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Studying how population sizes change over time is an important part of biology. For example, the main goal in ecology is being able to predict and describe interactions between different populations and between populations and their environments. In infection epidemiology, we consider interactions between populations of hosts (e.g. humans) and populations of pathogens (e.g. viruses or bacteria). In genetic microbiology, observing how quickly a purified (isogneic, clonal) population of cells increases with time during a controlled laboratory experiment can tell us a lot about the health of those cells. In both subjects, observations of population size, repeated over time, are robust and conceptually straightforward techniques to measure population behaviour. Although measurements of population size are simple, sometimes as simple as counting population numbers directly, they can be noisy or can be the final outcome of a set of complicated interactions between populations and their environments. Interpreting noisy or complex population dynamics (changes in population size over time) directly can be difficult. However, in such cases, mathematical modelling of population dynamics can help us to unravel the processes affecting populations. Mathematical models are essentially tools to help us make accurate and precise quantitative predictions based on hypotheses about how the world works. By comparing population dynamics predicted by a model with those observed experimentally, we can use statistics to make explicit, reproducible, fair, systematic claims about the plausibility of the hypotheses underlying the model.

In microbiological studies, one of the most fundamental tools for examining and comparing the health of populations is to isolate microbial populations and observe how they grow in a controlled environment. Researchers can choose a suitable specific environment in order to examine specific aspects of cell biology. For example, to study maximum achievable growth rates, you could grow cells at optimum temperature and humidity and on a substrate containing an ideal mixture of nutrients. Alternatively, to study the response of cells to a drug or to a poison, these substances can be added to the ideal growth substrate in order to measure their effect on growth rate.

Growth rate is a particularly informative phenotype (measurable characteristic of an organism) because it tells us a great deal about the health of cells. Outside of the laboratory environment cells are likely to be in competition with other cells for space and nutrients and are therefore faced with evolutionary selection pressure. Evolutionary fitness is the probability that genetic material from a population will be carried on to the next generation. Fitness is the characteristic of a population which is maximised by evolution. This probability of carrying on genetic material depends directly on the rate at which population members can proliferate relative to competitors: even marginally slow-growing populations will be rapidly out-competed.

An interesting feature of populations of cells, as distinct from general, ecological models, is that cell growth is almost always so vigourous that the “birth” of new cells is the overwhelmingly dominant force driving population behaviour. In populations of complex organisms, population size is usually strongly affected by death processes as well as birth. Another way of looking at this is that the lifespan of complex organisms is usually of the same order of magnitude as the time between reproduction, whereas the lifespan of cells is typically much greater than that.

- Modelling population growth
- Exponential
- Logistic
- Generalised logistic
- Stochastic logistic models
- Beware analytic solutions: important criterion for choosing parameter inference tool
- Competition in QFA
- The implications of observed levels of heterogeneity in real populations
- Population size monotonicity (unlike uncontrolled ecological populations)
- Stochastic models of growth

- Real data: capturing growth curves: QFA, spectrophotometer
- Fitting population models to real growth curve data
- Measuring growth phenotypes without a model
- Comparing growth rates (or any quantitative phenotype) to infer genetic interaction
- Small scale, quantitative experiment (high-throughput vs bench scale “reductionist”)
- Genome-wide