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## Carrying Capacity

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**Carrying Capacity**Spawning habitat Summer rearing Winter rearing Smolt Photo by John McMillan**Definition**Carrying Capacity = Number of individuals (K) the resources of a given area can support usually through the most unfavorable period of the year. • Tied to Limiting Factors**Population Regulation**• Density Independent Regulation = Population growth is not affected by population density; population persistence is explained by unpredictable environmental variability (Andrewartha and Birch). • Density Dependent Regulation = Population growth is affected by mechanisms whose effectiveness increases as population size increases (Nicholson, Lack, and Elton).**Evidence of Density Dependence**• Plot of population size and population growth rate (or surrogates such as mortality, natality, productivity, recruits, individual growth rates, movement). • There is a negative relationship between population size and growth rate, which means that carrying capacity may be estimated.**Methods for Estimating Carrying Capacity**• Time series of population growth over time (logistic function) • Habitat modeling (maximum number of fish within each habitat type; PHS) • Stock-recruitment modeling (Ricker, Beverton-Holt, or Smooth Hockey Stick)**Assumptions**• Assume we can define a population unambiguously. • Assume that we can measure population size accurately. • Assume that we have a biologically relevant time-step over which to measure the population growth rate. • Assume a uniformity of nature.**Habitat Models**• Habitat capacity can be estimated as the product of habitat area and fish/habitat relationships. • Percent Habitat Saturation Model (PHS) • Estimate the number of fish at maximum spawning escapement.**Stock-Recruitment Modeling**• Fit Ricker, Beverton-Holt, and Smooth Hockey Stick models to stock (eggs) and recruitment (fry, parr, smolts) data. • Ricker: • Beverton-Holt: • Smooth Hockey Stick:**Chiwawa Spring ChinookHabitat Model**• No habitat modeling has been completed in the Chiwawa River basin. • No estimates of PHS have been calculated. • Maximum parr and yearling smolt production likely occurred in 2002 when 1,725 spawners escaped in 2001. • One can also select the maximum number of parr and smolts.**Chiwawa Spring ChinookStock-Recruitment Model**• Stock-recruitment functions were fit successfully to parr and yearling smolt data.**Chiwawa Spring ChinookStock-Recruitment Model**Parr: Smolt: