Phenological and geographic patterns of walleye pollock (Theragra chalcogramma) spawning in the western Gulf of Alaska
Intangible: More than 20 years of egg sample data were used to reconstruct the geographic and phenological patterns of walleye pollock (Theragra chalcogramma) spawning aggregations in the Gulf of Alaska (GOA). The examined time series (1972, 1978-1979, 1981-2000) contained a official occasion of climate change (i.e., 1988-1989) and the rise and fall of the GOA Pollock population wealth and crops. We compared results from two generalised additive model (GAM) formulations: one assuming no reversal of egg distribution and phenology over the analysed time series (fixed) as well as the other declaring such changes (fixed) across an epoch ascertained from the data.
Results from both model conceptualisations corroborate the presence of a high egg concentration in Shelikof Strait, historically the main spawning place of Pollock in the GOA.
Nevertheless, model results also emphasise the existence of other secondary, and perhaps transitory, centres of egg distribution at various places along the shelf and slope areas of the GOA. Furthermore, results from the fixed (and mathematically exceptional) formula suggest the wealth of the non-Shelik of aggregations has grown over time, together with a tendency for earlier incident and displacement toward shallower areas of the high egg density regions
Marine fish are for the most part oviparous with external fertilisation, and to successfully replicate, they depend on a number of trusted cues (timing) and clues (place) enabling them to assemble in large numbers at an identical site and time. The procedures influencing the time (phenology) as well as the place (geography) are scientifically intriguing and badly understood (Cury 1994). Also, for commercial marine species, the spawning site is usually the place where the crops and evaluation surveys happen, having essential direction consequences for understanding the phenology and geography of fish spawning customs.
The aim of the study will be to characteristic spawning aggregations of walleye Pollock (Theragra chalcogramma) in the western Gulf of Alaska (GOA, from Kodiak Island to Unimak Pass), where most of the whole Gulf Pollock lives. This really is executed by means of an evaluation of the egg distribution data in a span (late 1970s to 2000) that contained a official occasion of climate change (i.e., 1988-1989; Hare and Mantua 2000) and the rise and fall of the GOA Pollock population and crop.
Now establishes the second-biggest single-species fishery in the world (State of World Fisheries and Aquaculture (SOFIA) 2004). Most of the landings come from the Okhotsk Sea and Bering Sea, however a sizeable Pollock stock, at present estimated to be somewhat over 200 000 tonnes (spawning biomass), is within the GOA (Dorn et al. 2002). Previously this fishery has supported crops exceeding 300 000 tonnes.
Historically, Pollock has spawned during a 2-week interval in the ending of March as well as the start of April in the Shelikof Strait, between Kodiak Island along with the Alaska Peninsula . Through the past decade, however, spawning in the Shelikof Strait has significantly diminished (Dorn et al. 2002). The drop-off may in part be described through an overall co-occurring fall of the Pollock population. Yet, in other places along the Alaska Peninsula (Dorn et al. 2002) and in coastal regions (Anderson and Piatt 1999), Pollock biomass has really improved, indicating that along with a decrease of the Shelikof people, either a shift of mature distribution or changes in local population abundances may have happened.
Pollock ichthyoplankton surveys in the GOA have taken place since the 1970s, and even though the spatial and temporal coverage hasn’t been consistent , these data provide a distinctive chance to rebuild the spawning location of mature Pollock in a span in which possible changes in spawning customs might have happened. For the purpose of assessing the Pollock egg distribution, we developed an innovative model framework that allows for changes in spatial and temporal patterns of the density data. Such a framework might be easily applied to other systems where the interaction between spatial and temporal dynamics is of interest or to find changes in species distribution in regard to comparing external regimes.
The data examined in this study include Pollock egg density (amounts x 10 [m.sup.-2]), accumulated during the ichthyoplankton surveys of the Alaska Fisheries Science Center (AFSC, Seattle, Washington) in the GOA. We define spawning places and time on the basis of the spatial and temporal distribution of Pollock eggs. Data on walleye pollock eggs were extracted from the Ichthyoplankton Cruise Database (IchBase), which encompasses a 30-year time series of ichthyoplankton data from cruises during 1972-2000 ran by AFSC and associate associations in the Gulf of Alaska .
In April and early May surveys, a 333 mesh on bongos and Tucker’s was used to prevent extrusion of yolk sac larvae, and in late May, a 505 mesh was utilised to prevent internet clogging from alga. Use of these various nets has no material impact on sampling of eggs due to their comparatively large size as well as the tough chorion that prevents extrusion. All tows were quantitative and oblique, ran in a standardised way using flow-meters. If bottom depth was less than 200 m, then the tows were made up to 10 m off the bottom.
Otherwise the tow was discontinued at 200 m. Grabs were maintained in 5% formalin and returned to the lab. They were sorted, identified to species, and quantified at the Plankton Sorting and Identification Center, Szczecin, Poland. Ichthyoplankton ids were confirmed by the taxonomic team at AFSC. The sampling grid crossed the whole ledge area of the western GOA, from Unimak Pass to the southwest and to the mouth of Cook Inlet to the northeast. But due to the common notion that pollock spawning was consistently positioned in the Shelikof Strait, sampling has been more extreme in this place.
Ichthyoplankton sampling in the GOA began in 1972 and continues to this very day. Yet, in our evaluation, we restrict our study to the 1972-2000 period. Before 1981, just the subsequent years were tried: 1972, 1978, and 1979. After 2000, most of the sampling just happened after in the year and was focused on larvae. In a few years there was more than one survey. To enable a similar temporal and depth coverage among years, we just contained tows crossing from the 75th to the 150th Julian day and around depths of 33-403 m, the variety which should mainly comprise most of pollock spawning action in the GOA .
In defining spawning places from the entire egg data, we implicitly assume the diffusion and drift of eggs from the spawning occasion to the period of the grab are minimal. The Alaska Coastal Current (ACC) is mainly accountable for the drift of pollock eggs and larvae in this area. On the other hand, the ACC is a surface current (60 m depth) and therefore isn’t likely to create a broad spatial displacement of eggs, which can be found at greater depths, especially during the very early phases (Kendall and Kim 1989).
We used generalised additive models (GAM) to scrutinize the patterns of pollock egg density in the GOA. Samples with no eggs (zero density) were taken out of the investigation, as well as the rest of the data were log-transformed to normalise the distribution and reduce heterosexuality. The independent variables (hereon covariates) were the position of the sampling defined by latitude and longitude, the natural logarithm of bottom depth in metres, and also the Julian day of the grab.
Underside depth was log-transformed to enable a uniform distribution through the tried depth range. The Julian day as well as the positional effects are also contained to correct for differences in time and place of sampling among years. The examined egg data included 3557 observations gathered over 23 years, with an average amount of 154 nonzero observations annually .
We compared two different model formulas: one assuming no changes of egg distribution and time over years (fixed spawning design and standing model) as well as the other assuming a change in egg distribution and time happening during an epoch to be ascertained from the data (fixed spawning design and fixed model). Especially, let be the natural logarithm of egg density at time t (time expressed in Julian day), year y, latitude [empty set], and longitude [lambda]. Let [b.sub.([empty set],[lambda]]) be the log-transformed underside depth. The fixed model may be written as follows:
where [e.sub.t,y,([empty set],[lambda])] is a random error assumed to be normally distributed with zero mean and finite variance, [a.sub.y] is an intercept permitted to transform for every year contained in the investigation, and also the gs are nonparametric smooth functions. In words, the model in eq. 1 presumes the egg density at a specified time of the year (t), year (y), and place ([empty set], [lambda]) is a function of place, bottom depth, and time of the year.
Moreover, the model in eq. 1 presumes that these effects are constant throughout the sampling interval, and any source of variability at a specified place, depth, and time is entirely because of the general variation of annual mean egg density (i.e., spawning output signal). The standard error estimates of the egg density forecasts on a natural logarithmic scale are representative of the coefficient of variability (standard deviation over average) on the untransformed scale (Lewontin 1966). Therefore, standard error approximations are here revealed as an indicator of the temporal variability of the spawning activity in the analyzed place.
The fixed version has the following formula:
In sharp contrast to the fixed model (eq. 1), in the fixed version the functions that link the egg density with place, bottom depth, and time of the year are permitted to change over two comparing temporal intervals. The two intervals are divided by the year [y.sup.] to be ascertained from the data. It is necessary to notice that given [y.sup.], the model in eq. 2 becomes a completely additive conceptualization of these kind:
where [u.sub.y] is an index variable using a value of either 0 or 1, depending on whether the year y is [less than or equal to] or “>> than [y.sup.*], respectively. In both versions 1 and 2, the one dimensional effects ([g.sub.2] and [g.sandwich.3]) are fitted by natural cubic splines (Wood 2004), while the two dimensional effect ([g.sub.1]) is matched with thin plate splines
The hunt for the brink year ([y.sup.]) is done by embracing the strategy described in Ciannelli et al. (2004) and Stenseth et al. (2006). In brief, the model in eq. 3 is fit for as many brink years as there are years in the temporal range contained in the investigation, except for those instances that resulted in having less than 10% of the data samples in every single interval. The last brink year ([y.sup.]) corresponds to that of the model with the lowest generalized cross validation (GCV) score, a measure of the predictive squared error of the fitted model (Green and Silverman 1994).
The resultant fixed version is subsequently equated with the fixed model (eq. 1) using the actual CV score. Basically, the CV quantifies the out-of-sample predictive error of the model and in the current use is ascertained as follows. A random sample of 200 observations (greater than the average of the sampled stations in each year) is excluded from the data set. The remaining observations are accustomed to match a fixed (eq. 1) or fixed (eq. 3) version using a varying threshold ([y.sup.*]) to be ascertained from the routine described above.
The thus-found models are subsequently used to forecast the value of the out-of-sample 200 data instances as well as the relative mean squared forecast errors. This routine is repeated 500 times, with all the closing actual CV of every version being the average of the 500 realizations. All the investigations were carried out in R, using the “tgam” library (developed by K.S. Chan).
A possible issue of the egg distribution data was presented by the irregular temporal and spatial sampling coverage of the field data. In particular, in later years, sampling happened mainly in the latter part of the year (i.e., after the end of April) and was concentrated in the Shelikof area (Table 1). Thus, there were fewer samples accessible the southwestern section of the Alaska Peninsula, especially early in the year. To make certain the results from the fixed model weren’t due to a change in sampling coverage, we performed a bootstrap analysis to gauge the likelihood of finding a fixed egg pattern from an inherent fixed egg distribution with irregular sampling coverage.
The evaluation was created as follows. The estimated fixed egg model (eq. 1) was used to forecast the egg density in precisely the same time and places of the entire egg data. Within each year, scaled residuals from the fixed model were randomly added to these forecasts. We refer to the recently foreseen egg distribution as the simulated egg data to distinguish it from the total egg data derived from the field samples.
Both the fixed (eq. 1) and fixed (eq. 2) versions were fitted to the simulated egg data, as well as the difference between both versions’ GCV ([DGCV.sup.*]) was got.
The exact same procedure on the simulated egg data was replicated 1000 times to get 1000 [DGCV.sup.]. A similar difference was likewise obtained from the models matched to the entire egg data (DGCV). Lastly, the chance of calling a fictitious fixed egg distribution pattern from an inherent stationary process was discovered as the fractions of the [DGCV.sup.] being greater in relation to the DGCV.
Egg density and distribution
The standing model shown significant effects from standing, bottom depth, and time of the year on the distribution of pollock eggs. The model explained 79.9% of the observed variance and had a actual CV score of 1.736. Most of the egg density was forecast to happen in the Shelikof Strait area (Fig. 2). Nevertheless, additional and secondary (in relation to density) centres of egg distribution were also identified in several places along the Alaska Peninsula, e.g., Unimak Pass and the Shumagin and Semidi islands.
Generally, the forecasts in the Shelikof area had the lowest standard error, suggesting a greater yearly equilibrium of spawning activity, whereas around the Shumagin Islands and Unimak Pass and in a variety of places over the shelf break, the standard error was bigger . In line with previous studies on pollock spawning behaviour, the time of the egg density peaked between the 90th as well as the 110th day of the year (corresponding to 30 March–19 April; Fig. 3), with an additional peak of small intensity around the 140th day of the year (19 May). The underside depth had a positive impact on egg density, with summits at depths greater than 240 m .
The GCV profile of the fixed egg model (eqs. 2 and 3) had a unique minimum between the years 1989-1990, suggesting a change in egg distribution throughout that time Model forecasts suggested that after 1989, the Shelikof Strait was no longer the only main centre of pollock egg density. The truth is, similar egg densities were also forecast to happen along the Alaska Peninsula, especially in the area of Unimak Pass .
The predicted effects of sampling day and depth also changed over these two intervals. After 1989, egg densities rose earlier in the year and at shallower depths compared with pre-1989 approximations . The described fixed model clarified 82.4% of the observed difference in egg density and had a actual CV of 1.556, a noticeable improvement over the fixed version.
The difference in GCV between the fixed as well as the fixed egg models (DGCV) was 0.201. The same difference averaged over 1000 realizations of the simulated egg data ([DGCV.sup.]) was -0.021. The likelihood of [DGCV.sup.] being greater than DGCV was age 6) in the Shelikof region fell drastically after 1984-1985, and with them also the “tradition” to house in Shelikof may have been seriously reduced. So mature pollock from other spawning areas might have entrained just matured people toward other spawning places. Although appealing, the detailed theory isn’t definitively supported by our data and doesn’t exclude the presence of other mechanisms (e.g., reduction of genetic diversity).
An alteration in the relative prosperity of various genetically different subpopulations is, in addition, likely to describe changes of spawning designs. Really, loss of the genetic memory of a people driven to extinction would lead to the loss of that spawning population over any practical awareness of time.
A genetically predetermined homing strategy, coupled with the presence of multiple spawning places, also entails the existence of several genetically different stocks, powerful natal homing, as well as the existence of larval retention areas that restrict the degree of larval drift and blending among stocks (MacLean and Evans 1981; Iles and Sinclair 1982).
The evidence collected so far on pollock is conflicting about whether genetically different populations appear in the GOA (Bailey et al. 1999; O’Reilly et al. 2004). Additionally, no genetic stock evaluation was done on fish from the Shumagin and Unimak places. The flow design of the Alaska Coastal Current supports the continuity of temporally consistent and predictable larval retention areas (Bailey et al. 1997). Eddies and fronts in the Shelikof area tend to locally keep larvae. On the flip side, eggs spawned in the Shumagin Island region are seemingly not kept in the neighborhood place (Dougherty et al. 2007).
Otolith microchemistry investigations on the GOA pollock have suggested that larval pollock encounter distinct water masses throughout their early ontogeny (Fitzgerald et al. 2004), further corroborating the existence of multiple spawning aggregations. Really, more genetic and otolith analyses on samples from distinct areas within the GOA during various life stages would be instrumental to better comprehend the interaction between population structure and spawning aggregations in this place.
Some discussion of the data restriction is acceptable. Through time the egg survey has shifted somewhat to mainly occur in the later portion of the year (after mid-April). So we cannot fully eliminate the chance that the reported transition of egg distribution was due to the irregular sampling scheme. On the other hand, the consequence of the corroborative evaluation presents more signs toward a real shift in egg distribution as opposed to an outcome of the sampling scheme.
Also, field data on mature people also corroborates the incidence of a real change in spawning routines. For instance, even though the GOA acoustic survey found a sudden decline of mature pollock in the Shelikof Strait, the catches from the coastal surveys of the Alaska Department of Fish and Game have stayed pretty steady (Dorn et al. 2002). Likewise, since the ending of the 1980s, the little net survey performed by the AFSC found an increase of pollock biomass in coastal regions (Anderson and Piatt 1999)–an increase that lasts.
Eventually, it is necessary to see that the reported shift of egg distribution wasn’t only caused by a change in the spatial pattern, but in addition in the time of egg wealth. It’s difficult to envision how a progressive delay of the survey might have caused earlier summits of egg density in more recent years. Therefore, it’s more likely the irregular sampling coverage has hampered the complete detection of the shift in egg distribution, rather than creating it.
This data set, as typical of many other marine and terrestrial sampling data sets, is defined by means of an inflation of zero counts (zero-inflated counts), which are difficult to categorize within the accessible statistical distribution families and might also bias variability estimates and inferences (Welsh et al. 1996). In our evaluation, we simply modelled the nonzero counts for just two reasons. First, we were primarily interested in finding “centres” of pollock egg wealth, i.e., places where egg density is higher than the average background value.
In such conditions, the removal of zero egg tows (found mainly in places or times of the year of consistently tight eggs) shouldn’t change the ending results. Second, due to the protocol adopted to sort the ichthyoplankton samples, our data set is constituted of egg density values rather than egg counts. So we couldn’t use exponential distribution families that enable overdispersion (e.g., Poisson, negative binomial).
An average strategy used to model zero-inflated data, also called two step strategy or conditional modeling, is to first model the presence-absence using a binomial distribution and then to model the wealth conditional on the existence using, as an example, a truncated Poisson or negative binomial distribution (Welsh et al. 1996). Fox et al. (2000), among others, used the two step strategy to model distribution of fish eggs.
Even though the two step strategy keeps the information carried by the zero counts and generates unbiased forecasts, it makes inference instead complex as there are two sets of external effects to take into account, those from the presence-absence and those from the wealth model, often with contradictory results (Barry and Welsh 2002).
In our particular case, the usage of a binomial distribution family for modelling the presence-absence of pollock egg restricts our capability to find shifts in centres of egg pollock distribution. Actually, the chance of discovering eggs in a high density area may change little over time, while the wealth may change significantly. In spite of these concerns, it’s still recommendable that a process be developed to model zero-inflated counts in future programs. Ideally, this kind of process ought to be constant (i.e., related to noncount data), nonlinear, and nonadditive.
The recent work by Rigby and Stasinopoulos (2004) expands the GAM to the so called GAMLSS (generalized additive models for location, scale, and shape) that enables these more general conditional response distributions. An edge of the GAMLSS is that, unlike the favorite two-stage estimation strategy which uses the zero and also the nonzero data individually, it eases a coherent inference with all the entirety of the zero-inflated data.
No matter the environmental mechanisms that caused a reversal of pollock egg distribution in the GOA, its incidence can have repercussions on the existence of the early life stages as well as on recruiting success. As an example, the uniformity of spawning activity in the Shelikof area is the effect of locally and consistently favorable physical and biological characteristics. By comparison, the likelihood of survival achievement of pollock eggs spawned in non-Shelikof areas could possibly be more dependent on ephemeral environmental conditions and might represent a bethedging strategy of the species.
In the Shelikof Strait, advantageous characteristics comprise a deep trench (the Sea Valley) that cuts into the ledge and goes to the Strait and also the existence of the nutrient-load southwestward-vagrant ACC. The existence of the deep trench enables pollock embryos to reside in relatively deep waters where they’re able to see advantageous thermal and density surroundings (Kendall and Kim 1989). The existence of the ACC prefers egg and eating larval advection towards productive nursery places along the Alaska Peninsula (Hinckley et al. 2001).
Sadly, the interaction of crop strategies with population structure and spawning geography in marine fish is mostly ignored from the direction stadiums (Rowe and Hutchings 2003). As an example, the crop of several marine school fish is centered on mature people collecting in spawning or feeding places.
Although such practice may favor a delay in the age of maturation over short evolutionary time scales (Heino and Godo 2002), it could likewise cause a bigger percentage of the living population to spawn in secondary and likely best places or result in loss of genetic diversity as the end result of inbreeding (Hoarau et al. 2005).
These mechanisms can result in a rapid population decline, especially at low densities (i.e., Allee effect), if really the environmental advantages of spawning in secondary places are borderline. B
ehaviorally mediated effects can magnify the speed of the decline, as has been proposed to spell out the alternation in abundance of anchovy and sardine (i.e., “school snare theory”; Bakun and Cury 1999).
Now the crop of walleye pollock, although greatly reduced from the 1980s, is still concentrated in the Shelikof Strait area (Dorn et al. 2002).
In the event the scenario of behaviorally restricted spawning-site philopatry is right, the effect of such crops on the restoration and recruiting of the Shelikof spawning aggregation ought to be critically analyzed.
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