads of sodium alginate, so equal numbers can be put into each tube of an experiment.

The compensation point

A plant is doing two opposite things at once. Photosynthesis takes carbon dioxide in and gives oxygen out; respiration does the reverse, and never stops. What you measure from outside is the difference between them.

Describe the drawing

A graph against light intensity with zero marked by the horizontal axis. A dashed curve shows gross photosynthesis rising from zero and flattening; a straight coral line shows respiration going on at the same rate whatever the light; and a solid cyan curve, the net rate, is the gap between them. The net curve starts below the axis in the dark, crosses zero at a marked point where photosynthesis and respiration are equal, and rises above it thereafter.

At dawn, light intensity is low and photosynthesis is slower than respiration, so the plant releases carbon dioxide overall: it is running at a loss, living off stores. As the light strengthens, photosynthesis speeds up until it exactly matches respiration. At that intensity there is no net gas exchange at all, which is the compensation point, and above it the plant begins to accumulate organic matter.

Compensation point

The light intensity at which the rate of photosynthesis exactly equals the rate of respiration, so there is no net exchange of carbon dioxide or oxygen.

Compensation period

The time taken from first light for a plant to reach its compensation point. None of the A-level specifications this site follows uses the term.

Species differ in where their compensation point sits, and it explains a good deal about where they grow. A shade plant on a woodland floor reaches compensation at a low intensity, so it can survive under a closed canopy; a sun plant of open ground needs far more light before it breaks even and would starve in the same spot. It also explains why seedlings under dense weeds die: they never spend enough of the day above their compensation point to build anything.

Applying limiting factors in a glasshouse

Commercial growers control all three factors, and the arithmetic decides whether doing so is profitable. The figures below are typical commercial values rather than fixed thresholds; the settings that pay vary with crop, season and site.

Carbon dioxide. Outdoor air is about 0.04 per cent carbon dioxide, which is well below what rubisco could use. Enriching a glasshouse to around 0.10 per cent typically lifts yield by a fifth to a third in tomatoes and cucumbers. The gas often comes from burning natural gas or propane, which conveniently supplies heat at the same time. Above roughly 0.15 per cent the benefit tails off and the plants may be damaged, so more is not better indefinitely.

Temperature. Most glasshouse crops are run somewhere between 20 and 25 °C. Warmer speeds the enzymes of the Calvin cycle, but it also speeds respiration, which spends the sugars the crop is supposed to accumulate, and past about 30 °C the stomata begin to close and rubisco takes up more oxygen. There is an optimum and it is not simply 'as hot as possible'.

Light. Supplementary lamps extend the effective day through a northern winter, which is why glasshouse tomatoes are available in February. Lamps are the expensive option, and a grower will only run them while the extra crop is worth more than the electricity.

Net primary productivity and transfer to consumers

Step back from the single leaf to a whole field, and the question becomes how much chemical energy the plants there capture in a year. Gross primary productivity is the total: everything fixed by photosynthesis. But the plants respire a substantial share of it themselves, commonly 20 to 50 per cent, and what is left is what actually accumulates as new plant material.

NPP = GPP − RNet primary productivity is gross primary productivity minus the energy lost in respiration by the producers. NPP is what is available to the organisms that eat them.

Describe the drawing

A downward cascade of energy. Two lines at the top give the sunlight arriving on a square metre in a year and the far smaller amount fixed as gross primary productivity. Beneath them three boxes, one for producers carrying their net primary productivity after respiration is subtracted, one for primary consumers and one for secondary consumers, each holding roughly a tenth of the energy of the box above. Arrows between the boxes are labelled with the percentage passed on, and side arrows show where the rest of the energy goes.

Productivity is a rate per unit area, so it is quoted as energy per square metre per year: kJ m⁻² year⁻¹. Both parts of the unit are needed, because a number of kilojoules alone cannot be compared between a field and a forest.

Most of the sunlight falling on a field is never captured. Some misses the leaves entirely and lands on soil; some is reflected off the waxy cuticle; some is transmitted straight through; much of it is at wavelengths the pigments do not absorb, the green band among them. What is absorbed usefully typically fixes one to three per cent of the incoming energy.

percentage transfer = (energy in the level ÷ energy in the level below) × 100Use the same units on top and bottom, and be clear which two levels you are comparing before you divide.

Between trophic levels the losses have four familiar causes. Not all of the plant is eaten: roots, wood and litter are left behind. Not all of what is eaten is digested; the indigestible part leaves as faeces. Some of what is absorbed is excreted, as urea in mammals. And a large share is respired to power movement, and in birds and mammals to maintain body temperature. Only what is left builds new tissue and is available to the next level.

That last cause explains a pattern worth quoting. Transfer to a mammal or a bird is often only 5 to 10 per cent, because keeping a constant body temperature is expensive; transfer to an insect or a fish can be considerably higher. It is also the argument behind eating lower down the chain: feeding grain to people rather than to cattle avoids one ninety-per-cent loss.

Where those numbers come from, and the consumer's version

Every figure above is an energy per unit area per year, but energy cannot be weighed directly. What is measured is biomass, which is then converted.

Biomass is measured as dry mass, because fresh mass is mostly water and the water content of a sample varies with the weather on the morning it was cut. A sample is dried in an oven at around 80 °C and reweighed repeatedly until the mass stops falling, and that constant mass is the figure used. Waiting for constant mass is the whole technique: weigh once and you have measured how damp the sample was.

Turning that dry mass into energy needs a calorimeter. A known dry mass is burned in oxygen inside a sealed vessel surrounded by a known volume of water, and the temperature rise of the water gives the energy released. Divide by the mass and you have the energy per gram, which scales up to the kJ m⁻² year⁻¹ the tables quote. Neither step leaves the sample usable afterwards, so a figure of this kind is obtained once from a set of organisms and never again from those same ones.

Consumers have their own productivity expression. A herbivore does not photosynthesise, so its production starts from the energy it ingests and subtracts the energy it does not retain.

N = I − (F + R)Net production of a consumer is the chemical energy in the food it ingests, minus the energy lost in faeces and urine, minus the energy lost in respiration. What is left is new tissue, and only that is available to the next trophic level.

The bracket is part of the expression. F and R are subtracted together because both are losses from the same intake. Writing N = I − F + R adds the respiratory loss back in and, whenever R exceeds F, gives a net production larger than the energy ingested, so a value of N greater than I indicates the bracket has been dropped.

Pyramids of numbers, biomass and energy

A food chain can be drawn as a pyramid: one horizontal bar for each trophic level, producers at the base, each bar as wide as the quantity at that level. Pearson Edexcel's Biology B names three kinds, and they measure different things.

A pyramid of numbers counts the individuals at each level in an area. It is the easiest to obtain: counting needs no special equipment and leaves the organisms alive. It takes no account of size, though, so one oak counts the same as one caterpillar, and a single large producer feeding thousands of herbivores gives a pyramid with a narrow base, inverted at the bottom. Parasites do the same higher up, many fleas on one host. The numbers can also span so many powers of ten that the bars cannot be drawn to scale.

A pyramid of biomass gives the dry mass of the organisms at each level per unit area, at one time, in g m⁻². It allows for size, so the oak counts for its mass, and most are upright. Measuring dry mass means killing the organisms, so the figures are estimates from samples. The pyramid is also a snapshot, which hides how fast each level is replaced, and equal masses of different tissue can hold different amounts of energy: a gram of fat holds about twice the energy of a gram of carbohydrate.

A pyramid of energy gives the energy passing through each level per unit area per year, in kJ m⁻² year⁻¹: the productivity figures from earlier in this lesson. It can never be inverted, because every level gets its energy from the level below and loses most of it, and the efficiency of each transfer can be read straight off it. It is the hardest to obtain, needing biomass measured through a whole year and its energy found by calorimetry. All three share one difficulty: an omnivore feeds at more than one level and has to be divided between them.

Describe the drawing

Three ecological pyramids stacked one above the other, each with producers at the bottom. The pyramid of numbers for one oak tree has a narrow base of one tree under a wide bar of twenty thousand caterpillars and a narrow bar of four birds. The pyramid of biomass for open-water plankton is also inverted at its base: 5 grams of phytoplankton per square metre under 15 grams of zooplankton, with 3 grams of small fish above. The pyramid of energy for the same plankton narrows at every level, from 8000 to 960 to 110 kilojoules per square metre per year.

The plankton pair in the figure is the case to understand. When the sample is taken there are 5 g of phytoplankton per square metre under 15 g of zooplankton. That is possible because phytoplankton cells can divide within a day or so, and they are eaten about as fast as they grow, so over a year the producers make many times their own standing biomass. The energy pyramid for the same water is built on that production over the year, and it is upright.

Pyramid of numbers

A diagram of the number of individual organisms at each trophic level in an area.

Pyramid of biomass

A diagram of the dry mass of organisms at each trophic level per unit area, at one time.

Pyramid of energy

A diagram of the energy passing through each trophic level per unit area per year; it is never inverted.

Farming for a more efficient transfer

AQA's specification asks how production is affected by farming practices designed to increase the efficiency of energy transfer, and names two: simplifying food webs to reduce energy losses to non-human food chains, and reducing respiratory losses within a human food chain. OCR asks for the same idea as the ways human activities can manipulate the transfer of biomass through ecosystems.

A field of wheat is the base of a food web. Weeds compete with the crop for light, water and mineral ions, so some of the sunlight that wheat could have fixed is fixed by plants nobody harvests. Insects and fungi eat or infect the crop, and the energy in what they take passes into non-human food chains. Herbicides remove weeds, insecticides and fungicides control pests, and biological control does the same job with a predator or parasite of the pest. Each cuts the energy lost to non-human food chains, so a larger share of the net primary productivity ends up in the harvested crop.

In livestock the loss to cut is respiration, R in N = I − (F + R). Animals kept in warm sheds lose less heat to their surroundings, so they respire less to keep their body temperature up. Animals kept in pens move less, so less energy goes on muscle contraction. Both leave more of the energy ingested as net production, which is growth. Feed that is easily digested and rich in protein cuts F as well, and animals are slaughtered young, while most of what they eat still goes into growth rather than into maintaining an adult body.

Each method has costs as well as a gain in yield. Herbicides and pesticides remove species that other wildlife depends on, and pests evolve resistance to them. Keeping animals indoors and confined raises welfare concerns, and disease spreads quickly between animals kept close together. An evaluation answer names the gain in energy transfer and at least one cost.