ULANOWICZ ET AL.: IDENTIFYINC. CLIMATIC FACTORS INFLUENCING MARYLAND LANDINGS 



however, may be more sensitive to shorter term 

 deviations from this average. In an effort to 

 quantify these deviations we devised four differ- 

 ent ways of treating each of the original four time 

 series to yield 26 annual series of environmental 

 data. 



The first of these methods, calculating the 

 annual average, has already been mentioned. 

 But the annual mean conveys little information 

 on the cumulative amount of stress or benefit ex- 

 perienced by the populations because of the ex- 

 treme high or low values of environmental vari- 

 ables. To portray the cumulative effects of these 

 deviations, we defined variables analogous to the 

 degree-days of agricultural science. Here the 

 effect of a variable is assumed to be manifested 

 only when its value goes beyond a certain "bias- 

 level." If, for example, the organism is assumed 

 to be cold stressed when the water temperature 

 falls below 4°C, then 3 successive days of 1°C 

 water temperature will contribute 9 degree-days 

 towards the index of cold stress. 



For each of the four variables recorded, a high 

 and a low bias level were chosen so that when 

 conditions exceeded these bounds at Solomons, 

 we estimated that there were significant regions 

 throughout the Maryland section of the Chesa- 

 peake Bay where fish and shellfish were prob- 

 ably stressed (or benefited) by the large excur- 

 sions from the norm. These bias levels are shown 

 in Table 1. 



Of course, the fishery might be responding to 

 individual episodes of stress, rather than the 

 yearly cumulative value. We, therefore, elected 

 to measure the lengths of the longest episodes 

 during a year that a variable was beyond the bias 

 values. These episodes were intermediate time- 

 scale phenomena (on the order of 1 to several 

 weeks), and we wished to avoid contamination 

 from high frequency events. For example, salin- 

 ity may have remained above 16.2 ppt for all of a 

 28 d period, save on the 15th day when it dropped 

 to 16.1 ppt. To characterize the episode as 14 d in 

 duration would clearly be erroneous. To avoid 

 such contamination we chose a "gap-interval" for 



Table 1.— Parameters used in calculating 

 cumulative variables and episodes. 



Variable 



High bias 



Low bias 



Salinity 16.2 V, 10.5V. 



Water temperature 26.5°C 4°C 



Air temperature 30°C 0°C 



Precipitation 3 cm/d' cm/d 



'This value becomes 0.01 cm/d in calculating rain 

 episodes, i.e., any day it rains is counted 



each variable ranging from 3 to 5 d. If the vari- 

 able went beyond the bias level for a duration 

 not exceeding the gap interval, the episode was 

 not terminated, although the days on which the 

 lapse occurred were not tallied in the episode 

 length. Thus, the episode of high salinities men- 

 tioned above would be counted as 27 d. 



Finally, the possibility remains that the stocks 

 might be acutely affected by short-term, intense 

 stresses. We felt this eventuality would be re- 

 flected in the annual extremes of each variable. 



These four operations, when applied to the four 

 daily time series, yielded 26 annual time series of 

 interest. (Cumulative and extreme low precipi- 

 tations are uniformly zero by definition, and pro- 

 vide no information.) These series constituted the 

 possible "predictor vectors" from which those 

 yielding the best multiple regressions would be 

 chosen. The values for the 26 variables calcu- 

 lated for the years 1938-76 are listed in Ulano- 

 wicz, Caplins, and Dunnington (1980). 



REGRESSION METHODOLOGY 



In most fish stocks, year class size is considered 

 to be established by the juvenile stage (Cushing 

 1975). For example, oyster spat set (analogous to 

 juvenile stages of finfish) is a good indicator of 

 spawning success (Galtsoff 1964). Thus, recruit- 

 ment (and subsequently harvest) is often corre- 

 lated to those conditions in the past which helped 

 determine the level of juvenile success. In popu- 

 lations where all individuals in a year class are 

 recruited into the fishery at the same age, and 

 annual landings consist primarily of a single 

 year class, a significant correlation might be 

 obtained when the environmental variable in 

 question was lagged against landings by the 

 number of years equivalent to the age at recruit- 

 ment. 



For most species harvested in Maryland, re- 

 cruitment is not simultaneous for all members of 

 a year class; landings in 1 y r may consist of mem- 

 bers of several or many year classes. Thus, envi- 

 ronmental characteristics important to estab- 

 lishing year class strength may be partially 

 correlated with landings recorded over several 

 years, and vice versa. In order to account for such 

 extended partial recruitment, stepwise regres- 

 sions were employed, allowing the contribution 

 of a given environmental variable to be assessed 

 by successively lagging that independent vari- 

 able by annual increments so as to encompass the 

 lifespan of most of the stock being fished, i.e., 



613 



