Richard Melville Cormack is one of the giants who developed the theory of mark-recapture. Referring to his key paper in 1964, and the papers published back-to-back in 1965 by George Jolly and George Seber, the “Cormack–Jolly–Seber model” is central to the development of mark-recapture methods for estimating survival.

Richard was born on 12 March 1935. His father was Principal of Stow College of Engineering in Glasgow. From the age of 7, Richard attended Glasgow Academy, and later entered directly into the second year at King’s College, Cambridge, intending at the time to be a theoretical astronomer. He secured first class honours in Special Mathematics from London as an external student in 1954, and second class honours in Mathematics from Cambridge in 1955. After changing direction, he left Cambridge in 1956 with a Distinction in the Diploma in Mathematical Statistics.

Richard’s PhD, undertaken while a lecturer at Aberdeen, was completed in 1961. Richard’s period at Aberdeen (1956–1966) coincided with a golden era for statistics there, and his colleagues included D. J. Finney, Bill Brass, Peter Fisk, David M. G. Wishart, Michael Sampford, Robert Curnow, George Jolly and Andrew Rutherford (the last four being members of the ARC Unit of Statistics). In common with a number of these colleagues, he moved to Edinburgh in 1966, holding a Senior Lectureship there until 1972, when he became the first Professor of Statistics at St Andrews.

Richard’s groundbreaking contributions to mark-recapture in the early 1960s continued when he addressed the issue of heterogeneity in capture probabilities, publishing a test for heterogeneity in Biometrics in 1966. Then in 1972, in another Biometrics paper, he showed the logic behind capture-recapture estimates, making the methods more accessible and understandable to the user community. In 1981, jointly with Philip North, Richard published important insights into mark-recovery models. His work on log-linear models for mark-recapture led to papers in Biometrika in 1984 (with Ron Sandland) and 1991 (with Peter Jupp), and in Biometrics in 1989, and, additionally, to four book chapters. There was also a sequence of Biometrics capture-recapture papers in the 1990s: on modelling covariates (1990), on interval estimation (1992) and on variance estimation (1993). After retirement in 1994, his publications in mark-recapture were mostly as co-author in epidemiology studies.

Richard also published on other diverse topics, often with scientists from other disciplines. His 1971 review of classification, read to the Research Committee of RSS and later appearing in JRSS A, is a classic, and while his 1988 exposition on statistical challenges in the environmental sciences (also in JRSS A) has had substantially less impact, it too showed his characteristic incisiveness. His contributions to a wide range of committees, working groups, visiting groups and scientific organisations (including council member for NERC and the Freshwater Biological Association) were substantial. He was elected a member of the ISI in 1962 and a Fellow of the Royal Society of Edinburgh in 1974. He held various offices within the Biometric Society, as Secretary of the British Region 1970–1977, Regional President 1990–1992 and President of the International Society 1980–1981. He served on the Council and various committees of the Royal Statistical Society.

Richard married Edith Whittaker on 1st September 1960, at King’s College Chapel, Aberdeen. Edith is a plant ecologist, and a past chairperson of the Fife and Kinross Branch of the Scottish Wildlife Trust and of the Friends of St Andrews Botanic Garden; she was also a founding member of the Garden’s Education Trust. Their son Andrew is a European Chartered Engineer working for the JANET network, while their daughter Anne is a Marketing Manager.

Photography has been a passion of Richard’s for many decades. He was a lecturer and judge for 40 years for the Scottish Photographic Federation, and was placed on their roll of honour. He has held exhibitions in Dundee (Land of the Berbers), St Andrews (Growth and Form) and Aberdeen (Walking in the North), and has given many talks.

Richard firmly established the University of St Andrews as a centre for statistical ecology, a strength that continues today.

In a career spanning more than 50 years, George Arthur Frederick Seber has made significant contributions in many areas of statistics as well as foundational work in capture–recapture modeling. Seber was born in 1938 in Australia to New Zealand parents and moved back to New Zealand where he completed almost all of his schooling. After graduating with bachelors and masters degrees from the University of Auckland, Seber studied for his Ph.D. at Manchester on a Commonwealth Scholarship. In his first year, he was supervised by John Darroch with David Silvey taking over supervision for the final 18 months of the degree. Seber’s Ph.D. thesis was remarkably fruitful leading to three papers in Biometrika, two in the Annals of Mathematical Statistics and one in the Journal of the Royal Statistical Society B. The topics covered were broad mixing foundational work on linear model theory with capture–recapture problems. His solution to the multi-sample single recapture problem anticipated the general solution to the open population problem that Seber published in 1965 concurrent with the work of George Jolly.

Seber has been a prolific writer of books including classical texts on the linear model and nonlinear regression. His comprehensive book The Estimation of Animal Abundance appeared in two editions. He has recently completed four books and is working on a book on open population capture recapture.

Seber took up an invited personal Chair in Biometrics at the University of Otago in 1971, and then the foundational Chair in Statistics at the University of Auckland in 1973. Seber developed a remarkable statistics group built around people such as Jeffrey Hunter, Alan Lee, Alastair Scott, Chris Triggs and Chris Wild, all of whom went on to hold Chairs in Statistics and to head Departments of Statistics in New Zealand. Seber was elected a Fellow of the Royal Society of New Zealand (RSNZ) in 1997 and in 1999 was awarded the Hector Medal by the RSNZ.

We review developments from the late 1950s, starting with the work of John Darroch, that led to the models of Cormack [Biometrika 51 (1964) 429–438], Jolly [Biometrika 52 (1965) 225–247] and Seber [Biometrika 52 (1965) 249–259] that are commemorated in this volume. We emphasize some of the fundamental contributions that were pivotal and often ahead of their time. We look at how these early contributions helped to shape the field and illustrate important concepts in statistics, including sufficiency, ancillarity, partial likelihoods, missing data and model fitting in the presence of latent variables. We also identify two curiosities. The first is the long-held and mistaken belief that the maximum likelihood estimators for various capture–recapture models are in common. Using various notions of ancillarity, we show that the maximum likelihood estimators from partial models (like the Cormack–Jolly–Seber model) will in general differ from full likelihood approaches (such as the Jolly–Seber model). The second is the belief that model specification in terms of latent variables is a relatively recent advance. We highlight how Jolly (1965) used a state-space model to describe the problem, using latent variables to separate the capture and mortality processes. We show how Markov chain Monte Carlo can be used to fit this model and how it relates to other capture–recapture models specified in terms of latent variables.

The models of Cormack, Jolly and Seber (CJS) are remarkable in providing a rich set of inferences about population survival, recruitment, abundance and even sampling probabilities from a seemingly limited data source: a matrix of 1’s and 0’s reflecting animal captures and recaptures at multiple sampling occasions. Survival and sampling probabilities are estimated directly in CJS models, whereas estimators for recruitment and abundance were initially obtained as derived quantities. Various investigators have noted that just as standard modeling provides direct inferences about survival, reversing the time order of capture history data permits direct modeling and inference about recruitment. Here we review the development of reverse-time modeling efforts, emphasizing the kinds of inferences and questions to which they seem well suited.

Sparked by the need to inform the response to the spread of HIV/AIDS in drug-injecting populations in the 1980s and the desire to base local, national and international responses to tackling drug use in the 1990s on solid epidemiological data, the mark-recapture method has increasingly been used to estimate the prevalence of drug use. Richard Cormack provided support and advice to some of the first United Kingdom and European studies to estimate drug use prevalence in this way. The approach he outlined, using macros that he developed, has led to the mark-recapture method being used to systematically assess the use of drugs such as heroin or other opioids in the United Kingdom and across Europe. We review the development of the method when applied to estimating the size of drug-using populations, including the use of Bayesian methods. We discuss its limitations and various criticisms that have been voiced.

We consider count data modeling, in particular, the zero-truncated case as it arises naturally in capture–recapture modeling as the marginal distribution of the count of identifications of the members of a target population. Whereas in wildlife ecology these distributions are often of a well-defined type, this is less the case for social and medical science applications since study types are often entirely observational. Hence, in these applications, violations of the assumptions underlying closed capture–recapture are more likely to occur than in carefully designed capture–recapture experiments. As a consequence, the marginal count distribution might be rather complex. The purpose of this note is to sketch some of the major ideas in the recent developments in ratio plotting and ratio regression designed to explore the pattern of the distribution underlying the capture process. Ratio plotting and ratio regression are based upon considering the ratios of neighboring probabilities which can be estimated by ratios of observed frequencies. Frequently, these ratios show patterns which can be easily modeled by a regression model. The fitted regression model is then used to predict the frequency of hidden zero counts. Particular attention is given to regression models corresponding to the negative binomial, multiplicative binomial and the Conway–Maxwell–Poisson distribution.

There has been a rapid growth in spatial capture–recapture (SCR) methods in the last decade. This paper provides an overview of existing SCR models and suggestions on how they might develop in future. The core of the paper is a likelihood framework that synthesises existing SCR models. This is used to illustrate similarities and differences between models.

The key difference between conventional capture–recapture models and SCR models is that the latter include a spatial point process model for individuals’ locations and allow capture probability to depend on location. This extends the kinds of inferences that can be drawn from capture–recapture surveys, allowing them to address questions of a fundamentally spatial nature, relating to animal distribution, habitat preference, movement patterns, spatial connectivity of habitats and dependence of demographic parameters on spatial variables.

State-based Cormack–Jolly–Seber (CJS) models have become an often used method for assessing states or conditions of free-ranging animals through time. Although originally envisioned to account for differences in survival and observation processes when animals are moving though various geographical strata, the model has evolved to model vital rates in different life-history or diseased states. We further extend this useful class of models to the case of multivariate state data. Researchers can record values of several different states of interest, for example, geographic location and reproductive state. Traditionally, these would be aggregated into one state with a single probability of state uncertainty. However, by modeling states as a multivariate vector, one can account for partial knowledge of the vector as well as dependence between the state variables in a parsimonious way. A hidden Markov model (HMM) formulation allows straightforward maximum likelihood inference. The proposed HMM models are demonstrated with a case study using data from a California sea lion vital rates study.

Capture–recapture studies increasingly rely upon natural tags that allow animals to be identified by features such as coat markings, DNA profiles, acoustic profiles, or spatial locations. These innovations greatly increase the number of capture samples achievable and enable capture–recapture estimation for many inaccessible and elusive species. However, natural features are invariably imperfect as indicators of identity. Drawing on the recently developed Palm likelihood approach to parameter estimation in clustered point processes, we propose a new estimation framework based on comparing pairs of detections, which we term the trace-contrast framework. Importantly, no reconstruction of capture histories is needed. We show that we can achieve accurate, precise, and computationally fast inference. We illustrate the methods with a camera-trap study of a partially marked population of ship rats (Rattus rattus) in New Zealand.

Mark-recapture (MR) methods are commonly used to study wildlife populations. Taking advantage of modern genetics one can generalize from “recapture of self” to “recapture of closely-related kin”. Abundance and other demographic parameters of adults can then be estimated using, if necessary, only samples from dead animals (live-release is optional). This greatly widens the scope of MR, e.g. to commercial fisheries where large-scale tagging is impractical, and enhances the power of conventional MR studies where live release and tissue sampling is possible. We give explicit formulae for kinship (i.e., recapture) probabilities in general and specific cases. These yield a pseudo-likelihood based on pairwise comparisons of individuals in the samples. It is shown that the pseudo-likelihood approximates the full likelihood under sparse sampling of large populations. Experimental design is addressed via the principle of maximizing the Fisher information for parameters of interest. Finally, we discuss challenges related to kinship determination from genetic data, focusing on current limitations and future possibilities.

Peter Gavin Hall was born in Sydney, Australia, on 20th November, 1951, and grew up in the Sydney suburb of Oatley. He received a Bachelor of Science with first class honours from the University of Sydney in 1974, a Master of Science from the Australian National University in 1976 and a Doctor of Philosophy from the University of Oxford in 1976. In 1976–1978, he was Lecturer in Statistics at the University of Melbourne. During 1978–2006, he served as Lecturer, Senior Lecturer, Reader and Professor of Statistics at the Australian National University. He became Professor of Statistics at the University of Melbourne in 2006, Australian Laureate Fellow in 2012 and was Director of the Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers in 2014–2015. In 2005, he commenced a one-quarter professorial position at the University of California, Davis. Peter has published 4 books and more than 600 research articles. He has made seminal contributions concerning the bootstrap, rates of convergence, functional data analysis, martingale theory, measurement error models, nonparametric function estimation and smoothing parameter selection. Honours include the following: Officer of the Order of Australia; Fellow of the Australian Academy of Science, Fellow of the Academy of the Social Sciences in Australia, Fellow of the Royal Society of London, Fellow of the Institute of Mathematical Statistics and Fellow of the American Statistical Association; Corresponding Fellow of the Royal Society of Edinburgh, and Foreign Associate of the U.S. National Academy of Sciences; honorary doctorates from the Université catholique de Louvain, the Universidad de Cantabria, the University of Glasgow and the University of Sydney; the Committee of Presidents of Statistical Societies Award and the Guy Medal in Silver from the Royal Statistical Society. He married Jeannie Jean Chien Lo on 15th April, 1977. His mother, Ruby Payne-Scott, had a distinguished scientific career as the first woman in radio astronomy and her story is published as Under the Radar. The First Woman in Radio Astronomy: Ruby Payne-Scott (2009) Springer. In 2015, Peter was diagnosed with acute leukaemia. He passed away on 9 January, 2016, in Melbourne, Australia.

This conversation took place in Melbourne, Australia, on 11 March and 1 April, 2015.