Small populations

Introduction

Brief introduction on why small populations are of interest: how many gibbons in Semonggoh Nature Reserve? bears or clouded leopards in Kubah or Gading National Parks? What happens if a population is very small, say 2 or 3 animals? Will it survive? What if they’re all males, or all females? Pure chance has a role.

Dice game

The trifids game uses painted cubes (dice), with two black faces, two red faces and two yellow faces. It begins with a starting population (say, 5) and each throw represents a year. Each trifid has equal chances of dying (black face up), surviving (yellow) or surviving and having one baby (red). After each throw the black dice are removed and one extra dice added for each red one.

(Obviously the choice of colours and their meanings is arbitrary, but avoid colours which colour-blind students would have difficulty in distinguishing. The chance of dying must equal the chance of having one off-spring.)

To reinforce the idea of separate populations, we imagined a series of islands with a small number of trifids marooned on each (think of the islands formed when a reservoir fills up). Each 'island' was represented by a 'sticky' (a Post-It note or equivalent) on the whiteboard.

We began with a few throws of the dice using the Data Projector to make sure everyone understood how do it. 

Then students worked in pairs (one throwing and the other keeping score). Each run began with a population of 5, and continued for 20 throws (20 'years') or until the population falls to zero. The number of years that the population survived (up to a maximum of 20) is noted and written on a sticky on the whiteboard. (The first time we did this, we asked students to record and graph the size of the population year by year, but that proved a distraction from the main point of the game, so we dropped it later.) 

When each pair had tried this for 3 or 4 populations starting with 5 trifids, we grouped the stickies on the whiteboard to form a frequency histogram showing surviving populations vs time.

Computer simulation

This works in exactly the same way as the Trifids game with dice, except that it is automated (and uses a random number generator to throw the dice), so students can follow one population for 100 generations in a few milliseconds. Personally I think it is important to begin with the 'real' dice before going on to the computer simulation: people understand that the way a die falls is random, but random-number generation by a computer is not so obviously just a matter of luck. (And anyway they are pseudo-random numbers, not truly random.)

The simulation uses MS Excel and can be downloaded in .zip format here. See the ‘Explanations’ worksheet of the Excel file for more details.

Students again work in pairs at the computer, some pairs running simulations with 1, 5, 10, and 20 as the starting populations. Pairs recorded the number of years of survival for 20 trials, and then swapped their results so that each pair could build up a complete table on the ‘Summary’ spreadsheet and see a complete graph of probabilities.

Conclusion

Conclude from game and simulation that small populations are at risk of disappearing, even if ‘nothing goes wrong’; no population is 100% certain to continue for ever, but larger populations are more viable than small ones.