Bayesian Learning and Predictability in a Stochastic Nonlinear Dynamical Model

Bayesian inference methods are applied within a Bayesian hierarchical modelling framework to the problems of joint state and parameter estimation, and of state forecasting. We explore and demonstrate the ideas in the context of a simple nonlinear marine biogeochemical model. A novel approach is proposed to the formulation of the stochastic process model, in which ecophysiological properties of plankton communities are represented by autoregressive stochastic processes. This approach captures the effects of changes in plankton communities over time, and it allows the incorporation of literature metadata on individual species into prior distributions for process model parameters. The approach is applied to a case study at Ocean Station Papa, using Particle Markov chain Monte Carlo computational techniques. The results suggest that, by drawing on objective prior information, it is possible to extract useful information about model state and a subset of parameters, and even to make useful long-term forecasts, based on sparse and noisy observations

The functional response of a generalist predator

Peer reviewedPublisher PD

Assessing the Health of Richibucto Estuary with the Latent Health Factor Index

The ability to quantitatively assess the health of an ecosystem is often of great interest to those tasked with monitoring and conserving ecosystems. For decades, research in this area has relied upon multimetric indices of various forms. Although indices may be numbers, many are constructed based on procedures that are highly qualitative in nature, thus limiting the quantitative rigour of the practical interpretations made from these indices. The statistical modelling approach to construct the latent health factor index (LHFI) was recently developed to express ecological data, collected to construct conventional multimetric health indices, in a rigorous quantitative model that integrates qualitative features of ecosystem health and preconceived ecological relationships among such features. This hierarchical modelling approach allows (a) statistical inference of health for observed sites and (b) prediction of health for unobserved sites, all accompanied by formal uncertainty statements. Thus far, the LHFI approach has been demonstrated and validated on freshwater ecosystems. The goal of this paper is to adapt this approach to modelling estuarine ecosystem health, particularly that of the previously unassessed system in Richibucto in New Brunswick, Canada. Field data correspond to biotic health metrics that constitute the AZTI marine biotic index (AMBI) and abiotic predictors preconceived to influence biota. We also briefly discuss related LHFI research involving additional metrics that form the infaunal trophic index (ITI). Our paper is the first to construct a scientifically sensible model to rigorously identify the collective explanatory capacity of salinity, distance downstream, channel depth, and silt-clay content --- all regarded a priori as qualitatively important abiotic drivers --- towards site health in the Richibucto ecosystem.Comment: On 2013-05-01, a revised version of this article was accepted for publication in PLoS One. See Journal reference and DOI belo

Analysing the natural population growth of a large marine mammal after a depletive harvest

An understanding of the underlying processes and comprehensive history of population growth after a harvest-driven depletion is necessary when assessing the long-term effectiveness of management and conservation strategies. The South American sea lion (SASL), Otaria flavescens, is the most conspicuous marine mammal along the South American coasts, where it has been heavily exploited. As a consequence of this exploitation, many of its populations were decimated during the early 20th century but currently show a clear recovery. The aim of this study was to assess SASL population recovery by applying a Bayesian state-space modelling framework. We were particularly interested in understanding how the population responds at low densities, how human-induced mortality interplays with natural mechanisms, and how density-dependence may regulate population growth. The observed population trajectory of SASL shows a non-linear relationship with density, recovering with a maximum increase rate of 0.055. However, 50 years after hunting cessation, the population still represents only 40% of its pre-exploitation abundance. Considering that the SASL population in this region represents approximately 72% of the species abundance within the Atlantic Ocean, the present analysis provides insights into the potential mechanisms regulating the dynamics of SASL populations across the global distributional range of the species.Fil: Romero, Maria Alejandra. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue. Instituto de Biología Marina y Pesquera Almirante Storni; ArgentinaFil: Grandi, Maria Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Centro para el Estudio de Sistemas Marinos; ArgentinaFil: Koen Alonso, Mariano. Fisheries And Ocean Canada. Northwest Atlantic Fisheries Centre; CanadáFil: Svendsen, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue. Instituto de Biología Marina y Pesquera Almirante Storni; ArgentinaFil: Ocampo Reinaldo, Matías. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue. Instituto de Biología Marina y Pesquera Almirante Storni; ArgentinaFil: Garcia, Nestor Anibal. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Centro para el Estudio de Sistemas Marinos; ArgentinaFil: Dans, Silvana Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Centro para el Estudio de Sistemas Marinos; Argentina. Universidad Nacional de la Patagonia; ArgentinaFil: González, Raul Alberto Candido. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional del Comahue. Instituto de Biología Marina y Pesquera Almirante Storni; ArgentinaFil: Crespo, Enrique Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Centro Nacional Patagónico. Centro para el Estudio de Sistemas Marinos; Argentina. Universidad Nacional de la Patagonia; Argentin

Which future for the Hurunui? Combining choice analysis with stakeholder consultation

The future of the Hurunui River and its catchment has been hotly contested between those who seek to store and/or divert water from the river in order to increase agricultural production and those who would like to see the river undeveloped and the quality of natural resources in the river and catchment improved. The Canterbury Regional Council wished to develop an approach to manage catchment nutrient loads across the region in order to achieve the objectives of its Natural Resources Regional Plan (NRRP) for water quality and aquatic habitats. Our approach, combining stakeholder consultation with choice analysis, was developed and tested in the Hurunui catchment in 2010-2011. The policy objective of the choice experiment was to describe and quantify the preferences of Canterbury Region residents with respect to existing conditions (the status quo) and potential future land use and water quality scenarios for the catchment. It was envisaged that this quantitative information on preferences across the region would be used by policy makers at the same time as they considered the outcomes of the stakeholder deliberative process. At the conclusion of the consultation process there was ‘general acceptance’ of a future development strategy for the Hurunui catchment that would maintain water quality in the main river at 2005-2009 levels while improving the tributaries to 1990-1995 water quality. Results from the choice experiment are broadly supportive of this approach. Canterbury region residents would require substantial compensation (mean $244-$315 per household per year) before they would accept a decline in water quality in the main river or in the tributaries. Willingness to pay for improvements in the main river is lower with a mean of $25-$33 per house hold per year

Data limited fisheries : Incorporating expert knowledge into stock assessment

Stock assessment is a critical step in fisheries management, since it directly estimates reference points that help determine whether a population’s size is acceptable and subsequently, to set harvest levels. Therefore, many international agreements require that all exploited aquatic populations are assessed quantitatively. However, for the majority of the worlds’ harvested fish stocks, data is lacking. Such fisheries are often referred to as data-poor or data-limited and are a major challenge for stock assessment scientists and fisheries managers, since the traditional approaches to stock assessment cannot be implemented. The necessity to assess the status of all fisheries, led to the development of models tailored to data-limited situations. In this thesis, I first introduced the characteristics of data-limited fisheries, and then described the various quantitative indicators and models developed to assess them, some of which are widely used in real assessment schemes. I reviewed the approaches by their input requirements and their biological realism. Compared to the models used to assess data-rich stocks, models tailored to data-limited stock assessment contain a large degree of uncertainty and therefore, I recommended further exploration of the existing datalimited approaches. This thesis continued by focusing on a particular group of data-limited assessment methods, which are based on stock reduction analysis. Although such models can cope with low data availability, at the same time, they are particularly sensitive to the misspecification of relative stock status (expressed as the current biomass level relative to virgin biomass), a critical input requirement. However, stock status is unavailable for the majority of data-limited stocks. Therefore, I explored different sources of information used to estimate stock status under such circumstances. First, I considered the use of fisheries experts’ opinion and presented a method to elicit expert knowledge using a novel, user-friendly on-line application. To evaluate the experts’ ability to predict stock status, I compared the elicited distributions to stock statuses derived from data-rich models. In this work, I explored the performance of experts with different levels of experience in stock assessment, since scientific expertise is not evenly distributed throughout the world, and quantified how well they performed relative to each other. The results indicated that the true stock status is the most significant factor accounting for bias in expert opinions, followed by their experience level. Nevertheless, expert opinions are often used to inform management decisions and this thesis revealed that for data-limited stock assessment, expert elicited stock status priors potentially can be highly biased, leading to highly biased harvest recommendation levels. A way to overcome this issue is by calibrating expert judgment. To achieve this, my coauthors and I developed a hierarchical Bayesian model for expert calibration. The model’s main assumption is that experts’ biases vary as a function of the true value of the parameter, as identified in the expert elicitation experiment. Experts’ bias function was explicitly modeled, following the supra-Bayesian approach, using Gaussian processes to construct the prior, and the results of the expert elicitation experiment were used as calibration data to infer the posterior. The constructed models were tested both with simulated data and with the expert elicitation results. The tested models for expert judgment calibration, substantially improved stock status predictions compared to those that were uncalibrated and in comparison to vague uniform guesses, thereby demonstrating the value of calibration in minimizing expert bias. In the last article included in this thesis, uncalibrated and calibrated expert opinion derived stock status priors were compared to productivity and susceptibility (PSA) vulnerability scores and catch trend-derived (Boosted regression trees; BRTs) stock status priors. Furthermore, the performance of each of these methods was evaluated and compared to a commonly used prior that assumes a stock is at B40% (i.e. 40% of the virgin biomass). First, I evaluated the degree of bias in estimating true stock status and then, the effect of bias on the estimation procedure of overfishing limits (OFLs) in the specific assessment models for ten data-rich stocks. All, with the exception of fisheries experts with no experience in stock assessment, provided more accurate priors about stock status than the B40% rule. Experts with experience in stock assessment produced particularly informative and accurate priors, exemplifying their important role in the assessment procedure. Based on the performance evaluation and the data requirements for constructing a stock status prior, I recommended a procedure for selecting the most appropriate prior(s).Kalakantojen tilan arvioinnin tavoitteena on päätellä, onko kalakannan tila biologisesti hyvä ja asettaa tulevaisuuden kalastustavoitteet. Huoli maailman kalakantojen tilasta on johtanut kansainvälisiin sopimuksiin kalakantojen kestävästä käytöstä – näiden sopimuksien velvoitteiden täyttäminen edellyttää kalakantojen tilojen arvioimista. Useista kalakannoista ei kuitenkaan ole saatavilla arviointiin tarvittavia lähtötietoja – tällaisia kantoja kutsutaan ’dataköyhiksi’ kalakannoiksi. Dataköyhien kalakantojen arviointi ja sääntely on haastavaa, sillä perinteisiä arviointimenetelmiä ei lähtötietojen puuttuessa voida käyttää. Tästä johtuen on perinteisien arviointimenetelmien tilalle kehitetty erityisiä työkaluja dataköyhien kalakantojen arviointiin. Tässä väitöskirjassa esittelen aluksi dataköyhien kalakantojen tyypilliset piirteet sekä dataköyhien kalakantojen arviointiin kehitetyt ja yleisesti käytetyt menetelmät. Seuraavaksi tarkastelen esittelemiäni menetelmiä niiden vaatimien lähtötietojen sekä biologisen realismin näkökulmista. Verrattuna sellaisiin kantoihin, joista arvioinnin lähtötietoja on runsaasti saatavilla, voidaan dataköyhien kantojen arviointimenetelmien todeta olevan epävarmoja ja niiden jatkokehittely tarpeen. Väitöskirjassani keskityn erityisesti menetelmätyyppiin, jossa mallinnus perustuu kannan nykyisen sekä kalastamattoman biomassan suhteen perusteella määritettyyn kannan nykytilaan. Tällaisten menetelmien etuna on se, että niitä voidaan käyttää myös silloin, kun mallinnuksen lähtötiedot ovat rajalliset, mutta toisaalta ne ovat herkkiä kannan nykytilan määrityksen suhteen, mikä voi mahdollisesti johtaa liikakalastukseen. Koska useiden dataköyhien kalakantojen osalta kannan nykytilan arviointiin tarvittavat tiedot ovat puutteellisia, tarkastelen työssäni vaihtoehtoisia tiedonlähteitä. Selvitän asiantuntija-arvioiden käyttöä kannan tilan määrittämisessä uuden, käyttäjäystävällisen verkkosovelluksen avulla. Tulokset antavat viitteitä siitä, että kalakantojen arviointiin perehtyneet asiantuntijat kykenevät menestyksekkäästi määrittämään kannan nykytilan, kun taas toisaalta asiantuntijat, joilla ei ole kokemusta kannan arvioinnista usein yliarvioivat kalakannan nykytilan. Ottaen huomioon, että väitöskirjani perusteella asiantuntijoiden arviot eivät ole riippumattomia ja että toisaalta heidän näkökulmiaan usein kysytään kalastuksen sääntelystä päätettäessä, on asiantuntija-arvioita tarpeen kalibroida. Kehitimme yhteistyökumppaneideni kanssa hierarkkiseen Bayesilaiseen tilastolliseen päättelyyn perustuvan menetelmän, ja osoitimme, että sen avulla asiantuntijaarvioita voidaan huomattavasti tarkentaa verrattuna kalibroimattomiin arvioihin. Väitöskirjani viimeisessä osajulkaisussa kehittämämme menetelmän avulla kalibroituja ja kalibroimattomia nykytila-arvioita vertailtiin muiden dataköyhien kantojen nykytilan määritykseen kehiteltyjen menetelmien antamaan nykytiloihin. Menetelmiä verrattiin usein tehtyyn oletukseen, että kalakannan nykytila on noin 40% tasolla suhteessa kalastamattomaan biomassaan. Kaikkien tutkittujen menetelmien paitsi aikaisempaa kokemusta vailla olevien asiantuntijoiden todettiin tuottavat tarkemmat ennusteet kuin 40% oletus. Erityisesti kalakantojen arviointiin perehtyneet asiantuntijat tuottivat hyvin tarkkoja ennusteita, mikä korostaa asiantuntijatiedon roolia kalakantojen arviointimenetelmissä

A Bayesian approach to modelling field data on multi-species predator prey-interactions

Multi-species functional response models are required to model the predation of generalist preda- tors, which consume more than one prey species. In chapter 2, a new model for the multi-species functional response is presented. This model can describe generalist predators that exhibit func- tional responses of Holling type II to some of their prey and of type III to other prey. In chapter 3, I review some of the theoretical distinctions between Bayesian and frequentist statistics and show how Bayesian statistics are particularly well-suited for the fitting of functional response models because uncertainty can be represented comprehensively. In chapters 4 and 5, the multi- species functional response model is fitted to field data on two generalist predators: the hen harrier Circus cyaneus and the harp seal Phoca groenlandica. I am not aware of any previous Bayesian model of the multi-species functional response that has been fitted to field data. The hen harrier's functional response fitted in chapter 4 is strongly sigmoidal to the densities of red grouse Lagopus lagopus scoticus, but no type III shape was detected in the response to the two main prey species, field vole Microtus agrestis and meadow pipit Anthus pratensis. The impact of using Bayesian or frequentist models on the resulting functional response is discussed. In chapter 5, no functional response could be fitted to the data on harp seal predation. Possible reasons are discussed, including poor data quality or a lack of relevance of the available data for informing a behavioural functional response model. I conclude with a comparison of the role that functional responses play in behavioural, population and community ecology and emphasise the need for further research into unifying these different approaches to understanding predation with particular reference to predator movement. In an appendix, I evaluate the possibility of using a functional response for inferring the abun- dances of prey species from performance indicators of generalist predators feeding on these prey. I argue that this approach may be futile in general, because a generalist predator's energy intake does not depend on the density of any single of its prey, so that the possibly unknown densities of all prey need to be taken into account

Statistical Modelling of Marine Fish Populations and Communities

Sustainable fisheries management require an understanding of the relationship between the adult population and the number of juveniles successfully added to that population each year. The process driving larval survival to enter a given stage of a fish population is highly variable and this pattern of variability reflects the strength of density-dependent mortality. Marine ecosystems are generally threatened by climate change and overfishing; the coupling of these two sources have encouraged scientists to develop end-to-end ecosystem models to study the interactions of organisms at different trophic levels and to understand their behaviours in response to climate change. Our understanding of this important and massively complex system has been constrained historically by the limited amount of data available. Recent technological advances are beginning to address this lack of data, but there is an urgent need for careful statistical methodology to synthesise this information and to make reliable predictions based upon it. In this thesis I developed methodologies specifically designed to interpret the patterns of variability in recruitment by accurately estimating the degree of heteroscedasticity in 90 published stock-recruitment datasets. To better estimate the accuracy of model parameters, I employed a Bayesian hierarchical modelling framework and applied this to multiple sets of fish populations with different model structures. Finally, I developed an end-to-end ecological model that takes into account biotic and abiotic factors, together with data on the fish communities, to assess the organisation of the marine ecosystem and to investigate the potential effects of weather or climate changes. The work developed within this thesis highlights the importance of statistical methods in estimating the patterns of variability and community structure in fish populations as well as describing the way organisms and environmental factors interact within an ecosystem

Best practices for the provision of prior information for Bayesian stock assessment

This manual represents a review of the potential sources and methods to be applied when providing prior information to Bayesian stock assessments and marine risk analysis. The manual is compiled as a product of the EC Framework 7 ECOKNOWS project (www.ecoknows.eu). The manual begins by introducing the basic concepts of Bayesian inference and the role of prior information in the inference. Bayesian analysis is a mathematical formalization of a sequential learning process in a probabilistic rationale. Prior information (also called ”prior knowledge”, ”prior belief”, or simply a ”prior”) refers to any existing relevant knowledge available before the analysis of the newest observations (data) and the information included in them. Prior information is input to a Bayesian statistical analysis in the form of a probability distribution (a prior distribution) that summarizes beliefs about the parameter concerned in terms of relative support for different values. Apart from specifying probable parameter values, prior information also defines how the data are related to the phenomenon being studied, i.e. the model structure. Prior information should reflect the different degrees of knowledge about different parameters and the interrelationships among them. Different sources of prior information are described as well as the particularities important for their successful utilization. The sources of prior information are classified into four main categories: (i) primary data, (ii) literature, (iii) online databases, and (iv) experts. This categorization is somewhat synthetic, but is useful for structuring the process of deriving a prior and for acknowledging different aspects of it. A hierarchy is proposed in which sources of prior information are ranked according to their proximity to the primary observations, so that use of raw data is preferred where possible. This hierarchy is reflected in the types of methods that might be suitable – for example, hierarchical analysis and meta-analysis approaches are powerful, but typically require larger numbers of observations than other methods. In establishing an informative prior distribution for a variable or parameter from ancillary raw data, several steps should be followed. These include the choice of the frequency distribution of observations which also determines the shape of prior distribution, the choice of the way in which a dataset is used to construct a prior, and the consideration related to whether one or several datasets are used. Explicitly modelling correlations between parameters in a hierarchical model can allow more effective use of the available information or more knowledge with the same data. Checking the literature is advised as the next approach. Stock assessment would gain much from the inclusion of prior information derived from the literature and from literature compilers such as FishBase (www.fishbase.org), especially in data-limited situations. The reader is guided through the process of obtaining priors for length–weight, growth, and mortality parameters from FishBase. Expert opinion lends itself to data-limited situations and can be used even in cases where observations are not available. Several expert elicitation tools are introduced for guiding experts through the process of expressing their beliefs and for extracting numerical priors about variables of interest, such as stock–recruitment dynamics, natural mortality, maturation, and the selectivity of fishing gears. Elicitation of parameter values is not the only task where experts play an important role; they also can describe the process to be modelled as a whole. Information sources and methods are not mutually exclusive, so some combination may be used in deriving a prior distribution. Whichever source(s) and method(s) are chosen, it is important to remember that the same data should not be used twice. If the 2 | ICES Cooperative Research Report No. 328 plan is to use the data in the analysis for which the prior distribution is needed, then the same data cannot be used in formulating the prior. The techniques studied and proposed in this manual can be further elaborated and fine-tuned. New developments in technology can potentially be explored to find novel ways of forming prior distributions from different sources of information. Future research efforts should also be targeted at the philosophy and practices of model building based on existing prior information. Stock assessments that explicitly account for model uncertainty are still rare, and improving the methodology in this direction is an important avenue for future research. More research is also needed to make Bayesian analysis of non-parametric models more accessible in practice. Since Bayesian stock assessment models (like all other assessment models) are made from existing knowledge held by human beings, prior distributions for parameters and model structures may play a key role in the processes of collectively building and reviewing those models with stakeholders. Research on the theory and practice of these processes will be needed in the future

Unravelling abiotic and biotic drivers of biodiversity change in local plant and invertebrate communities after 80 years - a re-visitation study on the Studland peninsula.

How ecological communities respond to long-term environmental change via changes in species richness and composition is an urgent question in the 21st century as anthropogenic forces drive biodiversity declines across taxa and regions. As environmental conditions change over time, effects may cascade through co-occurring taxa, directly disturbing some species and altering the structure of ecological networks to disturb others However, a paucity of data has meant that studies investigating abiotic and biotic drivers of biodiversity change over periods of decades are rare, particularly those spanning multiple co-occurring taxa. The aim of this thesis is to investigate how effects of long-term (ca. 80 years) environmental change propagate through co- occurring plant and insect communities, driving changes in species richness and composition across taxa. To achieve this aim I utilised a uniquely rich re-visitation study of species occurrence data on the Studland peninsula in the south of England. Data collection was led in the 1930s by the naturalist Cyril Diver, and in the 2010s by the National Trust in collaboration with a team of citizen scientists. I asked: 1) How have vascular plant assemblages of Studland changed in response to a changing abiotic environment between the 1930s and the present day?; 2) Have plant and insect taxa undergone congruent biodiversity changes under shifting environmental conditions?; 3) What abiotic and biotic factors relating to adult and larval ecological requirements have influenced long-term biodiversity change in Studland’s hoverflies?; 4) How are the plant and insect communities of Studland likely to change in coming decades under proposed management interventions? 1) Using multilevel models of differences in Ellenberg indicator values (EIVs) between assemblages of vascular plant species occurring in each time-period, I found that the most prominent driver of plant species compositional change was changing hydrological conditions, followed by successional processes. 2) Using hierarchical modelling of species loss/gains and a range of multivariate techniques, I found that species richness and compositional changes in plant and insect communities displayed cross-taxon congruence – correlated patterns of biodiversity change – over the ca. 80 year time-period, likely driven by a combination of abiotic and biotic change. 3) Hierarchical modelling of species loss/gains in the hoverfly community suggested that species richness in adult assemblages is limited by adult resource availability (plants) at highly localised scales, while compositional change is strongly affected by the availability of suitable larval microhabitat at the wider scale of a few kilometres. As with the plants, hydrological change was the main abiotic driver of change in the hoverfly community. 4) Bayesian Belief Network (BBN) models predicted that local management interventions to increase drainage and control ecological succession could benefit the taxa and habitats of Studland through increased species richness. However, BBN models also predicted that the health of the regional metacommunity is of utmost importance in maintaining a healthy local system. I have shown that congruent biodiversity change occurs across diverse plant and insect taxa, and is driven by changes in both abiotic and biotic conditions. These drivers do not act independently from one another, as demonstrated by effects of wetter winter conditions on hoverfly composition, coupled with effects of species richness change in the plant community, while the plant community was itself also responding to hydrological change via changing species composition. Crucially, my results suggest that the health of the regional metacommunity is of the utmost importance in maintaining a healthy local system when faced with environmental changes as seen at Studland; a reservoir of species available to take advantage of new conditions is vital. Therefore this work suggest a joint emphasis placed on local and regional conservation practices to mitigate effects of the anticipated acceleration in environmental change