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MODELING CUI-UI RECOVERY practical; even if undisturbed by humans, popu- lations eventually disappear. Natural alterations occur in the environment; social values and pres- sures change. A more practical approach is to con- sider indefinite as a time span that reflects dimin- ishing interest in more and more distant future events by our present society. Conservation bi- ologists are fond of thinking in terms of 1,000 years. But when we stop to consider that 1,000 years ago the Norman conquest was still three gen- erations in the future, a millenium begins to seem like a very long time. Thompson (1991) stated that though no theoretical rationale supports a univer- sal time period of persistence, consolation can be derived from the frequency with which researchers have used 100 years. This value, however, is too short for cui-ui because it covers only 2.5 life spans. A more reasonable and, in terms of a collective, societal attention span, realistic time frame is two centuries. This value is similar to the 250 years considered for the northern spotted owl Strix oc- cidentalis (Thomas et al. 1990). Accordingly, the definition of indefinite in this report is taken to be 200 years. There is never certainty that a population will persist for 200 years. At what level of probability are we to be satisfied that a species has recovered? In keeping with standard statistical procedure for distinguishing between a null hypothesis (extinc- tion) and its alternative, we suggest 95% as an acceptable level. Thompson (1991) suggested re- liance on this percentage because of the numerous researchers that have used similar values in the past. Models Used As noted above, we believe the driving envi- ronmental variable for cui.ui population dynam- ics is availability of water. Even many secondary factors, such as temperature effects on egg devel- opment and survival, are controlled largely by wa- ter supply. Accordingly, the model used to project the cui-ui population is driven by river flow. That is, it assumes that cui.ui reproduction and mor- tality are mediated solely through hydrologic con- ditions. This approach does not deny the possible importance of other ecological factors (e.g., pre- dation on larvae by other species). It merely re- flects our belief in the overriding influence of lake level and the efficacy of model simplicity. Because cui-ui population dynamics depend on hydrology, and because acquired water would be only supplemental to the underlying hydrological events, predictions of future fish population size 469 must reflect future natural hydrologic scenarios. These scenarios cannot be known with certainty. Thus, it is necessary to rely on probabilistic pro- jections. For such projections to be valid, two re- quirements must be considered. First, hydrologic sequences are likely to be au- tocorrelated-that is, a wet year might more likely be followed by another wet year than by a dry one or vice versa. Of course, the correlation between adjacent years might be positive and the correla- tion between years t and t + 2 might be negative. Any predicted future scenario must reflect such autocorrelations. Second, hydrologic events are correlated in space, at least within a watershed. For example, snowfall in the Truckee River watershed and water avail- ability in Stampede Reservoir, a reservoir dedi- cated to cui-ui in the Truckee River basin, affect available flow in the lower Truckee River. Any predicted future scenario must reflect these spatial relations. Information inherent in the above two require- ments can be captured by describing the proba- bility that a certain hydrological condition will occur at some point, A, as a function of what is happening at points B, C, etc., and what has hap- pened at point A in previous years. Such a de- scription is known as a conditional probability density function. If we possessed such a density function and if, in addition, we knew point A's history and also the upcoming conditions at B, C, etc., we would be able to predict the probability of the upcoming condition at A. If we were to obtain an expression that gave this probability for all points A, B, C, etc., simultaneously (a multi- variate conditional probability density function), we would be able to predict simultaneously the probability of any upcoming spatial configuration of conditions over the various points. In fact, we could do better than this: we could produce hy- pothetical spatial configurations of conditions in proportion to their probabilities of occurrence and thus generate representative samplings of condi- tions that faithfully reproduce the relations in the observed (historical) hydrological record. By stringing a number of such outputs together, year after year, we could even produce representative sequences of conditions over as long a period as we wished. These sequences could then be used to predict hypothetical scenarios of cui-ui population dynamics, each scenario being an equally likely future. Then if for some regime of supplemental water 20 out of every 100 such simulations led to population die off, for example, we could conclude