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Carrying Capacity

What Is It And Why Is It Important?

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Photo from NOAA Science Center

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)

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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.

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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).

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Evidence of Density Dependence

 Plot of population size

and population growth rate (or surrogates such as survival rates, natality, productivity, recruits, individual growth rates, movement).

 There is a negative

relationship between population size and growth rate.

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200 400 600 800 1,000 1,200 500 1,000 1,500 2,000 2,500

Parr/Spawner

Chiwawa Spring Chinook

100 200 300 400 500 600 700 800 500 1,000 1,500 2,000 2,500

Smolts/Spawner Number of Spawners

Methods for Estimating Carrying Capacity

Time series analysis Stock-recruitment modeling Habitat modeling

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Time Series Analysis

 Plot population size over

time.

 Logistic function

𝑂𝑢 = 𝐿 1 + 𝐿 − 𝑂0 /𝑂0 𝑓−𝑠𝑢 𝑒𝑂 𝑒𝑢 = 𝑠𝑂 1 − 𝑂 𝐿

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Number Time

Logistic Growth

Carrying Capacity

K

Stock-Recruitment Modeling

 Fit Ricker, Beverton-Holt, and

Smooth Hockey Stick models to stock (spawners) and recruitment (fry, parr, smolts) data.

 Ricker:

𝑭(𝑺) = 𝜷𝑻𝒇−𝜸𝑻 𝑳 = 𝜷 𝜸 𝒇−𝟐

 Beverton-Holt:

𝑭 𝑺 = 𝜷𝑻 𝜸 + 𝑻 𝜷 = 𝑳

 Smooth Hockey Stick:

𝑭(𝑺) = 𝑺∞ 𝟐 − 𝒇

−

𝜷 𝑺∞ 𝑻

𝑺∞ = 𝑳 8

100 200 300 400 500 600 200 400 600 800 1000

Recruits Parents

Smooth Hockey Stick Model

Pop 1 Pop 2 Pop 3 Pop 4 50 100 150 200 250 300 200 400 600 800 1000

Recruits Parents

Ricker Model

Pop 1 Pop 2 Pop 3 Pop 4

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 𝐸𝑗 𝑦 𝑈

𝑗

 Others include Net Rate of

Energy Intake (NREI) models, Habitat Suitability (HSI) models, and Quantile Regression Forest (QRF) models.

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ISEMP/CHaMP (2015)

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

• ver which to measure population growth rate.

 Assume a uniformity of nature.

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Chiwawa Spring Chinook

Stock-Recruitment Models

 Stock-recruitment

functions were fit successfully to parr and yearling smolt data.

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20,000 40,000 60,000 80,000 100,000 120,000 500 1,000 1,500 2,000

Number of Smolts Number of Spawners

B-H Model Ricker Model Hockey Stick

40,000 80,000 120,000 160,000 200,000 500 1,000 1,500 2,000

Number of Parr Number of Spawners

Chiwawa Spring Chinook

B-H Model Ricker Model Hockey Stick

Chiwawa Spring Chinook

Stock-Recruitment Models

Parr: Smolt:

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Model Parameter Population capacity (K) Productivity Stock size 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 ∞ Model Parameter Population capacity (K) Productivity Stock size 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 ∞

Chiwawa Spring Chinook

Ricker Model: Quantile Regression

 Selecting 90% Reference

Interval:

 Carrying Capacity (K) 90,557 vs 50,572  Stock Size 833 vs 917

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20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 500 1,000 1,500 2,000

Number of Smolts Number of Spawners

Chiwawa Spring Chinook

Ricker Model

Mean 90% RI

Chiwawa Spring Chinook

Habitat Model: Quantile Regression Forest Model

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So What Do We Do With It?

Couples Counseling

 Used in life-cycle models to

predict effects of different 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.

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Managers (Mars) Researchers (Venus)

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