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{)1158 > collected data are to be used for calculating population size, without any assumptions about historical data. However, at some point the noisy independent estimates must be somehow integrated into longer-term assessments of population change. One way to do that integration is to plot the independent estimates then use visual or statistical regression methods to identify trend patterns. The problem with this simple "state reconstruction" approach is that it fails to offer guidance about causes of decline (e.g. changes in recruitment of young fish versus changes in survival rate) and to properly weight estimates of varying quality due to changes over the years in sampling methods, locations, etc. Within-year methods for stock assessment using mark-recapture experiments are easily understood. We go out and mark a known number of fish, then examine what proportion of later samples are made up of these indi viduals. So for example if we mark 500 fish, and find that marked fish are 20% of the fish seen in recapture samples later that year, we would conclude that 500 is 20% of the population size, i.e. the population size was 2500. It does not, of course, work this nicely in the field. The percentage of fish marked in recapture samples can vary a lot by chance alone (luck of the draw): marked fish may be less vulnerable to capture later than unmarked ones (wariness, movement induced by sampling), movement of fish into and out of the marking region may dilute the mark rate, and there may be differential loss of tagged fish or tags. So any single point estimate must be treated with great caution. More complex assessment models, such as the ones we have called "ASMR" (Age-Specific Mark-Recapture) and "Supertag" in Grand Canyon studies, attempt to integrate information and estimates over time by using knowledge or assumptions about how the observations are linked through population dynamics processes. That is, we first build an accounting model for population changes (how the numbers of fish of each age die off over time over the months and years after they recruit to the population), then use this model to predict the observed historical data (both within the most recent year and from past years), then use statistical estimation methods to find the population model parameters (recruitment and survival rates) that best agree with the data. So when such a method is "looking" at the 2001 data, it is using calculations of the 2001 population structure (numbers of fish of various ages) that are based in part on observations of those fish made in earlier years when the fish were younger. Any such approach requires a key assumption, namely that the survival rates of fish from year to year are at least somewhat predictable. Part of the model development and testing process is to search for indications about whether such assumptions have been violated. We do see some indications that survival rates of age 3 and older chub have varied over time, and there is consistent, strong variation in survival rate with age of fish-older fish appear to have consistently higher annual survival rates. One way to think about the integrated assessment methods is that they produce point estimates for each year of population trend, as we could obtain from fitting a line through independent annual population estimates. But the points along the assessment model trend line are calculated from population dynamics accounting relationships (recruitment and survival) rather than just some trend formula that is "unconstrained" by any knowledge of ecological relationships that have given rise to the trend. Further, the assessment model trend estimate for each year consists of both fish that were seen (tagged) in earlier years (and are likely to have survived to the year in question), and fish that were first seen in later years, but at sizes and ages implying that they Draft - April 21, 2003 3