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Squawfish Population Viability Analysis --July 1993 Page 33 even to a much lower equilibrium density. This means that viability from the standpoint of resilience to major catastrophes is reduced. 3.4 Allee Effects In thinking about Allee Effects the question to ask is: at low population density, in what way could the addition of another individual benefit the survi val or reproduction of the other individuals of the population? The only thing that makes sense for the squawfish involves mate acquisition and spawning success. It is well documented that adult squawfish migrate to spawn. Indeed; their migration distances are tremendous. Tyus (1991) cites evidence of 100 kilometer migration-for-spawning distances. Since this must be costly in terms of energy and also mortality risk, one must ask what benefit compensates for this cost. Possibly the fish aggregate at a location on the river that has increased fitness potential, for example, a location that lies just upstream of good nursery habitat for the post hatch juveniles. However, it is clear that some movement for mate seeking would be required in any case, as at 14 adults per kilometer a single fish is not guaranteed a neighbor of the opposite sex. Additionally, denser aggregations make for better fertilization probabilities. Assuming normal mass action dynamics, the chance that an egg is fertilized increases with the density of sperm. Thus, if twice as many fish aggregate, the production of fertilized eggs could be four times as great. Of course, if sperm actively seek eggs and are produced in excess, then all eggs will be fertilized regardless of the number of adult males present. The truth may lie somewhere in between. One hatchery study found only 33% fertilization. In any case, this idea is probably amenable to experimental investigation. Following this logic there could be a threshold density of adults at which point fewer adults will lead to smaller spawning aggregations, to a lower fraction of fertilized eggs and to disproportionately lower reproduction. Assuming that recruitment is proportional to the production of fertilized eggs, the population could enter a positive feedback loop that would drive it extinct in a deterministic fashion. Figure 3.3 illustrates this possibility.