Spatial patterns of ARIMA modeled rates of change of atherinids (Chirostoma spp.) and goodeid Chapalichthys encaustus from Lake Chapala, México

Abstract

We implemented the first systematic sampling fish survey from June 1997 to February of 1999 in Lake Chapala. Atherinid ( Chirostoma spp.) and “pintilla” goodeid Chapalichthys encaustus mean densities ranged between 0.11–2.15 and 0.04–2.92 fish/m 3, respectively. Atherinids reached maximum densities of 4.28 fish/m 3 near Ajijic city and “pintilla” goodeids peaked at 12.28 fish/m 3 near the municipal discharge of Jocotepec City. Shifts from atherinid dominant to “pintilla” goodeid dominant were detected in areas influenced by municipal discharges from Jocotepec, Ajijic, Chapala and Tizapán cities, and Lerma River inflow. Municipal discharges induced shifts in fish community structure by reducing the abundance of the more profitable atherinids to a level where less profitable goodeids increased in the fish community. Time series modeling of non-stationary atherinid and “pintilla” goodeid density and biomass series revealed two patterns of dynamics in Lake Chapala. We found density-independent Integrated Moving Average (IMA) models for atherinid rates of change in areas influenced by municipal discharges from Jocotepec, Ajijic, Chapala and Tizapán cities, and Lerma River inflow. MA parameters ( θ 1) indicated random-shock environmentally-driven time series dynamics. Density-dependent integrated autoregressive (ARI) models were found for atherinid rates of change at all other sampling stations. First-order ARI models found had φ 1 parameters between −1 and 0, which indicated density-dependent quasi-cyclic dynamics through time. Variances explained by ARI models were higher at the western than at the eastern region of Lake Chapala. Rate of dampening of forecasted quasi-cycles for atherinids and pintilla goodeids was higher at the eastern than western region of Lake Chapala. Pollution effect on quasi-cyclic fish population patterns are analogous to overfishing in regards that pollution-induced mortality removes part of the fish stock, and consequently the effect of density-dependent compensatory mechanisms tend to diminish as pollution levels increase. Cyclic second-order ARI models were found near San Luis Soyatlán for atherinids and pintilla goodeids.