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. .. '. i" .,. .... I, .. .' ,.' T ~', II. :~ ,f^' r \~ must have been present in that year. That is, the assessment model trend estimates use sampling information both forward and backward in time, and thus should be most accurate for years (mid 1990s) where there are many surrounding observations. Conversely, they are least accurate for the most recent year(s), particularly for younger (recruiting) fish, about which we have the fewest direct observations. Integrated assessment methods involve first constructing a population accounting model, to produce a table of predicted numbers of fish at age (or size) over time given input estimates of initial age structure, recruitments, and age-time survival patterns. These predicted numbers are then compared to observed capture and recapture patterns, using statistical measures called "likelihood functions" that estimate the odds of obtaining the data if the population model estimates were correct. Then the model estimates are systematically varied (using computer search routines) to seek the "maximum likelihood" estimates. There are two basic ways to carry out the population accounting calculations, called "stock synthesis" and "virtual population analysis". In the stock synthesis approach, the numbers of fish of each age present in 1989 and each cohort of young fish recruited since 1989 is treated as a separate unknown, and population structure is calculated forward in time from these starting numbers. This is what we did with "Supertag", and to reduce the number of unknowns we assumed the population to have a stable age structure in 1989. We did not notice that the size-age data available for the early 1990s contain a much larger proportion of older fish than would a stable age distribution, and we now interpret that bulge as indicative of considerably higher recruitments during the 1970s-80s than in more recent years. In the virtual population analysis approach, we simply reverse the population accounting calculations. We initialize the accounting calculations with estimates of numbers of fish at age in the most recent year, and we back-calculate how many additional fish must have been present in earlier years (and ages) in order to account for numbers of fish tagged and recaptured over time while allowing for natural mortality along the way. We believe that this approach gives a much better estimate of the population age structure in 1989, from which we can make inferences about how much higher recruitments must have been prior to 1989 in order to have produced that initial age structure. This approach has been implemented in a relatively simple (annual data only) way in a spreadsheet model called "Tagage" or" Annual -ASMR", and we are currently developing a much more detailed implementation that will make better use of within- year information (e.g. within-year mark-recapture observations; Monthly - ASMR) to improve the estimates of both long-term recruitment trend and of the most recent population size. In Grand Canyon adaptive management, a key issue is whether various management policies can improve humpback chub juvenile survival and recruitment. Integrated stock assessment methods are particularly critical for recruitment assessments. Our first real chance to look quantitatively at the abundance of each year class or cohort of chubs as it recruits, is in the late fall of the year aftcr that cohort has reached age 2+, when many of the fish have reached the 150mm body length at which it is safe to tag them with PIT tags. In the last few years, fall mark-recapture programs in the Little Colorado River have started to give us such early point estimates of recruitment, but these estimates are quite unreliable (unknown and variable propOltion of each cohort large Draft - April 21,2003 4