FRWS 6400
2/13/2016
Lab 12 – Simulating Supplementation Strategies for Maintaining a
Cutthroat Trout Population
Objectives: The objective of this lab is to learn how to re-create a population model from
information provided in a paper. We will use a paper by Robert Hilderbrand (2002), who
was a PhD student at USU, to build a model for a small cutthroat trout population. In his
paper, Hilderbrand states that “Many interior populations of cutthroat trout are at increased
risk for extinction because of small population size and the limited length of habitable
streams. Further, many of these streams cannot be altered to provide adequate conditions for
population persistence. I constructed a stage-based, stochastic population model to (1)
evaluate reintroduction strategies for streams capable of population restoration, and (2)
evaluate the feasibility of maintaining populations through periodic stocking.”
Hilderbrand’s paper deals with issues common to biologists managing small populations.
We will build the model step by step and then, next week, run Monte Carlo simulations to
evaluate several reintroduction and supplementation strategies for this small population.
1. Using the data in Table 1 (see class website for electronic copy) build a pre-birth pulse
census, discrete time, density independent population model. Use an initial population
size of 625 divided equally between stages 2, 3, and 4. Build your model for 100 time
steps to emulate Hilderbrand’s model. Calculate  for this model.
2. Use a carrying capacity of 2500 and include density dependence using a Beverton-Holt
type density dependence function of the form:
N t 1




1

 Nt 
   1 
1   K  N t 


What is  for year 99?
3. Following Hilderbrand, incorporate temporal stochasticity for the density dependent
model by randomly generating a normally distributed value with a standard deviation
(SD) of 0.09 around each stage transition probability and truncating this distribution at
3 SD. (Not worrying about fecundity).
4. The population is considered viable and persistent when at least 95% of populations
(simulations or runs) in a simulation did not go extinct before 100 years. What percent
of the time does the population go extinct when the initial population size is 125, divided
equally between stages 2, 3, and 4?
Literature cited:
Hilderbrand, R. H. 2002. Simulating supplementation strategies for restoring and maintaining
stream resident cutthroat trout populations. North American Journal of Fisheries
Management 22:879-887.
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FRWS 6400
2/13/2016
Functions and formulas you will use for this lab:
N(t+1) = N(t) + B(t) – D(t) to incorporate demographic stochasticity
N(t+1) = N(t)(1 + b – d) to incorporate temporal stochasticity
CRITBINOM(trials,probability_s,alpha) – demographic stochasticity
BETAINV(probability,alpha,beta,A,B) – temporal stochasticity
(
=IF TRIM (ISERR ( MIN(E14:E43) ) ) ="TRUE", "", MIN(E14:E43)
)
=COUNTIF(F14:F43,">0")-1 – to calculate years to crash
COUNTIF(range,criteria)
Range is the range of cells from which you want to count cells.
Criteria is the criteria in the form of a number, expression, or text that defines which cells will
be counted. For example, criteria can be expressed as 32, "32", ">32", "apples".
{=FREQUENCY(B12:B1011,$F$12:$F$18)}
FREQUENCY(data_array,bins_array)
Note The formula in the example must be entered as an array formula. After copying the
example to a blank worksheet, select the range A13:A16 starting with the formula cell. Press F2,
and then press CTRL+SHIFT+ENTER
=IF($B11<=C$9,0,1) – for time to crash calculations
=SUM(C11:C1010)/COUNT(C11:C1010) – to calculate probabilities
=ROUND(E15*S_doe,0)
ROUND (number or function, #digits)
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