Gaussian processs framework for temporal dependence and discrepancy functions in Ricker-type population growth models

Marcelo Hartmann, Geoffrey R Hosack, Richard M Hillary, Jarno Petteri Vanhatalo

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Density dependent population growth functions are of central importance to population dynamics modelling because they describe the theoretical rate of recruitment of new individuals to a natural population. Traditionally these functions are described with a fixed functional form with temporally constant parameters and without species interactions. The Ricker stock-recruitment model is one such function that is commonly used in fisheries stock assessment. In recent years, there has been increasing interest in semi-parametric and temporally varying population growth models. The former are related to the general statistical approach of using semi-parametric discrepancy functions, such as Gaussian processes (GP), to model deviations of data around the expected parametric function. In the latter, the reproductive rate, which is a key parameter describing the population growth rate, is assumed to vary in time. In this work, we introduce how these existing Ricker population growth models can be formulated under the same statistical approach of hierarchical GP models. We also show how the time invariant semi-parametric approach can be extended and combined with the time varying reproductive rate using a GP model. Then we extend these models to the multispecies setting by incorporating cross-covariances among species with a continuous time covariance structure using the linear model of coregionalization. As a case study, we examine the productivity of three Pacific salmon populations. We compare the alternative Ricker population growth functions using model posterior probabilities and leave-one-out cross validation predictive densities. Our results show substantial temporal variation in maximum reproductive rates and reveal temporal dependence among the species, which have direct management implications. However, our results do not support inclusion of semi-parametric discrepancy function and they suggest that the semi-parametric discrepancy functions may lead to challenges in parameter identifiability more generally.
Original languageEnglish
JournalAnnals of Applied Statistics
Volume11
Issue number3
Pages (from-to)1375-1402
Number of pages28
ISSN1932-6157
DOIs
Publication statusPublished - Sep 2017
MoE publication typeA1 Journal article-refereed

Fields of Science

  • 112 Statistics and probability
  • Marginal likelihood
  • Model evidence
  • Population growth
  • Fisheries
  • Density dependence
  • Temporal dependence
  • Interspecific dependence

Cite this

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title = "Gaussian processs framework for temporal dependence and discrepancy functions in Ricker-type population growth models",
abstract = "Density dependent population growth functions are of central importance to population dynamics modelling because they describe the theoretical rate of recruitment of new individuals to a natural population. Traditionally these functions are described with a fixed functional form with temporally constant parameters and without species interactions. The Ricker stock-recruitment model is one such function that is commonly used in fisheries stock assessment. In recent years, there has been increasing interest in semi-parametric and temporally varying population growth models. The former are related to the general statistical approach of using semi-parametric discrepancy functions, such as Gaussian processes (GP), to model deviations of data around the expected parametric function. In the latter, the reproductive rate, which is a key parameter describing the population growth rate, is assumed to vary in time. In this work, we introduce how these existing Ricker population growth models can be formulated under the same statistical approach of hierarchical GP models. We also show how the time invariant semi-parametric approach can be extended and combined with the time varying reproductive rate using a GP model. Then we extend these models to the multispecies setting by incorporating cross-covariances among species with a continuous time covariance structure using the linear model of coregionalization. As a case study, we examine the productivity of three Pacific salmon populations. We compare the alternative Ricker population growth functions using model posterior probabilities and leave-one-out cross validation predictive densities. Our results show substantial temporal variation in maximum reproductive rates and reveal temporal dependence among the species, which have direct management implications. However, our results do not support inclusion of semi-parametric discrepancy function and they suggest that the semi-parametric discrepancy functions may lead to challenges in parameter identifiability more generally.",
keywords = "112 Statistics and probability, Marginal likelihood, Model evidence, Population growth, Fisheries , Density dependence, Temporal dependence, Interspecific dependence",
author = "Marcelo Hartmann and Hosack, {Geoffrey R} and Hillary, {Richard M} and Vanhatalo, {Jarno Petteri}",
year = "2017",
month = "9",
doi = "10.1214/17-AOAS1029",
language = "English",
volume = "11",
pages = "1375--1402",
journal = "Annals of Applied Statistics",
issn = "1932-6157",
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Gaussian processs framework for temporal dependence and discrepancy functions in Ricker-type population growth models. / Hartmann, Marcelo; Hosack, Geoffrey R; Hillary, Richard M; Vanhatalo, Jarno Petteri.

In: Annals of Applied Statistics, Vol. 11, No. 3, 09.2017, p. 1375-1402.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Gaussian processs framework for temporal dependence and discrepancy functions in Ricker-type population growth models

AU - Hartmann, Marcelo

AU - Hosack, Geoffrey R

AU - Hillary, Richard M

AU - Vanhatalo, Jarno Petteri

PY - 2017/9

Y1 - 2017/9

N2 - Density dependent population growth functions are of central importance to population dynamics modelling because they describe the theoretical rate of recruitment of new individuals to a natural population. Traditionally these functions are described with a fixed functional form with temporally constant parameters and without species interactions. The Ricker stock-recruitment model is one such function that is commonly used in fisheries stock assessment. In recent years, there has been increasing interest in semi-parametric and temporally varying population growth models. The former are related to the general statistical approach of using semi-parametric discrepancy functions, such as Gaussian processes (GP), to model deviations of data around the expected parametric function. In the latter, the reproductive rate, which is a key parameter describing the population growth rate, is assumed to vary in time. In this work, we introduce how these existing Ricker population growth models can be formulated under the same statistical approach of hierarchical GP models. We also show how the time invariant semi-parametric approach can be extended and combined with the time varying reproductive rate using a GP model. Then we extend these models to the multispecies setting by incorporating cross-covariances among species with a continuous time covariance structure using the linear model of coregionalization. As a case study, we examine the productivity of three Pacific salmon populations. We compare the alternative Ricker population growth functions using model posterior probabilities and leave-one-out cross validation predictive densities. Our results show substantial temporal variation in maximum reproductive rates and reveal temporal dependence among the species, which have direct management implications. However, our results do not support inclusion of semi-parametric discrepancy function and they suggest that the semi-parametric discrepancy functions may lead to challenges in parameter identifiability more generally.

AB - Density dependent population growth functions are of central importance to population dynamics modelling because they describe the theoretical rate of recruitment of new individuals to a natural population. Traditionally these functions are described with a fixed functional form with temporally constant parameters and without species interactions. The Ricker stock-recruitment model is one such function that is commonly used in fisheries stock assessment. In recent years, there has been increasing interest in semi-parametric and temporally varying population growth models. The former are related to the general statistical approach of using semi-parametric discrepancy functions, such as Gaussian processes (GP), to model deviations of data around the expected parametric function. In the latter, the reproductive rate, which is a key parameter describing the population growth rate, is assumed to vary in time. In this work, we introduce how these existing Ricker population growth models can be formulated under the same statistical approach of hierarchical GP models. We also show how the time invariant semi-parametric approach can be extended and combined with the time varying reproductive rate using a GP model. Then we extend these models to the multispecies setting by incorporating cross-covariances among species with a continuous time covariance structure using the linear model of coregionalization. As a case study, we examine the productivity of three Pacific salmon populations. We compare the alternative Ricker population growth functions using model posterior probabilities and leave-one-out cross validation predictive densities. Our results show substantial temporal variation in maximum reproductive rates and reveal temporal dependence among the species, which have direct management implications. However, our results do not support inclusion of semi-parametric discrepancy function and they suggest that the semi-parametric discrepancy functions may lead to challenges in parameter identifiability more generally.

KW - 112 Statistics and probability

KW - Marginal likelihood

KW - Model evidence

KW - Population growth

KW - Fisheries

KW - Density dependence

KW - Temporal dependence

KW - Interspecific dependence

U2 - 10.1214/17-AOAS1029

DO - 10.1214/17-AOAS1029

M3 - Article

VL - 11

SP - 1375

EP - 1402

JO - Annals of Applied Statistics

JF - Annals of Applied Statistics

SN - 1932-6157

IS - 3

ER -