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Paper: Temporally varying natural mortality: Sensitivity of a virtual population analysis and an exploration of alternatives

The paper

Temporally varying natural mortality: Sensitivity of a virtual population analysis and an exploration of alternatives

by

Shanae Allen, William Satterthwaite, David Hankin, Diana Cole and Michael Mohr

will appear in Fisheries Science, and is available online early at http://www.sciencedirect.com/science/article/pii/S0165783616302958

Abstract:

Cohort reconstructions (CR) currently applied in Pacific salmon management estimate temporally variantexploitation, maturation, and juvenile natural mortality rates but require an assumed (typically invariant)adult natural mortality rate (dA), resulting in unknown biases in the remaining vital rates. We exploredthe sensitivity of CR results to misspecification of the mean and/or variability of dA, as well as the potentialto estimate dAdirectly using models that assumed separable year and age/cohort effects on vital rates(separable cohort reconstruction, SCR). For CR, given the commonly assumed dA= 0.2, the error (RMSE) inestimated vital rates is generally small (≤ 0.05) when annual values of dAare low to moderate (≤ 0.4). Thegreatest absolute errors are in maturation rates, with large relative error in the juvenile survival rate. Theability of CR estimates to track temporal trends in the juvenile natural mortality rate is adequate (Pearson’scorrelation coefficient > 0.75) except for high dA(≥ 0.6) and high variability (CV > 0.35). The alternativeSCR models allowing estimation of time-varying dAby assuming additive effects in natural mortality,fishing mortality, and/or maturation rates did not outperform CR across all simulated scenarios, and areless accurate when additivity assumptions are violated. Nevertheless an SCR model assuming additiveeffects on fishing and natural (juvenile and adult) mortality rates led to nearly unbiased estimates of allquantities estimated using CR, along with borderline acceptable estimates of the mean dAunder multiplesets of conditions conducive to CR. Adding an assumption of additive effects on the maturation ratesallowed nearly unbiased estimates of the mean dAas well. The SCR models performed slightly betterthan CR when the vital rates covaried as assumed. These separable models could serve as a partial checkon the validity of CR assumptions about the adult natural mortality rate, or even a preferred alternativeif there is strong reason to believe the vital rates, including juvenile and adult natural mortality rates,covary strongly across years or age classes as assumed.

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Publications

New paper by Eleni, Rachel, Byron and colleagues

The Annals of Applied Statistics
2016, Vol. 10, No. 3, 1572–1589
DOI: 10.1214/16-AOAS949
© Institute of Mathematical Statistics, 2016

OPEN MODELS FOR REMOVAL DATA

BY ELENI MATECHOU, RACHEL S. MCCREA1, BYRON J. T. MORGAN,
DARRYN J. NASH AND RICHARD A. GRIFFITHS

University of Kent

Individuals of protected species, such as amphibians and reptiles, often
need to be removed from sites before development commences. Usually, the
population is considered to be closed. All individuals are assumed to (i) be
present and available for detection at the start of the study period and (ii) remain
at the site until the end of the study, unless they are detected. However,
the assumption of population closure is not always valid. We present
new removal models which allow for population renewal through birth and/or
immigration, and population depletion through sampling as well as through
death/emigration. When appropriate, productivity may be estimated and a
Bayesian approach allows the estimation of the probability of total population
depletion. We demonstrate the performance of the models using data on
common lizards, Zootoca vivipara, and great crested newts, Triturus cristatus.

Read the full paper here https://kar.kent.ac.uk/55734/

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Conferences/Meetings/Workshops, News

Model Averaging meeting

15th of September 2016, 2-4.45pm

Maths Lecture Theatre
School of Mathematics, Statistics and Actuarial Science
University of Kent

Jointly organised by the Environmental Statistics Section of the RSS and the East Kent local RSS group

The meeting is free and open to all but please register your intention to attend (for hospitality purposes)

Doodle poll

Meeting organiser: Dr Eleni Matechou

Programme:

  • Professor Richard Chandler, UCL, 2-2.45pm
The interpretation of climate model ensembles
Almost all projections of future climate, and its impacts, rely at some level on the outputs of numerical models (simulators) of the climate system. These simulators represent the main physical and chemical (and, in some cases, biological) processes in the atmosphere and oceans. However, different simulators give different projections of future climate – indeed, the choice of simulator can be the dominant source of uncertainty in some applications. It is therefore becoming common practice to consider the outputs from several different simulators when making and using climate projections. The question then arises: how should the information from different simulators be combined? There are many challenging statistical issues here. Two key ones are (a) that simulators cannot be considered as independent (for example, many of them share common pieces of computer code); and (b) that no single simulator is uniformly better than another so that simple techniques, such as assigning weights to simulators, are not defensible. This talk will review the issues involved and present a Bayesian framework for resolving them. The ideas will be illustrated by considering projections of future global temperature. The talk is based on joint work with Marianna Demetriou.

 

  • Professor Jonty Rougier, University of Bristol, 2.45-3.30pm
Ensemble averaging and mean squared error
In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process.  It is an interesting observation that the ensemble mean often out-performs at least half of the ensemble members in mean squared error (measured with respect to observations).  This despite the fact that the ensemble mean is typically ‘less physical’ than the individual ensemble members (the state space not being convex).  In fact, as demonstrated in the most recent IPCC report, the ensemble mean often out-performs all or almost all of the ensemble members.  It turns out that that this is likely to be a mathematical result based on convexity and asymptotic averaging, rather than a deep insight about climate simulators.  I will outline the result and discuss its implications.

 

  • Coffee Break, 3.30-4pm

 

  • Dr Kate Searle, CEH, 4-4.45pm
Ecology isn’t rocket science….it’s harder: a practitioner’s perspective on the development of ecological analyses in complex systems
Understanding how environmental drivers influence the seasonal dynamics and abundance of species is key to developing predictive models for populations over space and time. This is particularly important in disease ecology where the phenology and seasonal abundance of vector species and hosts is a key determinant of disease risk. In this talk I will present a summary of collaborative research between ecologists and statisticians aimed at developing models that describe and predict the seasonal abundance of key insect vector species. These models were particularly challenging because insect vectors tend to show rapid rises and falls in population size across orders of magnitude, and may also be entirely absent from some regions at certain times of the year. Developing a model that is robust to these data-driven challenges required some novel statistical developments (and a lot of suffering on the part of both the ecologists and the statisticians!). This seminar will describe the evolution of our modelling approaches over a four-year study, culminating in a (reasonably) successful modelling framework for drawing inference and predictions in highly eruptive populations. Finally, I will highlight difficulties in applying model averaging techniques within the context of ecological models with typically low explanatory power.

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Papers

New paper by Eleni and colleagues in Environmental and Ecological Statistics

Bayesian analysis of Jolly-Seber type models;

Incorporating heterogeneity in arrival and departure

Eleni Matechou, Geoff K. Nicholls, Byron J. T. Morgan, Jaime A. Collazo, James E. Lyons

 

Abstract

We propose the use of finite mixtures of continuous distributions in modelling the process by which new individuals, that arrive in groups, become part of a wildlife population. We demonstrate this approach using a data set of migrating semipalmated sandpipers (Calidris pussila) for which we extend existing stopover models to allow for individuals to have different behaviour in terms of their stopover duration at the site. We demonstrate the use of reversible jump MCMC methods to derive posterior distributions for the model parameters and the models, simultaneously. The algorithm moves between models with different numbers of arrival groups as well as between models with different numbers of behavioural groups. The approach is shown to provide new ecological insights about the stopover behaviour of semipalmated sandpipers but is generally applicable to any population in which animals arrive in groups and potentially exhibit heterogeneity in terms of one or more other processes.

Read the full paper (open-access) Matechou_et_al_2016_Bayesian_analysis_of_Jolly_Seber_type_models_EES

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Conferences/Meetings/Workshops

NERC Advanced Training Course

Statistical models for wildlife population assessment and conservation

 

9-13 January 2017

 

University of Kent

 

Deadline for applications: 5pm on Friday 14th of October 2016.

We have 30 fully-funded places (inc. travel and accommodation) and priority is given to NERC-funded PhD students but if spaces remain we are able to offer the funded places to other PhD students and early-career researchers.

Please e-mail a completed Application Form to R.S.McCrea@kent.ac.uk.

Within the environmental sector there is currently a shortage of practitioners equipped with the statistical modelling skills to carry out reliable population assessments. Consequently, environmental impact assessments (EIAs) and development mitigation projects often use population assessment protocols that are not fit-for-purpose1. The skills shortage arises because (1) recent advances in statistical models for population assessment are largely confined to the academic sector with little penetration to the end-users; and (2) although many postgraduate programmes have a statistical modelling training component, this often fails to expose PhD students to new models in the area and the potential applications these have for conservation practice2. This training programme will provide a cohort of PhD students and early career researchers/practitioners with the relevant modelling skills required for a career that involves wildlife population assessment for conservation.

 

  1. Griffiths, Foster, Wilkinson and Sewell (2015). Science, statistics and surveys: a herpetological perspective. Journal of Applied Ecology. doi: 10.1111/1365-2664.12463
  2. McCrea and Morgan (2015). Analysis of capture-recapture data. Chapman & Hall/CRC Press, Florida.

 

Proposed programme of the course

 

The workshop will focus on ecological questions that arise in conservation practice and use real case study data. Training will include individual-based models, such as capture-recapture, but will also embrace scenarios more frequently used in EIA, such as batch-marked, presence/absence, site occupancy and counts. Applications will include newts, butterflies, birds, bees, beetles, ibex and bats. Each module will be accompanied by a practical computer session using R and each module builds on the last so that delegates build a portfolio of statistical skills.

 

Training outcomes:  By the end of the course, attendees will be able to:

  • construct, interpret and fit relevant stochastic models, use different methods of inference, understand the pros and cons of Bayesian and classical methods and the use of prior information;
  • personalise R code to undertake modelling of their own research data;
  • understand data needs for animal population assessments for EIAs and conservation;
  • analyse animal population data to meet both conservation and commercial needs.

Draft timetable:

 

Module 1: Background in statistics and R (Monday PM)
  • Likelihood and probability theory
  •  Bayesian inference
  • Basic model assessment (AIC/absolute GOF)
  • Practical session: Introduction

 

Plenary session and Round table discussions (Tuesday AM)

 

Module 2: Understanding statistical uncertainty (Tuesday PM)
  • Imperfect detection
  • Data types, relationships and summaries.
  • Introduction to data sets/case studies (bees, butterflies, newts, mallards etc)
  • Practical session: converting format of data and summarising complex data.

 

Module 3: Model fitting and assessment (Wednesday AM+PM)
  • Estimating abundance
  • M0,Mtbh, removal
  • CR/RR
  • Occupancy
  • Practical session: model fitting, optimisation, use of packages.

 

Module 4: Modern challenges (Thursday AM)
  • Citizen science data
  • Small/sparse data and big data issues
  •  Cost-effectiveness in study design and statistical power.
  • Informative prior information.
  • Practical session: power analyses and adapting models

 

Module 5: Advanced stochastic modelling (Thursday PM)
  • modelling movement
  •  state uncertainty
  • species interaction
  • spatial models
  • integrated modelling
  • Practical session: use of Rjags, Bayesian graphical models using MCMC.

 

One-to-one consultation sessions (Friday AM)

 

Module 6: Advanced aspects of R (Friday AM)
  • Practical session: self-lead worksheets
  • Multistate examples
  • PR diagnosis
  • Diagnostic GOF testing
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Conferences

SE@K at ISEC

Byron, Diana, Eleni, Emily, Ming and Takis attended the International Statistical Ecology Conference in Seattle, 28th June to 1st July.

On 28th June Eleni talked about Open models for removal data, in a contributed session on Abundance Estimation. Talk Slides

talk1

In the same session Emily talked about Extensions of recent models for butterfly abundance.

On 29th June Byron gave a Plenary talk with the title Citizen Science, Trick or Treat.

Also on 29th June Takis gave a talk on Efficient, flexible estimation of time to decay signs in indirect survey methods, in the second contributed session on Abundance Estimation.

In the same session Ming gave a talk on New removal approaches for reptile and amphibians.

Then Eleni gave her second talk on Count data collected using a robust design, in the third session on Abundance Estimation. Talk Slides

talk2

Later the same day Diana gave a talk on Extensions to the Hybrid Symbolic-Numeric Method for investigating identifiability in a contributed session on Capture-Recapture. Talk Slides

DianaTalkimage

 

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Papers

Paper: Parameter redundancy in discrete state-space and integrated models

Diana and Rachel’s Paper, Parameter redundancy in discrete state-space and integrated models, is available online early in the Biometrical Journal at http://onlinelibrary.wiley.com/doi/10.1002/bimj.201400239/abstract

Abstract: Discrete state-space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as non-identifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state-space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state-space models using discrete analogues of methods for continuous state-space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.

 

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