Presence or absence: predicting the probability of population survival

Posted by Lloyd Stringer @lloydstringer2

With it being St Patrick’s day, I thought it appropriate to give you a little overview of one aspect of my research, population growth modelling, with a Paddy’s day theme.

Factoid- Student’s t-test was developed by William Sealy Gosset (publishing under the pseudonym Student) while working as a chemist at Guinness brewery.

Every year about this time, NZ experiences a mass migration of barrels of Guinness that require population management. Luckily, NZ has a biosecurity team of 4.7M people to help deal with this population outbreak (perhaps this isn’t what contributors to the Biosecurity 2025 document had in mind).

Guinness tanker

Developing a population growth model, is a key aspect to developing a management strategy. This isn’t readily available for some modelling targets, but luckily the biology of Guinness is well documented and experienced, so few assumptions are required.

While it does appear in hotels throughout the country for much of the year, it isn’t until we see the migration, that the shear overload causes additional pubs to sprout taps to dispense this nutritious bounty. During non-outbreak periods, population replacement approximately matches mortality. However, we’ve discovered that on March 17, during a peak outbreak time, population density displays exponential growth. It is a wonder that we don’t see masses of migrating Guinness pints moving about the landscape, but we find that nature has a unique way of dealing with the bounty.

lots of guinness poured

During times of plenty, particularly Paddy’s day, natural Guinness niches (pubs) produce music that is heard over a large area, and this brings in Guinness’ natural predator… Homo sapiens. The probability of H. sapiens being attracted to Guinness as a function of distance has been tested for quiet niches. During the Paddy’s day celebration, the number of individuals arriving at niches is 37 times greater than average. It is assumed that this increase in attraction range is due to the sound produced by the various Irish bands and clinking of glasses. Having this larger area of attraction increases the probability of Guinness being consumed, thus the probability of survival is reduced.

Psurvival-music = (1-Pconsumption)×Nconsumers_music/ha

With Nconsumers_music a function of the number of consumers expected to be attracted per ha with the increase in the attractive range of the niche with music over a quiet niche. We find that population growth changes from a predicted λ = 0.04 (without music) to λ = -0.002 (with music). If we start with an initial population of 1000 pints of Guinness, then we are likely to have 16 h before a musical pub runs dry.

drinking guinness

Of course, there will be variation around some of these estimates, especially climatic conditions. Canterbury for example has warm dry conditions predicted. This favours a rapid decline of the population (an additional 5%), further with Paddy’s day occurring on a Friday allowing for a sleep-in the following day, it is expected that the Guinness survival rate (warm and dry + sleep-in) will be 10% lower than λ = -0.002 estimated above to λ = -0.025, so population will be expected to only last ~3h.

By understanding a little about the potential growth rates of a population we can estimate the probability of survival of a population. It appears that for this year at least Guinness population will be managed naturally by the sleep-in, however, if pubs wish to increase the mortality rate the Guinness, increasing the ambient temperature of the pub will reduce Guinness survival rates.

Please note, many data were harmed during the writing of this piece.

Lloyd Stringer is a PhD student at the School of Biological Sciences at the University of Auckland, and scientist in the Biosecurity Group and Plant & Food Research, Lincoln. He is studying the effects of population management tools on insect Allee thresholds. He is supervised by Max Suckling, Jacqueline Beggs, and John Kean

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