Ken B. Newman

Hidden Process Models For Animal Population Dynamics

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).

Monte Carlo Inference for State―Space Models of Wild Animal Populations

SUMMARY We compare two Monte Carlo (MC) procedures, sequential importance sampling (SIS) and Markov chain Monte Carlo (MCMC), for making Bayesian inferences about the unknown states and parameters of state-space models for animal populations. The procedures were applied to both simulated and real pup count data for the British grey seal metapopulation, as well as to simulated data for a Chinook salmon population. The MCMC implementation was based on tailor-made proposal distributions combined with analytical integration of some of the states and parameters. SIS was implemented in a more generic fashion. For the same computing time MCMC tended to yield posterior distributions with less MC variation across different runs of the algorithm than the SIS implementation with the exception in the seal model of some states and one of the parameters that mixed quite slowly. The efficiency of the SIS sampler greatly increased by analytically integrating out unknown parameters in the observation model. We consider that a careful implementation of MCMC for cases where data are informative relative to the priors sets the gold standard, but that SIS samplers are a viable alternative that can be programmed more quickly. Our SIS implementation is particularly competitive in situations where the data are relatively uninformative; in other cases, SIS may require substantially more computer power than an efficient implementation of MCMC to achieve the same level of MC error.

STATE-SPACE MODELING OF ANIMAL MOVEMENT AND MORTALITY WITH APPLICATION TO SALMON

A stochastic model for the movement and eventual mortality of an individual animal is formulated as a combination of three components: initial spatial location, survival status at any point in time, and spatial translation between points in time. Alternative theories about survival and migration can be expressed in terms of different models for any of the three components. The model can be extended to groups of animals, spatially and/or temporally aggregated, by appropriate integration. When information about animal counts is partial or inexact, as from mark-recapture or harvest data, state-space models are a natural framework for estimating both unknown parameters and animal abundance. As an example, a multivariate, linear normal state-space model that explicitly incorporates each of the three individual animal components is formulated for the migration and harvest of Pacific coho salmon (Oncorhynchus kisutch). Using recoveries of tagged coho salmon caught in ocean fisheries and associated measures of fishing effort, the Kalman filter and maximum likelihood are used to estimate parameters of the processes, and the Kalman smooth is used to estimate abundances. Given estimated parameters and current harvest and effort data, real-time management of exploited populations could be improved by using the Kalman prediction algorithm.

Accounting for demographic and environmental stochasticity, observation error, and parameter uncertainty in fish population dynamics models

Abstract Bayesian hierarchical state-space models are a means of modeling fish population dynamics while accounting for both demographic and environmental stochasticity, observation noise, and parameter uncertainty. Sequential importance sampling can be used to generate posterior distributions for parameters, unobserved states, and random effects for population models with realistic dynamics and error distributions. Such a state-space model was fit to the Sacramento River winter-run Chinook salmon Oncorhynchus tshawytscha population, where a key objective was to develop a tool for predicting juvenile out-migration based on multiple sources of data. One-year-ahead 90% prediction intervals based on 1992−2003 data, while relatively wide, did include the estimated values for 2004. Parameter estimates for the juvenile production function based on the state-space model formulation differed appreciably from Bayesian estimates that ignored autocorrelation and observation noise.

Hierarchical Modeling of Juvenile Chinook Salmon Survival as a Function of Sacramento–San Joaquin Delta Water Exports

Abstract A multiyear study was carried out in the Sacramento–San Joaquin Delta system to examine the relationship between the survival of out-migrating Chinook salmon Oncorhynchus tshawytscha and the amount of water exported from the system by the two major pumping stations in the southern portion of the delta. Paired releases of groups of coded-wire-tagged juvenile late-fall-run Chinook salmon were made at two locations in the delta, one in the main-stem Sacramento River and one in the interior portion of the delta where they were more likely to be directly affected by the pumping stations. Shortly after release, the fish were recovered downstream by a midwater trawl, and over a 2–4-year period the fish were recovered in ocean fishery catches and spawning ground surveys. A Bayesian hierarchical model for the recoveries was fit that explicitly accounted for the between-release variation in survival and capture probabilities as well as the sampling variation in the recoveries. The survival of the interior ...

Predation on Juvenile Salmonids by Smallmouth Bass in the Lower Granite Reservoir System, Snake River

Abstract We estimated the consumption of juvenile salmon Oncorhynchus spp. and steelhead O. mykiss by smallmouth bass Micropterus dolomieu in the tailrace and forebay of the Lower Granite Dam and compared this consumption with that in the two major river arms of the upper Lower Granite Reservoir, Snake River, Idaho–Washington. We examined over 9,700 smallmouth bass stomachs from April through August during 1996 and 1997. Juvenile salmonids were not a major component of smallmouth bass diets by weight and number at any location in either 1996 or 1997. Of the approximately 8,600 stomach samples containing food items, only 67 had juvenile salmonid remains. Juvenile salmonids accounted for approximately 11% of smallmouth bass diets by weight in the forebay in 1996 and 5% in the Snake and Clearwater river arms in 1997, with smaller proportions at other locations. Crustaceans and nonsalmonid fishes were the dominant prey items by weight at all locations in 1996 and 1997 except for the Snake River arm in 1996, w...

Modelling paired release-recovery data in the presence of survival and capture heterogeneity with application to marked juvenile salmon

Products of multinomial models have been the standard approach to analysing animal release-recovery data. Two alternatives, a pseudo-likelihood model and a Bayesian nonlinear hierarchical model, are developed. Both approaches can to some degree account for heterogeneity in survival and capture probabilities over and above that accounted for by covariates. The pseudo-likelihood approach allows for recovery period specific overdispersion. The hierarchical approach treats survival and capture rates as a sum of fixed and random effects. The standard and alternative approaches were applied to a set of paired release-recovery salmon data. Marked juvenile chinook salmon (Oncorhynchus tshawytscha) were released, with some recovered in freshwater as juveniles and others in marine waters as adults. Interest centered on modelling freshwater survival rates as a function of biological and hydrological covariates. Under the product multinomial formulation, most covariates were statistically significant. In contrast, under the pseudo-likelihood and hierarchical formulations, the standard errors for the coefficients were considerably larger, with pseudo-likelihood standard errors five to eight times larger, and fewer coefficients were statistically significant. Covariates, significant under all formulations, with important management implications included water temperature, water flow and amount of water exported for human use. The hierarchical model was considerably more stable with regard to estimated coefficients of training subsets used in a cross-validation.

Hierarchic modeling of salmon harvest and migration.

Using fishery recoveries from a tagged cohort of coho salmon, the ocean spatial-temporal abundance of the cohort is predicted using a state-space model. The model parameters, which reflect spatial distribution, mortality, and movement, vary considerably between different cohorts. To evaluate the effect of proposed management plans on a future cohort, uncertainty in the cohort-specific parameters is accounted for by a hierarchic model. As an application, release-recovery and fishing effort data from several cohorts of a hatchery-reared coho salmon stock originating from Washington state are used to calculate maximum likelihood estimates of the hyperparameters. Markov chain Monte Carlo is used to approximate the likelihood for the hyperparameters. The Markov chain simulates the sampling distribution of the state-space model parameters conditional on the data and the estimated hyperparameters and provides empirical Bayes estimates as a by-product. Given the estimated hyperparameters and the hierarchic model, fishery managers can simulate the variation in cohort-specific parameters and variation in the migration and harvest processes to more realistically describe uncertainty in the results of any proposed management plan.

A Comparison of the Sequential Gaussian and Markov-Bayes Simulation Methods for Small Samples

We compared the performance of sequential Gaussian simulation (sGs) and Markov-Bayes simulation (MBs) using relatively small samples taken from synthetic datasets. A moderate correlation (approximately r = 0.70) existed between a continuous primary variable and a continuous secondary variable. Given the small sample sizes, our objective was to determine whether MBs, with its ability to incorporate the secondary information, would prove superior to SgS. A split-split-plot computer experiment was conducted to compare the two simulation methods over a variety of primary and secondary sample sizes as well as spatial correlations. Using average mean square prediction error as a measure of local performance, sGs and MBs were roughly equivalent for random fields with short ranges (2 m). As range increased (15 m) the average mean square prediction error for sGs was less than or equal to that for MBs, even when number of noncollocated secondary observations was twice the number of collocated observations. Median variance within nonoverlapping subregions was used as a measure of the local heterogeneity or surface texture of the image. In most situations sGs images more faithfully reflected the true local heterogeneity, while MBs was more erratic, sometimes oversmoothing and sometimes undersmoothing.

Bayesian Averaging of Generalized Linear Models for Passive Integrated Transponder Tag Recoveries from Salmonids in the Snake River

Abstract Bayesian methods provide a means of explicitly accounting for uncertainty in the choice of model used to interpret fisheries data. The probability of a given model being the correct model conditional on the data, the posterior probability, is a measure of the degree of belief and strength of evidence for the model. Bayesian model averaging uses these posterior probabilities to make weighted inferences, thus providing a solution to the problem of selecting a single model from a group of models that seem nearly equivalent by conventional statistical criteria. The approach is applied to a generalized linear model analysis of survival for juvenile and mature adult spring chinook salmon Oncorhynchus tshawytscha and steelhead Oncorhynchus mykiss from the Snake River. The fish, tagged as juveniles with passive integrated transponders (PIT), outmigrated from freshwater habitat to the ocean during 1989–1991, and include some of the first PIT tag recoveries of adult fish. Covariates used to model survival ...