Carrying Capacity What Is It And Why Is It Important? Photo from - PowerPoint PPT Presentation

Carrying Capacity What Is It And Why Is It Important? Photo from NOAA Science Center 1

Definition Carrying Capacity = Number of individuals or biomass the resources of a given area can support usually through the most unfavorable period of the year. Maximum Environmental Load  Linked to Tolerance Limits and Limiting Factors (aka  ecological concerns) Habitat Capacity (C)  2

Definition Population Capacity = Maximum equilibrium population size (K) estimated using population models such as the logistic equation or some stock-recruitment models.  Defines an upper limit to population growth as density increases. 3

Population Regulation  Density Independent Factors = 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 Chiwawa Spring Chinook 1,200  Plot of population size 1,000 and population growth Parr/Spawner 800 rate (or surrogates such as 600 survival rates, natality, 400 productivity, recruits, 200 individual growth rates, 0 0 500 1,000 1,500 2,000 2,500 movement).  There is a negative 800 relationship between 700 600 population size and Smolts/Spawner 500 growth rate. 400 300 200 100 0 0 500 1,000 1,500 2,000 2,500 Number of Spawners 5

Methods for Estimating Carrying Capacity  Time series analysis  Stock-recruitment modeling  Habitat modeling 6

Time Series Analysis  Plot population size over time. Logistic Growth  Logistic function Carrying Capacity 𝐿 K 𝑂 𝑢 = Number 𝐿 − 𝑂 0 /𝑂 0 𝑓 −𝑠𝑢 1 + 𝑒𝑂 𝑒𝑢 = 𝑠𝑂 1 − 𝑂 𝐿 0 Time 7

Stock-Recruitment Modeling Ricker Model 300  Fit Ricker, Beverton-Holt, and Pop 1 Pop 2 250 Smooth Hockey Stick models to Pop 3 Pop 4 Recruits 200 stock (spawners) and recruitment 150 (fry, parr, smolts) data. 100  Ricker: 50 𝑭(𝑺) = 𝜷𝑻𝒇 −𝜸𝑻 0 𝜷 0 200 400 600 800 1000 𝜸 𝒇 −𝟐 𝑳 = Parents  Beverton-Holt: Smooth Hockey Stick Model 𝜷𝑻 600 𝑭 𝑺 = 𝜸 + 𝑻 500 𝜷 = 𝑳 Recruits 400  Smooth Hockey Stick: 300 Pop 1 Pop 2 200 𝜷 − 𝑺∞ 𝑻 Pop 3 𝑭(𝑺) = 𝑺 ∞ 𝟐 − 𝒇 Pop 4 100 𝑺 ∞ = 𝑳 0 0 200 400 600 800 1000 Parents 8

Habitat Models  Habitat capacity can be estimated as the product of habitat area and fish/habitat relationships.  Percent Habitat Saturation Model (PHS) 𝑄𝐼𝑇 = 100 𝑦 𝐸 𝑗 𝑦 𝑈 𝑗  Others include Net Rate of Energy Intake (NREI) models, Habitat Suitability (HSI) models, and Quantile Regression Forest (QRF) models. ISEMP/CHaMP (2015) 9

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 population growth rate.  Assume a uniformity of nature. 10

Chiwawa Spring Chinook Stock-Recruitment Models Chiwawa Spring Chinook 200,000  Stock-recruitment B-H Model Ricker Model 160,000 Number of Parr Hockey Stick functions were fit 120,000 successfully to parr 80,000 and yearling smolt 40,000 data. 0 0 500 1,000 1,500 2,000 Number of Spawners 120,000 B-H Model 100,000 Ricker Model Number of Smolts Hockey Stick 80,000 60,000 40,000 20,000 0 0 500 1,000 1,500 2,000 11 Number of Spawners

Chiwawa Spring Chinook Stock-Recruitment Models Parr: Parameter Population Model Productivity Stock size capacity (K) A B Ricker 271.37 0.0009 114,749 271 1,149 Hockey Stick 11.61 314.44 110,747 314 1,055 Beverton-Holt 144,927.36 416.36 144,927 348 ∞ Smolt: Parameter Population Model Productivity Stock size capacity (K) A B Ricker 149.84 0.0011 50,572 150 917 Hockey Stick 10.75 172.33 46,494 172 809 Beverton-Holt 57,854.21 289.50 57,854 200 ∞ 12

Chiwawa Spring Chinook Ricker Model: Quantile Regression  Selecting 90% Reference Interval: Chiwawa Spring Chinook Ricker Model 160,000  Carrying Capacity (K) Mean 140,000 90% RI 120,000 90,557 vs 50,572 Number of Smolts 100,000  Stock Size 80,000 60,000 833 vs 917 40,000 20,000 0 0 500 1,000 1,500 2,000 Number of Spawners 13

Chiwawa Spring Chinook Habitat Model: Quantile Regression Forest Model 14

So What Do We Do With It? Couples Counseling  Used in life-cycle models to Managers Researchers predict effects of different (Mars) (Venus) recovery scenarios.  Used by hatchery managers to inform supplementation programs.  Used by harvest managers to set appropriate escapement and harvest levels.  Used by restoration practitioners to guide restoration actions. 15

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