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Squawfish Population Viability Analysis --July 1993 Page 5 From such a mathematical description, one first obtains the discrete growth rate (A), and thereafter one can do sensitivity analysis and make structural modifications. For species such as the grizzly bear and the desert tortoise, such a life historical representation is the foundation of the PV A. For a whole list of reasons, life historical data are extremely difficult to obtain for the Colorado squawfish. What follows, however, is an attempt to obtain a best approximation to squawfish demography. 1.2 Age or Size? Species with indeterminate growth are often treated with size-based models rather than age-based models. However, Caswell's (1989) recent book on matrix population methods shows that the two approaches are quite similar. For the Colorado squawfish, it seems that size and age are closely correlated for the pre-reproductive period of life. After this, there are some problems. Nonetheless, one can hope that the two might be used interchangeably in future work. Since age-based demography is mathematically more tractable, and is better discussed in the literature, the discussion to follow will be based on age. 1.3 What's Initially Left Out: Density, Time & Space Typically, demographic analyses makes many simplifying assumptions about the population. The entire river basin is assumed homogeneous; thus, spatial position does not matter--the fish are the same everywhere. The fraction of the fish in each age (or size) class is assumed to remain constant with time; that is, the size distribution is stable. The discrete growth rate, denoted A (lambda), on an arbitrary time scale, e.g., per year, is a constant. The basic dynamic is Nt+l = ANt. Sometimes, A is simply assumed to be 1.0. The total population size at which this constancy is reached is irrelevant, though it is doubtless set by density-related, ecological factors. There are no fluctuations about average values, and there is, consequently, no possibility of population extinction. Without a sense of this Ideal Demography, it is hard to incorporate properly the effects of population density , ecology, stochastic enviro~ental variation and spatial structure to the limit of patchiness. 1.4 Time Scales Population dynamics have intrinsic time scales that are largely governed by the demography of the individuals of the species. The generation time is a