Russell B. Millar

Estimating the size-selection curves of towed gears, traps, nets and hooks

A general statistical methodology for analysis of selectivity data from any type of fishing gear is presented. This formal statistical modelling of selectivity is built on explicit definitions of the selection process and specification of underlying assumptions and limitations, and this gives the resulting estimates of gear selectivity (and possibly fishing power) a clear interpretation. Application of the methodology to studies using subsampled catch data and to towed gears having windows or grids is outlined, and examples applied to passive nets and towed gears are presented. The analysis of data from replicate deployments is covered in detail, with particular regard to modelling the fixed and random effects of between-haul variation. Recent developments on the design of selectivity experiments are introduced and demonstrated.

Burdens of evidence and the benefits of marine reserves: putting Descartes before des horse?

An extensive literature has appeared since 1990 on the study of ‘no-take’ marine reserves and their potential to make significant contributions to the conservation and management of fisheries, especially in tropical environments (see Polunin 1990; Roberts & Polunin 1991; DeMartini 1993; Roberts 1997; Allison et al. 1998; Guenette et al. 1998). The literature describes many potential benefits of marine reserves to fisheries, including increases in spawner-biomass-per-recruit and increases in larval supply from protecting ‘source’ populations (Jennings 2000). The important word here is ‘potential’. Some claims made by advocates of marine reserves might be regarded as optimistic, whereas critics of reserves might sometimes have been unduly harsh. Conservation goals for marine reserves are often poorly defined, and differences of opinion regarding the efficacy of reserves for fulfilling any of their stated goals can frequently be attributed to a lack of good information with which to predict their effects. Here, we critically examine the literature from 1990–2001 to determine (1) the relative effort put into empirical and theoretical approaches to predict reserve effects, and (2) the quality of empirical evidence available to support theoretical predictions. It is not the purpose of this article to single out particular studies for criticism (although this is sometimes inevitable to provide examples), nor to draw conclusions concerning the efficacy of marine reserves.

Non-linear state space modelling of fisheries biomass dynamics by using Metropolis-Hastings within-Gibbs sampling

State space modelling and Bayesian analysis are both active areas of applied research in fisheries stock assessment. Combining these two methodologies facilitates the fitting of state space models that may be non‐linear and have non‐normal errors, and hence it is particularly useful for modelling fisheries dynamics. Here, this approach is demonstrated by fitting a non‐linear surplus production model to data on South Atlantic albacore tuna (Thunnus alalunga). The state space approach allows for random variability in both the data (the measurement of relative biomass) and in annual biomass dynamics of the tuna stock. Sampling from the joint posterior distribution of the unobservables was achieved by using Metropolis‐Hastings within‐Gibbs sampling.

Size-selectivity of lobster pots with escape-gaps: application of the SELECT method to the southern rock lobster (Jasus edwardsii) fishery in Victoria, Australia

We have utilised a relatively new modelling method, SELECT, to calculate size-selectivity curves for data from two escape-gap field experiments on southern rock lobster (Jasus edwardsii) in Victoria, Australia. Size-selectivity curves based on an asymmetric Richards model fitted the data better than the commonly used logistic model, possibly because of higher than expected retention of small lobsters. Theoretical size-selectivity curves, calculated from morphometric data, were remarkably close to size-selectivity curves obtained from one experiment. In a second experiment, we showed that retention probabilities for lobsters close to the legal minimum length were lower than that predicted by the theoretical size-selectivity curves. Size-selectivity curves confirm that the current escape-gap size of 60 mm is close to optimum for the legal minimum lengths used in the Victorian southern rock lobster fishery. Our analyses failed to support the common assertion that escape-gaps increase the fishing power of lobster pots.

ESTIMATING THE RELATIVE DENSITY OF SNAPPER IN AND AROUND A MARINE RESERVE USING A LOG-LINEAR MIXED-EFFECTS MODEL

Summary Angling from small recreational fishing boats was used as a sampling method to quantify the relative density of snapper (Pagrus auratus) in six areas within the Cape Rodney‐Okakari Point Marine Reserve (New Zealand) and four areas adjacent to the reserve. Penalized quasi-likelihood was used to fit a log-linear mixed-effects model having area and date as fixed effects and boat as a random effect. Simulation and first-order bias correction formulae were employed to assess the validity of the estimates of the area effects. The bias correction is known to be unsuitable for general use because it typically over-estimates bias, and this was observed here. However, it was qualitatively useful for indicating the direction of bias and for indicating when estimators were approximately unbiased. The parameter of primary interest was the ratio of snapper density in the marine reserve versus snapper density outside the reserve, and the estimator of this parameter was first-order asymptotically unbiased. This ratio of snapper densities was estimated to be 11 .3/:

FITTING NONLINEAR ENVIRONMENTAL GRADIENTS TO COMMUNITY DATA: A GENERAL DISTANCE-BASED APPROACH

A distance-based method is provided for the analysis and modeling of multivariate community data in response to a nonlinear gradient. Any reasonable dissimilarity measure can be used, and the method provides a natural extension from canonical analysis of principal coordinates (CAP) to nonlinear canonical analysis through the use of a link function, much like the extension of linear models to generalized linear models. The form of the nonlinear link function needs to be specified and will depend on the particular ecological system and the nature of the gradient. For example, an exponential decay curve could be used to model community structure after an environmental impact as a nonlinear function of time. This curve is used in our first example, where community structure is modeled as a nonlinear function of habitat size. Our second example uses a logistic curve to model change in community structure through a region of habitat transition from grassland to woodland. Computationally, this methodology uses a standard nonlinear optimization procedure to find the values of the parameters that maximize the correlation of the principal coordinates (obtained from an appropriately chosen distance measure) with the chosen form of nonlinear gradient. A simple randomization procedure is used to test the significance of the fitted nonlinear gradient over and above the fit of the linear gradient, and bootstrap confidence intervals for parameters are readily obtained. Any reasonable form of nonlinear gradient can be used, and it can be modeled as a nonlinear function of multiple environmental variables, making this a very flexible and versatile procedure for modeling multivariate ecological systems.

Much ado about nothings: using zero similarity points in distance-decay curves

Distance decay is used to describe the (usually exponential) decay in ecological similarity of assemblages between two sites as a function of their distance apart along an environmental gradient. Exponential distance-decay curves are routinely fitted by calculating the ecological similarity between each pair of sites, and fitting a linear regression to the points on a scatter plot of log-similarity vs. distance (x-axis). However, pairs of sites where the assemblages have no species in common pose a problem, because the similarity is zero, and the log transformation cannot be applied. Common fixes to this problem (i.e., either removing or transforming the zero values) are shown to have undesirable consequences and to give widely disparate estimates. A new method is presented as a special case of a generalized dissimilarity model. It is fitted very quickly and easily using existing software, and it does not require removal or transformation of the zero similarity points. Its simplicity makes it convenient for use in conjunction with the resampling methods that are routinely employed to test hypotheses, to obtain standard errors of estimated parameters, or to compare distance-decay curves. A word of caution about standard application of the bootstrap is noted, and modified bootstrap and jackknife alternatives are demonstrated.

The kinetics of monospermic and polyspermic fertilization in free-spawning marine invertebrates

The equation of Vogel et al. (1982) is widely used in fertilization studies of free-spawning marine invertebrates to predict the percentage of viable eggs that will be fertilized at any specified levels of gamete concentration and contact time. Here, the random collision model that underlies the Vogel et al. equation is extended to distinguish between monospermic and polyspermic fertilization, and separate equations for the percentages of monospermic and polyspermic fertilization are obtained. These equations provide an explanation for empirical observations which have shown a decreased percentage of successful egg development at high sperm concentrations. Comparison is made with an earlier heuristic attempt (Styan, 1998) to predict the extent of polyspermic fertilization, and it is found that this earlier method can underestimate the percentage of polyspermic fertilization by up to 10 percent. Moreover, the approach used here retains the flexibility to model changes in sperm concentration due to dispersal mechanisms, and is able to model different mechanisms for the block to polyspermy.

Mortality of discards from southeastern Australian beach seines and gillnets

Two experiments were done in an Australian estuary to quantify the mortalities and contributing factors for key species discarded during 8 and 9 deployments of commercial beach (or shore) seines and gillnets, respectively. In both experiments, bycatches (2347 individuals comprising 16 species) were handled according to conventional practices and assessed for immediate mortalities before live samples of selected species were discarded into replicate cages along with appropriate controls, and monitored for short-term mortalities (< or =10 d). All of the seined or gilled fish were alive prior to discarding. During the beach seine experiment, 20% of caged seined-and-discarded surf bream Acanthopagrus australis (n = 290) were dead after 5 d, with most mortalities occurring between the second and fifth day. In the gillnet experiment, 42 and 11% of gilled-and-discarded A. australis (n = 161) and lesser salmon catfish Neoarius graeffei (n = 67), respectively, died during a 10 d monitoring period, mostly within the first 5 d. There were no deaths in any controls for these fish. Mixed-effects logistic models revealed that the mortality of A. australis discarded from both gears was significantly (p < 0.01) and negatively correlated with their total length, while N. graeffei had a significantly (p < 0.05) greater (5-fold) probability of dying when jellyfish Catostylus sp. were present in the gillnet. Simple modifications to the operations of beach seines and gillnets and/or post-capture handling procedures, such as close regulation of size selectivity for the target species, careful removal of fish from meshes, and abstention from setting during high abundances of jellyfish will maximise the survival of discarded bycatch.

Increasing codend mesh openings: an appropriate strategy for improving the selectivity of penaeid fishing gears in an Australian estuary?

This study investigates the effects of increasing the lateral mesh openings in codends on the size and species selectivity of lagoon and river seines and a stow net used to target penaeid prawns (eastern king (Penaeus plebejus), school (Metapenaeus macleayi) and greasyback prawns (M. bennettae)) in Wallis Lake, New South Wales, Australia. Compared with conventional codends made from 36-mm diamond-shaped mesh, new designs made from 25- and 29-mm mesh hung on the bar (i.e. square-shaped mesh) significantly reduced the catches of non-target fish (by between 58 and 95%) and improved size selection for the targeted penaeids in the stow net and lagoon seine. In contrast, owing to gear-specific operational characteristics such as a slower hauling speed, there were few detectable effects of altering mesh openings in the codend of the river seine. The results are discussed in terms of the differences in the gears used and their particular selection mechanisms. We conclude that, pending further trials, codends made from a mesh size approaching 29 mm, hung on the bar, would provide appropriate size- and species-selection for Wallis Lake stow nets and lagoon seines. Further research is required, however, to examine the utility of operational changes to river seines and/or alterations to mesh size and configuration in the wings and body to improve selectivity.