Modeling common trends of zooplankton, atherinopsid, and barred splitfin time series in a shallow tropical lake.
Modeling efforts of Lake Chapala fisheries have included time series analysis of fish density and biomass time series of atherinopsids and barred splitfin (Becerra-Munoz et al., 2003). However, time series modeling did not provide any information on common trends among several fish density and biomass time series in Lake Chapala. Conversely, there is a statistical technique that detects common trends among multiple concurrent time series. Dynamic factor analysis (DFA) is a statistical technique for the analysis of relatively short (>15-25 points) multivariate time series; it identifies trends for a set of time series with a smaller number of common trends (Zuur et al., 2003a, 2007). For example, DFA has been applied to estimate underlying common trends among multiple time series of catch per unit effort of Norwegian lobster Nephrops norvegicus (Zuur et al., 2003b) and squid Loligo forbesi (Zuur and Pierce, 2004) with sea surface temperature and North Atlantic Oscillation index as the explanatory variables.
The analysis of common temporal trends of atherinopsid densities and biomass, along with physicochemical variables, may shed light on the main environmental variables influencing their population dynamics throughout Lake Chapala. The interrelationships between spatiotemporal distribution patterns of physicochemical variables and fish densities and biomass are not known in Lake Chapala. It is important to know whether or not common trends are spatially coherent throughout Lake Chapala because this information could provide a basis for improved atherinopsid stock assessment and fisheries management. The goals of the present study were to (1) identify common trends in zooplankton and fish density and biomass time series in Lake Chapala, and (2) elucidate the importance of water temperature, electrical conductivity, dissolved oxygen, pH, and alkalinity on these common trends.
[FIGURE 1 OMITTED]
METHODS--Study Site and Data Collection--From June 1997--February 1999, we implemented a survey for zooplankton, barred splitfin, and atherinopsids throughout Lake Chapala. Zooplankton and fish were collected monthly at 15 spatially systematic, equidistant sampling stations (except station [ST] 3) in Lake Chapala (Fig. 1). We used a zooplankton net with a 0.188-[m.sup.2] mouth area and a mesh size of 240 pm. The net-zooplankton samples were fixed in the field with a 70% ethanol solution. For the fish, we utilized a midwater trawl with a 6.6-[m.sup.2] mouth area and a 1.2-cm stretched mesh from the mouth to the cod end. A General Oceanics flowmeter (General Oceanics, Miami, Florida), suspended inside the zooplankton net, was set at the start of zooplankton collection and net trawling, and then read when the zooplankton net and trawl net reached the boat to estimate water flow through the zooplankton net and trawl net. Volume of water filtered was calculated as the product of estimated tow velocity and mouth areas of the zooplankton and trawl nets, respectively. Collected zooplankton was thoroughly washed and preserved with 70% ethanol in the field. Fish were placed in bags inside ice coolers. In the laboratory, fish were counted and their biomass was estimated as wet weight. Because thousands of atherinopsids were caught, the Chirostoma flock was analyzed as a group because their proper identification to species had to be done under a stereoscopic microscope. Zooplankton samples were measured for the total settled volume of all zooplankton collected by pouring each sample into an Imhoff cone and measuring the volume of zooplankton which had settled to the bottom of the cone overnight. Water temperature and dissolved oxygen were measured at the surface and bottom of each of the 15 stations with a YSI oxygen meter (Xylem, Inc., Yellow Springs, Ohio) with a long sensor cable calibrated in meters. Conductivity was recorded with a YSI conductivity meter (Xylem, Inc.); pH was measured at approximately 25 cm below the surface with a Corning pH-meter (Corning Life Sciences, Tewksbury, Massachusetts); and total alkalinity was estimated in the lab (American Public Health Association, 1985) from water samples collected approximately 25 cm below the surface that had been stored in ice coolers.
Statistical Analysis--Multiple time series were modeled as a function of a constant, a linear combination of 'M' common trends, explanatory variables, and noise. Instead of multiple 'N' time series, a linear combination of M common trends was estimated where M < N. The M trends represent tendencies (joint signals) across all the time series (Zuur et al., 2007). Multiple time series were selected and each group of selected time series was standardized (i.e., zero mean and standard deviation of 1). Different models containing one or two common trends were applied to standardized time series as well as models with and without explanatory variables. DFA models with minimum Akaike's Information Criterion were selected as best representing common trends (Zuur et al., 2007). Analyses were carried out in Brodgar software (DFA version 2.7.2, Highland Statistics, Inc., http://www.Brodgar.com).
RESULTS--We identified very similar common trends for the zooplankton and atherinopsid time series, which peaked during the winter. The common trends for density and biomass for atherinopsids were different temporally and peaked during the winter and summer, respectively. There were two common trends among the barred splitfin time series. The first common trend for barred splitfin density and biomass were remarkably similar, peaking during the summer, but the second trend exhibited an opposite behavior through time (Fig. 2).
The best DFA models per station had one common trend and one or two explanatory physicochemical variables, except for one near Mismaloya (ST 7), where all studied physicochemical variables were selected as explanatory. The order of importance of explanatory physicochemical variables to biological time series was defined by the selected DFA models per sampling station. We found that DFA methodology was useful to assess the overall importance of measured physicochemical variables on zooplankton and fish time series throughout Lake Chapala. Conductivity and pH were selected for stations near the cities of Jocotepec (ST 1) and Tizapan (ST 9). Alkalinity was the best explanatory variable for biological series near San Juan Cosala (ST 2). Water temperature was selected as the best explanatory variable near the cities of San Luis Soyatlan (ST 3), Chapala (ST 6), Emiliano Zapata (ST 11), Agua Caliente (ST 12), and Petatan (ST 15); conductivity and dissolved oxygen were best explanatory variables for Ajijic (ST 4) and west of Mezcala Island (ST 8); and conductivity was the best explanatory variable for the station near Palo Alto (ST 13). Alkalinity and conductivity were selected for DFA models near San Pedro Itzican (ST 10) and alkalinity and dissolved oxygen were selected for DFA models at San Nicolas (ST 5) and Ocotlan (ST 14). All measured physicochemical variables were selected for the DFA model for Mismaloya (ST 7).
[FIGURE 2 OMITTED]
DISCUSSION--Multiple time series can be considered strongly coherent, weakly coherent, or noncoherent. Lack of coherence is characterized by more than one common trend among time series, with only a few time series associated with each trend. Under strongly coherent survey time series, DFA usually identifies only one common trend to describe all series (Nye et al., 2010). Zooplankton density and atherinopsid density and biomass time series were strongly coherent in Lake Chapala, and barred splitfin density and biomass time series were weakly coherent. Zooplankton and atherinop sid series had only one distinctive common trend, which was both temporally similar and strongly coherent throughout Lake Chapala. Consequently, environmental policy for improved stock assessment and atherinopsid fisheries management can be done knowing that these biological series behave homogeneously temporally and spatially. The common trends in zooplankton and atherinopsid density were synchronized. The common trend of atherinopsid biomass time series peaked months after the common trend of zooplankton time series. Hence, other food resources consumed by atherinopsids, such as suspended clay-organic matter-bacteria aggregates (Lind and Davalos-Lind, 1991; Davalos-Lind and Lind, 2005), could be responsible for an additional fish biomass increase when zooplankton density exhibited a downward tendency. Hence, additional studies are necessary to investigate those other variables which might influence zooplankton and fish density dynamics in Lake Chapala. We identified patterns in the zooplankton and fish density time series that could not have been revealed by other, more-traditional approaches.
The Lake Chapala fisheries research survey was supported through grant IPN-CEGEPY 970468 from the Mexican National Polytechnic Institute. We are thankful to F. Villalpando Barragan for providing the map of Lake Chapala.
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Submitted 25 March 2015.
Acceptance recommended by Associate Editor, Mark Pyron, 21 January 2016.
Salvador Becerra-Munoz, * Hector R. Buelna-Osben, Juan M. Catalan-Romero
Pacific States Marine Fisheries Commission, P.O. Box 10, La Grange, CA 95329 (SBM) IPN-CIIDIR Michoacan, Justo Sierra 28 Centro, Jiquilpan, Michoacan, 59510, Mexico (HRBO, JMCR)
* Correspondent: email@example.com
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|Author:||Becerra-Munoz, Salvador; Buelna-Osben, Hector R.; Catalan-Romero, Juan M.|
|Date:||Mar 1, 2016|
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