Ecological Archives A024-051-A4

D. Andrew R. Drake, Nicholas E. Mandrak. 2014. Bycatch, bait, anglers, and roads: quantifying vector activity and propagule introduction risk across lake ecosystems. Ecological Applications 24:877–894. http://dx.doi.org/10.1890/13-0541.1

Appendix D. Probability distributions describing the availability of n propagules as bycatch to purchasing anglers.

TABLE D1. Characteristics of probability distributions describing the availability of n propagules as bycatch to purchasing anglers (i.e., bycatch parameters: P purchase (n propagules)). Encounter rates (i.e., P purchase (> 0 propagules) for baseline were based on empirical sampling; whereas, infestation and bycatch reduction represent a four-fold increase, and ninety percent reduction, respectively, in encounter rates relative to baseline.  The parameter lambda (λ ) describes the mean value of the Poisson distribution; whereas, the parameter mu (μ) describes the mean value of the zero-inflated negative binomial distribution, with additional parameters size (the overdispersion parameter) and zprob (the probability of structural zeros).

Probability Distribution

Model Scenario

λ

μ

size

zprob

Probability of purchasing n propagules

 

 

 

 

 

 

n = 0

n > 0
(Encounter Rate)

n = 1

n = 2

n = 10

Poisson

Baseline

0.00735

-

-

-

0.9927

0.0073
(~1 in 137)

0.007296

0.0000268

1.25E-28

 

Infestation

0.0294

-

-

-

0.9710

0.0290
(~1 in 35)

0.028548

0.0004197

1.29E-22

 

Bycatch Reduction

0.000735

-

-

-

0.9993

0.000734
(~1 in 1369)

0.000699

0.0000003

1.26E-38

                     

Zero-inflated negative binomial

Baseline

-

0.8

0.3

0.9773

0.9927

0.0073
(~1 in 137)

0.003354

0.0015855

4.20E-05

 

Infestation

-

0.8

0.3

0.9103

0.9710

0.0290
(~1 in 35)

0.013253

0.0062653

1.66E-03

 

Bycatch Reduction

-

0.8

0.3

0.9977

0.9993

0.000734
(~1 in 1369)

0.000339

0.0001607

4.26E-06


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