Once upon a time there was an algal cell. Her name was “x” and she lived all alone in a beautiful glass castle full of warm culture media in a bright room. Her castle was a conical shape, surmounted by a tall tower and she spent all day drifting around wherever the currents took her. But after some time living happily with all she needed, she started to get bored and, being a unicellular alga, she divided in order that she might have some company. Now she had a sister who was, confusingly, also called “x” and people who came and peered into their flask referred to them both as “2x” and remarked, condescendingly, how similar they both were, which was true as they were genetically identical. Being sisters, they soon had disagreements and stopped talking to each other and, in order to have someone to talk to, they both had to divide again. Now there were four sisters, all called “x” and most of their visitors referred to them as “4x”, except for one non-mathematical observer who got confused with so many cells all called “x”. He said “why?” and everyone said “y?”, so he said, “not ‘y’, ‘why’?” And the others all said “because” which didn’t answer his question but did stop him from asking any more questions.
The algal cells all lived happily in their flask full of culture media. Although there were now four of them, there were still plenty of nutrients for them and light still streamed in through the glass walls of her castle. Sometimes, x, x, x and x shared their dreams with each other. X dreamt of being carried away by Prince Charming, who would smother her with kisses (xxxxxx: very confusing) and make mad passionate love to her. X, x and x giggled when x told them her story although, in reality, the sex life of a unicellular alga usually involved a hasty coupling just as the pond dried out, leading to lots of mucus being produced and a long post-coital sleep in the mud after which their peace was disturbed by hordes of annoying zoospores. There was plenty of space in the glass castle and, as all this talk of sexual reproduction had made them excited, they all decided to divide again, and they named their sisters x, x, x and x. And, when the eight sisters had floated around, sunbathing and soaking up the delicious nutrients for a few hours, they all decided that they liked dividing, so they divided again. They had a discussion about what to call their sisters. X said that there were too many x’s but x disagreed and said that x is a good name for an algal cell. X and x agreed with x but the other two x’s sided with the first x. Eventually they got bored with arguing about names and decided to name their new sisters x, x, x, x, x, x, x and x. And, when they all divided again, they decided that changing their naming policy would be confusing, so their new sisters were named x, x, x, x, x, x, x, x, x, x, x, x, x, x, x and x. If anyone counted, they would probably find that there were now thirty-two cells, all called x. On their birthdays (which, as their doubling time was four hours, happened very frequently), they would receive a card from each sister, each signed with their name and two kisses. Sometimes two sisters would share a card, but that was confusing as the x who was celebrating her birthday was never sure if it was from x and x, each of whom had given her two kisses, or from x, x and x, each of whom had given her one kiss.
After a few more days, x (that is to say, the very first x) was floating around on a convection current when she felt a sudden chill. One of her sisters was floating between her and the light. No sooner had that sister drifted off, than another sister drifted into the light. X was cross. She felt that, as the matriarch of the algal colony, she had a right to soak up photons without interference from her sisters. She called over to x who was floating past, and told her not to block the light, only for x to call back that, technically, they were all matriarchs as the first x had divided into two and those two cells had also divided, so all the x’s, even the most recent generation (512 cells, all called “x”) were, in a way, matriarchs and all were genetically identical, which made individuality a problem and may be one reason why “phycology” is often confused with “psychology” by lay people. A few seconds later, the entire flask of algal cells were shouting at one another. X told x to get out of the light, only for x to shout at her to complain that she was using up more than her fair share of nitrogen. Her half-sister’s granddaughter shouted that she shouldn’t complain about x taking up too much nitrogen as nitrogen was not a limiting factor and it was actually phosphorus that x needed, and there was not enough of that because one of their sisters had just taken up the last molecule. So now x was not just in the shade, she was also hungry. So hungry, in fact, that she did not have enough energy to divide. All of her sisters, including x, x, x, x, x, x, x, x, x, x and x were in the same situation, and before too long none of them were dividing at all. They spent all their time complaining about each other. Those that had light but no nutrients argued with those that had nutrients but not enough light and those that had enough carbon or nitrogen said that according to the Redfield Ratio they were entitled to at least one atom of phosphorus for every fifteen molecules of nitrogen.
Poor x dreamt more than ever of being swept away by her gallant Prince Charming, even if that meant never seeing x, x, x or x ever again. Every time the convection currents took her to towards the glass walls of her castle she would look out and sigh deeply, hoping that she would see him riding towards her, dressed in a white coat and bearing either a long lance or, if that was not possible, a Pasteur Pipette. But then, being a poor planktonic cell, the convection currents would carry her away from the glass walls of her castle and she would no longer be able to see the world outside.
Finally, when life in the flask was getting so crowded that she would have to say “good morning x” 106 times every time she drifted through a millilitre of water, and she had almost given up hope of ever being rescued, she felt a gentle tug and then a great swirling, sucking sensation and she was swept into the narrow end of a Pasteur Pipette. “Heeeeeellllllp” she screamed, as all her sisters gradually receded into the distance, just before she passed out. She was plunged into a deep, deep sleep where she had a vivid dream of being plunged into a beautiful warm flask of fresh culture medium full of delicious nutrients and without any of her irksome sisters to bother her. It was, surely, a dream but when she slowly peered out through her eyespot, all she could see was beautiful clean water, without any other algal cells floating around. There was no sign of her Prince Charming but she was sure he would be along soon, to smother her with kisses (which were the only type of “x” she could contemplate without a shudder) after which she knew they would live happily, if not ever after, then at least until the next time that dX/dt = rX (1 – X/K)*.
– The End –
* Actually, the Verhulst equation of population dynamics is usually written as dN/dt = rN(1 – N/K) but “N” isn’t such a pretty name for an algal cell.