What it means for a factor to be limiting
Limiting factor
The factor in shortest supply at a given moment, which is holding the rate of a process back so that only increasing that factor increases the rate.
- Photosynthesis needs light, carbon dioxide and a suitable temperature all at once, and it can only run as fast as the least favourable of them allows.
- The limiting factor is whichever of them is furthest from its ideal level at that moment, because it is the one setting the ceiling on the rate.
- Only one factor is limiting at any given moment, and increasing any of the others has no effect at all while it stays that way.
- Increasing the limiting factor does raise the rate, and it keeps raising it until a different factor becomes the one in shortest supply.
- Once that happens, further increases in the first factor stop working and the second factor has to be raised instead.
- This is why speeding photosynthesis up in practice usually means raising two or three factors together rather than one on its own.
- On a bright but cold spring morning there is plenty of light, so temperature is the limiting factor and warming the plant is what raises the rate.
- In a warm, well-lit glasshouse the plant has light and warmth to spare, so carbon dioxide is usually the limiting factor because air holds so little of it.
- Deep inside a dense crop canopy the lower leaves are shaded by the ones above, so light is limiting for them even at midday.
- Water is a reactant too, but a plant short of water wilts and closes its stomata long before the shortage limits the reaction directly.
- A shortage of chlorophyll, caused by disease or by too little magnesium in the soil, can also hold the rate back whatever the conditions are.
How the limiting factor changes
- The limiting factor is not fixed; it changes as conditions change, so the same plant can be held back by different things at different times.
- Just before dawn there is no light at all, so no photosynthesis happens and the plant is only respiring.
- Through the early morning light intensity climbs quickly while the air is still cool, so light is limiting first and then temperature takes over.
- By the middle of a summer day both light and temperature are high, so carbon dioxide becomes the limiting factor.
- On a hot afternoon a plant short of water may close its stomata to reduce water loss, which cuts off the carbon dioxide supply and slows the rate further.
- Late in the evening light intensity falls away again and light becomes limiting for the second time that day.
- Across the seasons the pattern repeats on a longer scale, with temperature and day length limiting growth in a British winter and carbon dioxide limiting it on a bright summer day.
- This is why a crop grown outdoors in the United Kingdom puts on most of its biomass between late spring and late summer.
A tomato plant through one summer day
- At 555 a.m. the glasshouse is dark, so the rate is zero and the plant is respiring only.
- By 777 a.m. the light is climbing but the air is still at 12 ∘C12\ ^\circ\text{C}12 ∘C, so the rate is low and temperature is limiting.
- By 111111 a.m. the air has reached 25 ∘C25\ ^\circ\text{C}25 ∘C and the light is bright, so the plant is drawing carbon dioxide out of the air faster than it can diffuse in, and carbon dioxide is limiting.
- Opening a vent to let fresh air in raises the rate, while switching a lamp on at that moment would make no difference at all.
Reading graphs with more than one curve
- A graph that shows the interaction of two factors carries more than one curve, and each curve was measured at a different fixed level of the second factor.
- A graph of rate against light intensity, for instance, might carry one curve at 0.04%0.04\%0.04% carbon dioxide and a second at 0.4%0.4\%0.4% carbon dioxide.
- Along the steep part of any curve, the factor plotted on the horizontal axis is the limiting factor, because raising it raises the rate.
- Where a curve flattens into a plateau, the factor on the horizontal axis has stopped being limiting and the second factor has taken over.
- The height of a plateau tells you how much the second factor is allowing, so the curve measured with more carbon dioxide plateaus at a higher rate.
- The plateau on the upper curve also begins at a higher light intensity, because the plant can keep making use of extra light for longer before carbon dioxide runs short.
- To name the limiting factor at any labelled point, look at whether the curve is still rising there or has already levelled off.
- If it is still rising, the factor on the axis is limiting; if it has levelled off, the factor that differs between the curves is limiting.
- Two curves that lie on top of one another over the first stretch and only separate later show that the second factor was not limiting at low values of the first.
Working through a two-curve light-intensity graph
- Two curves show the rate of photosynthesis against light intensity, one at 0.04%0.04\%0.04% carbon dioxide and one at 0.4%0.4\%0.4%.
- Both curves rise together along the first steep stretch, so light is the limiting factor for both and the extra carbon dioxide is making no difference yet.
- The lower curve flattens at a rate of 202020 arbitrary units, which means carbon dioxide has become limiting for it at that point.
- The upper curve keeps rising and only flattens at 454545 units, because the higher carbon dioxide concentration lets the plant use more of the light.
- The difference between the plateaus is 45−20=2545 - 20 = 2545−20=25 units, and that gain came entirely from the tenfold increase in carbon dioxide.
- At a light intensity beyond both plateaus, adding more light does nothing to either curve, so the answer to what is limiting there is carbon dioxide.
Controlling the factors to raise crop yield
- A commercial grower controls all three factors at once inside a glasshouse or polytunnel, so that none of them is holding the crop back for long.
- Artificial lighting extends the working day and keeps the rate up in dull weather and through a British winter.
- Heaters and thermostats hold the temperature near the optimum, and ventilation stops it climbing past the point where enzymes start to denature.
- Carbon dioxide enrichment raises the concentration well above the 0.04%0.04\%0.04% in ordinary air, which is often the single largest gain available.
- A paraffin or propane burner is a common way of doing this because it raises the temperature and releases carbon dioxide at the same time, dealing with two factors from one piece of equipment.
- A faster rate of photosynthesis means more glucose, so more biomass, so a larger yield of fruit or leaf that the grower can sell.
- Controlling the conditions also lets a crop be grown out of season, when the price it fetches is higher.
- None of it is free, though, because lamps, heat and carbon dioxide all cost money, and the extra crop has to be worth more than the extra cost.
- A grower therefore aims for the most profitable rate rather than the fastest possible one, and will let a factor stay slightly limiting if removing that limit costs more than the extra crop earns.
- This is a straightforward comparison to make: if enrichment costs an extra £900\pounds 900£900 per week and lifts the crop's value by £1400\pounds 1400£1400 per week, it is worth doing.
Answering interaction and graph questions
- Name the limiting factor explicitly, because an answer that says the rate levels off without saying why gains little.
- Check whether the curve is still rising or already flat at the point the question names, since that is what identifies the limiting factor.
- Say that the second factor has become limiting when you explain a plateau, and name which factor it is.
- Explain a higher plateau by naming the factor that was increased and stating that it had been limiting the lower curve.
- Bring cost into an evaluation question about a grower, because a yield answer with no mention of cost misses the balance the question is asking for.
- Read values off both axes with their units when a question asks you to compare two curves at a stated point.
- State what is meant by a limiting factor.
- Explain why increasing light intensity does not always increase the rate of photosynthesis.
- Explain which factor is most likely to be limiting in a warm, brightly lit glasshouse and why.
- Describe what a higher plateau on a second curve tells you about the factor that was changed.
- Explain why a paraffin burner is a useful piece of equipment in a glasshouse.
- Explain why a grower may choose not to remove a limiting factor completely.