Historically, the growth of animals has been described by a variety of functions which relate size increase to a unit of time. These functions vary from a straight-line relationship to the more complex asymptotic-type curve. Fish growth is often represented by a function which is asymptotic to some average maximum size the fish will attain. A useful regression formula for representing these curves has three parameters, with a representing the asymptotic value of y. Stevens (1951) showed the utility of this basic curve by writing Gompertz's law, the logistic curve, and Mitscherlich's law in this form. It is also possible to write the growth curves of von Bertalanffy (1938) in this way.

The objective of this paper is to present a useful method for fitting Beverton's (1954) modification of the von Bertalanffy growth-in-length curve, but the method is adaptable to any curve which can be written in the basic form of equation. The tables in the Appendix, and the worked example should provide sufficient information for fitting a von Bertalanffy curve.

In the past, the methods used to fit a von Bertalanffy curve to observed fish length have required inefficient techniques such as guessing-by-eye (von Bertalanffy, 1938) or approximation-through-transformation (Beverton and Holt, 1957; Ricker, 1958). The method presented in this paper is not only easy to use, but is based on the efficient, well-accepted technique of least squares. Under the assumption of normality, the least squares method produces estimates which are equivalent to maximum likelihood estimates.

With computers, other iterative methods or an adaption of the described method may be used to obtain very accurate estimates of the parameters of the von Bertalanffy curve. Stevens (1951) developed an iterative procedure for fitting (1) and Nelder (1961) gives an iterative method for fitting a generalized logistic curve which includes (1) as a special case. Nelder's method does not require the x's to be equally spaced and assumes a constant variance for log y rather than for y. However, the following description and the tables in the Appendix should be useful to workers who do not have access to a computer.

Introduction

Methods

Results

Conclusion

This paper is a review of the biology of Sacramento perch (Archoplites interruptus) based mainly on recent studies of their distribution, ecology, physiology, and genetics. The Sacramento perch is the only member of the family Centrarchidae that is endemic to California. It is most closely related to the rock basses (Ambloplites spp.) and is thought to have split from its eastern cousins during the Middle Miocene Period (15.5 to 5.2 million years ago, MYA). Their native range includes the Central Valley, Pajaro and Salinas rivers, tributaries to the San Francisco Estuary (e.g., Alameda Creek), and Clear Lake (Lake County). Today, they are most likely extirpated from all of their native range. They are known to persist in 28 waters outside their native range: 17 in California, nine in Nevada, and one each in Utah and Colorado. Disappearance from their native range coincided with massive changes to aquatic habitats in the Central Valley and with the introduction of alien species, including other centrarchids. Unfortunately, many populations established outside their native range have also disappeared and are continuing to do so.

The goal of this investigation was to characterize the manual and automated response of residential customers to high-price "critical" events dispatched under critical peak pricing tariffs tested in the 2003-2004 California Statewide Pricing Pilot. The 15-month experimental tariff gave customers a discounted two-price time-of-use rate on 430 days in exchange for 27 critical days, during which the peak period price (2 p.m. to 7 p.m.) was increased to about three times the normal time-of-use peak price. We calculated response by five-degree temperature bins as the difference between peak usage on normal and critical weekdays. Results indicated that manual response to critical periods reached -0.23 kW per home (-13 percent) in hot weather (95-104.9oF), -0.03 kW per home (-4 percent) in mild weather (60-94.9oF), and -0.07 kW per home (-9 percent) during cold weather (50-59.9oF). Separately, we analyzed response enhanced by programmable communicating thermostats in high-use homes with air-conditioning. Between 90oF and 94.9oF, the response of this group reached -0.56 kW per home (-25 percent) for five-hour critical periods and -0.89 kW/home (-41 percent) for two-hour critical periods.

Fishes were sampled on the restored floodplain of the Cosumnes River in Central California in order to determine patterns of floodplain use. The floodplain was sampled for seven years (1998-2002, 2004-2005) during the winter-spring flooding season. The fishes fell into five groups: (1) floodplain spawners, (2) river spawners, (3) floodplain foragers, (4) floodplain pond fishes, and (5) inadvertent users. Eight of the 18 abundant species were natives, while the rest were aliens. There was a consistent pattern of floodplain use, modified by timing and extent of flooding. The first fishes to appear were floodplain foragers, inadvertent users, and juvenile Chinook salmon (river spawners). Next were floodplain spawners, principally Sacramento splittail and common carp. At the end of the season, in ponds of residual water, non-native annual fishes, mainly inland silverside and western mosquitofish, became abundant. Adult spawners left when inflow decreased; their juveniles persisted as long as flood pulses kept water levels up and temperatures low. Juvenile splittail and carp quickly grew large enough to dominate floodplain fish samples, along with smaller numbers of juvenile Sacramento sucker and pikeminnow (river spawners). Such juveniles left the Relatively few fishes that used the floodplain for spawning or rearing became stranded, except late season alien fishes. Most alien fishes had resident populations in adjacent river, sloughs, and ditches and were not dependent on the floodplain for persistence. This indicates that Central Valley floodplains managed to favor native fishes should have the following char- acteristics: (1) extensive early season flooding, (2) complete drainage by the end of the flooding season, (3) few areas with permanent water, (4) a mosaic of physical habitats, (5) regular annual flooding but with high variability in flood regime.