“Ecological problems” for university and school students. Column in ComputerreOnline #49

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Dmytro Shabanov
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The teacher gives the schoolchildren a problem: – My shoe size is 36, I live on the 7th floor, and I commute to work at school on trolleybus 42. The question: how old am I? Vovochka raises his hand: – Twenty‑eight! – Well done, correct! Now explain how you got the answer. – Simple. I am fourteen, and my father says I’m a half‑idiot. Teaching any subject is closely linked to assessing students’ achievements. It is helpful when the learning object is formalized. For example, you teach schoolchildren to solve differential equations, and then you check whether they can do it or not. Nothing is more convenient for a teacher than a good problem book! But the sciences are different. Some knowledge is well tested by problems, others with difficulty, and some not at all. Yet they still have to be tested! Fortunately, nothing will stop a true methodologist… The time of the Unified State Exam (in Russia) and independent testing (in Ukraine) is approaching. School teachers, tutors, course instructors, and textbook authors in a general push teach unfortunate children to solve “ecological problems.” They are always included in tests. An example? A suitable (allowing several important circumstances to be shown) problem is posted here. A schoolgirl, a naive soul, asks: “Based on the rule of the ecological pyramid, determine and explain how many algae and bacteria are needed for a 400‑kg dolphin to grow and be able to exist in the Black Sea!!??” The seasoned teacher with “guru” status answered: “We construct an approximate food chain: phytoplankton (algae and bacteria) – zooplankton – fish – dolphin. The ecological pyramid rule states that only 10 % of the mass or energy of the previous link passes to the next link. We calculate from the dolphin. If it weighs 400 kg, the mass of the previous link – fish – would be 4 000 kg, i.e., 4 tonnes; the mass of zooplankton would be 40 tonnes, and algae accordingly 400 tonnes.” The “guru” answer is flawless from the point of view that the reproducing student will receive the highest grade. But I have questions. It is not that the term “phytoplankton” should not be decoded as “algae and bacteria.” Phytoplankton consists only of free‑floating algae in the water column, and among all bacteria only cyanobacteria are included. My questions relate to the “ecological pyramid rule.” Wikipedia explains it as follows: “The amount of plant material that forms the base of the food chain is roughly ten times greater than the mass of herbivorous animals, and each subsequent trophic level also has a mass ten times smaller. This rule is known as Lindeman’s rule, or the 10 % rule.” The impression is somewhat spoiled by the fact that this is nonsense. What to cite? The best Russian‑language ecology textbook – the two‑volume work by M. Bigon, J. Harper, and K. Townsend. On p. 192 of the second volume there is a summary of data on the consumption efficiency of herbivorous animals. It discusses the ratio of biomass consumed by predators (in this case herbivorous predators) to its total amount. In our textbook this quantity is called exploitation efficiency (as in Eugene Odom’s textbook). In any case, we learn that herbivores consume a relatively small share of plant production. In water this figure does not exceed 25 %, on land – 15 % (usually much less). Plant food (at least leaves) is a difficult‑to‑digest product. Cell walls made of cellulose hinder digestion, and it contains less energy than meat. Not all energy contained in leaves is assimilated by herbivores. The proportion of energy extracted from food is shown by assimilation efficiency. Bigon and co‑authors (in agreement with other sources) indicate that leaf assimilation efficiency is close to 50 %. Finally, not all energy obtained from food will be stored in the consumer’s biomass. The ratio of energy accumulated in production to its assimilated amount is called production efficiency (i.e., net production efficiency). On p. 194 in Bigon et al. we learn that for herbivorous insects it is about 40 %, and for mammals it is an order of magnitude lower (1–3 %). Now we can calculate how the production of herbivorous animals relates to plant production. This quantity is called overall ecological efficiency, or Lindeman efficiency. To compute it, multiply (as fractions, not percentages) exploitation efficiency, assimilation efficiency, and net production efficiency. If we talk about locusts feeding on leaves, Lindeman efficiency would be 0.15 × 0.5 × 0.4 = 0.03. Note: 3 % is the upper limit of Lindeman efficiency for terrestrial ecosystems! It is calculated for grasses, for which we assumed they consist entirely of leaves. If we performed the calculation for trees, we would have to account for a substantial amount of wood, which is hard for herbivores to access. And if we calculated Lindeman efficiency for mammals, it would be less than 1 %. What does Wikipedia write? “The amount of plant material … is roughly ten times greater than the mass of herbivorous animals.” As we have seen, a realistic estimate is not a ten‑fold difference but a hundred‑fold, and a 10 % level of plant production cannot be reached by leaf‑eating herbivores at all. One clarification. When calculating efficiencies we used energy units, while Wikipedia talks about “amount of matter.” Unfortunately, this distinction only widens the gap between Wikipedia’s calculations and reality. The fact is that one kilogram of animal flesh contains more energy than one kilogram of leaves. Of course, not all plant biomass is the same. Assimilation efficiency when feeding on wood is 15 %, while when feeding on fruits and seeds it can reach up to 80 %, but, of course, “amount of plant material” must not be calculated solely from fruits and seeds. Alright, are the calculations based on the “10 % rule” valid for the next levels? No, and they are no more meaningful than computing an average hospital temperature, including the morgue and the fever ward. To illustrate, I will propose a problem to readers. I invented it in the early ’90s, during the post‑Soviet collapse. Many people then earned their salary in the products of their enterprises. Imagine a vermiculture specialist (earth‑worm farmer). This person receives a salary in worms – regularly brings home a large sack. For a strange whim he does not want the worms. He faces a choice: feed these worms to chickens in the yard or to carp in a pond. One kilogram of chicken product (meat and eggs) is equivalent for him to one kilogram of carp product (meat and roe). He must choose the animals that will provide him with a greater amount of food per kilogram of worms. According to school logic, chickens are equivalent to carp. Students I give this problem to often cite that chickens grow faster than carp. But, of course, the answer is different. The basis for this problem is an anecdote about Walter Nernst, a classic of thermodynamics. Nernst kept carp as a hobby. He was told that it would be more interesting to raise chickens. He replied: “I raise animals that are in thermodynamic equilibrium with the environment. Raising warm‑blooded animals means heating the world at my own expense.” Per kilogram of food, carp will yield several times greater growth than chickens, which spend a substantial part of the obtained energy on heat production. Let us see what difference may exist between animals that actively maintain a constant body temperature and those in relative equilibrium with the environment. A titmouse eats one kilogram of insects. A boa eats a kilogram of sea pig. How much weight will they gain? An excellent student and a “guru” teacher will confidently answer: 100 grams each! Nothing of the sort, and not only because there are no “centigram” titmice. Assimilation efficiency for insect‑eating animals is 60 %, for meat‑eaters 90 %. Net production efficiency for small birds is 1 %, for large reptiles up to 75 %. The titmouse will gain 6 g (1000 × 0.6 × 0.01 = 6), and the boa – two‑thirds of a kilogram (1000 × 0.9 × 0.75 = 675). Let us touch another circumstance important for evaluating “ecological problems.” In the dolphin problem they asked how much phytoplankton is needed for it “to grow and be able to exist.” Dolphins, like most mammals, experience a sharp slowdown of growth after reaching sexual maturity, practically stopping. How much phytoplankton is needed for a dolphin that has reached its 400 kg and no longer grows? According to the logic of the discussed problems – none at all. The “dolphin addition” is zero, so it requires zero fish, zero zooplankton, and zero phytoplankton. When I was a schoolboy, this circumstance surprised me. I even shared my doubts with the coolest methodologist teacher in the city, who was supposedly preparing me for the republican Olympiad. She said I was reasoning incorrectly, but did not explain why (“Can’t you read? Count as it is written!”). I wonder, do the schoolchildren who now think of this question receive equally substantive answers? I wanted to write that I compose this column for them, but I was afraid. No! They might realize that the teaching‑methodological literature that trains them in common sense is in deep conflict with reality. The errors I discuss are not only characteristic of “Wikipedia.” The same is written in all school textbooks, in all ecology textbooks for non‑biological specialties, and even in textbooks for biology faculties of pedagogical institutes! Imagine a teacher who himself learned the “10 % rule” and for many years teaches his students to use this nonsense in classes, Olympiads, and testing. What will he say to an unlearned person proving that a 10 % transfer from plants to herbivores never occurs, and that any subsequent level can only happen by chance? Then the students of those teachers end up at university – for example, in my class. When I give them a test task shown in the figure, they do not dare to trust their own calculations! Wrongly. The numbers in the task are based on correct research results, and there are no errors in it.

One of the test tasks I use when teaching ecology. The diagram is constructed according to "Odum's square".

Thus, tasks on the "ecological pyramid rule", despite their prevalence, are simply a misunderstanding. They only impose false ideas on students. There is no "ecological pyramid rule" in scientific ecology; in science, there are the first and second laws of thermodynamics. They are sufficient to understand why a decreasing amount of energy is transferred from one level to another. The amount of energy dissipated depends on the nature of its transformations. And finally, a bonus: an example of the "ecological pyramid rule" from the repeatedly cited "Wikipedia" article. It is not invented by an unknown joker, but taken from a book written with savage seriousness: Urikova N.V., "Factors Affecting the Ecological State of a System". "Let one person be fed by 300 trouts for a year. For their feeding, 90 thousand frog tadpoles are needed. To feed these tadpoles, 27,000,000 insects are necessary, which consume 1,000 tons of grass per year. If a person eats plant-based food, all intermediate stages of the pyramid can be excluded, and then 1,000 tons of plant biomass can feed 1,000 times more people." Do you know that hippos come out to graze on land at night? Apparently, in the author's fantasies, frog tadpoles do something similar. Just imagine: night, trouts splashing in the distance. A column of ninety thousand tadpoles is moving across the meadow, devouring insects. A thousand "ecologists" are coming towards them under the cover of darkness. They graze on grass, which the unfortunate victims of the tadpoles will not get...

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Dmytro Shabanov
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The Wonders of Sexual Reproduction "Ecological Problems" for Students and Schoolchildren Altruism and Simpson's Paradox

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