Astrid's abstract:

When students ask me about my research area, I often say it's "linear algebra (math 251) meets real analysis (math 212) in infinite dimensions". A monoid is a set with an associative binary operation and an identity (think the natural numbers). The associated algebra is generated by isometries acting on an infinite-dimensional space. I'll explain how this work and if time will talk about work with new monoids inside the famous Thompson group $F$.

John's abstract:

In this presentation I will highlight the importance of statistical modelling in three interesting applications, each done with researchers from the School of Biological Sciences here at VUW.

1. Invasive insects pose dangerous threats to natural ecosystems, endangered native taxa and human food supplies. In research that won the 2023 paper of the year award in the International Union for the Study of Social Insects' journal, we showed that, across 227 reported arthropod eradication attempts, the odds of successful eradication were almost 80% lower for social insects. Logistic regression modelling was the key statistical technique used. An editors' highlight article that accompanied our paper was titled, "The curse of invasive social insects".
2. Among social insects, many people's favourite is the honey bee. The Varroa mite is considered the greatest threat to apiculture worldwide. RNA interference (RNAi), using double-stranded RNA (dsRNA) as a gene silencing mechanism, has recently emerged as a next-generation strategy for mite control. In a 2024 paper, highlighted with a cover photo in Pest Management Science and currently downloaded over 12,100 times, we demonstrated that the majority of foundress mites exposed to either low or high doses of dsRNA failed to produce any offspring, while neither dose impacted pupal survival of the honey bees. Consequently, mite treatments using dsRNA have significant potential as an effective alternative to conventional methods for Varroa control, with broader implications for the utilization of RNAi as a next-generation tool in the management of pest species. A permutation-based analysis of variance (ANOVA) was the key statistical technique used.
3. The staghorn fern (Platycerium bifurcatum) is an epiphyte that lives in cooperative colonies whose members work together to build a communal water and nutrient store. These staghorn fern colonies are sometimes invaded by a related species, Zealandia pustulata, which causes sharp declines in the density and reproductive output of P. bifurcatum colonies. Using negative binomial hurdle models and beta regression as statistical tools, we investigated how invasion of staghorn nests affects the epiphytic distribution, growth and reproductive output of Z. pustulata along an elevational gradient on Lord Howe Island. It seems the invasion of P. bifurcatum nests alters the distribution of Z. pustulata, and also increases the rates of reproductive frond production, suggesting increased fitness in invasive individuals. Hence these two species of epiphytes interact in a novel way that is similar to 'social parasitism' in animals.