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# Carrying Capacity

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.

## Carrying Capacity

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1. Carrying Capacity Spawning habitat Summer rearing Winter rearing Smolt Photo by John McMillan

2. 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

3. 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).

4. 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.

5. 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)

6. 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.

7. 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.

8. 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:

9. 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.

10. Chiwawa Spring ChinookStock-Recruitment Model • Stock-recruitment functions were fit successfully to parr and yearling smolt data.

11. Chiwawa Spring ChinookStock-Recruitment Model Parr: Smolt:

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