## Upcoming seminars in Statistics | Seminars in Mathematics |

### Ken Dodds

*AgResearch*

Date: Thursday 28 February 2019

Time: 11:00 a.m.

Place: Room241, 2nd floor, Science III building

Sequencing technology provides information on genomes including an individual’s genotype at a site with variation, such as single nucleotide polymorphisms (SNPs). To reduce costs, the sequencing protocol may be designed to interrogate only a subset of the genome (but spread across the genome). One such method is known as genotyping-by-sequencing (GBS). A genotype consists of the pair of genetic types (alleles) at a particular position. Each sequencing result delivers a read from one of the pairs, and so does not guarantee that both alleles are seen, even when there are two or more reads at the position. Methods for accounting for this issue will be described for several different analyses including the estimation of relatedness, parentage assignment, testing for Hardy Weinberg equilibrium and the description of the genetic diversity of a population. These methods have applications in plant and animal breeding, ecology and conservation.

### Murray Efford

*Department of Mathematics and Statistics*

Date: Thursday 7 March 2019

Time: 11:00 a.m.

Place: Room 241, 2nd floor, Science III building

he density of some animal populations is routinely estimated by the method of spatially explicit capture–recapture using data from automatic cameras, traps or DNA hair snags. However, data collection is expensive and most studies do not meet minimum standards for precision. Improved study design is the key to improved power. Simulation is often recommended for evaluating study designs, but it can be painfully slow. Another approach for evaluating novel designs is to compute intermediate variables such as the expected number of detected individuals E(n) and the expected number of recapture events E(r). Computation of E(n) and E(r) is deterministic and much faster than simulation. Intriguingly, the relative standard error of estimated density is closely approximated by the reciprocal of the square root of whichever is smaller, and for maximum precision E(n) is approximately equal to E(r). I show how these findings can be applied in interactive software for designing ecological studies.

### Simon Spencer

*University of Warwick*

Date: Thursday 14 March 2019

Time: 11:00 a.m.

Place: Room 241, 2nd floor, Science III building

Model fitting for epidemics is challenging because not all of the information needed to write down the likelihood function is observable, for example the times of infection and recovery are not usually observed. Furthermore, the data that are available from diagnostic tests may not be perfectly accurate. These considerations are typically overcome by applying computationally intensive data augmentation techniques such as Markov chain Monte Carlo. To make things even more difficult, most of the interesting epidemiological questions are best expressed as model selection problems and so fitting just one model is not sufficient to answer them. Instead we must fit a range of different models, each representing an important epidemiological hypothesis, and then make meaningful comparisons between them. I will describe how to overcome (most of) these difficulties to learn about the epidemiology of Escherichia coli O157:H7 in cattle. This is joint work with Panayiota Touloupou, Bärbel Finkenstädt Rand, Pete Neal and TJ McKinley.

### Cheryl Quinton

*AbacusBio Limited, Dunedin*

Date: Thursday 28 March 2019

Time: 11:00 a.m.

Place: Room 241, 2nd floor, Science III building

Genetic improvement programs typically include a breeding objective that describes the traits of interest in the program and their importance. A breeding objective function is built that calculates the overall genetic value for each individual in a population based on the aggregate of trait predictions of genetic merit and trait economic values (EV). Most breeding objective functions are built as linear functions. Linear EVs have several advantages for ease of implementation and common quantitative genetics calculations, but they may be over-simplifications for diverse populations that span a wide range of economic and biological conditions. We have been helping an increasing number of breeding programs by applying non-linear EV functions. In these cases, more complex functions such as quadratic, exponential, and combinations are built to calculate the contribution of an individuals’ trait value to the overall aggregate merit combining multiple traits. Although breeding objectives with non-linear EV functions are more complex to implement, they can provide more specific and more robust valuation of traits and therefore of each individuals' overall genetic value. In this presentation, we describe some non-linear EV functions for prolificacy, wool quality, dystocia, and maternal ability in sheep and cattle breeding objectives.