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Fishery Bulletin 11 6(2) 
von Bertalanffy growth curve. Larvae that reached 160 
mm TL were considered developed enough to undergo 
metamorphosis and migrate to the ocean on the basis 
of the midpoint of the range of lengths at which larvae 
begin metamorphosis (120-200 mm TL, see previous 
section). We estimated the number of individuals that 
underwent metamorphosis of each age class (iV met ) with 
the following equation: 
N met = (1 ~ M] arv )Pmet(l ~ M met ), (5) 
where P met = the probability of metamorphosis; and 
M met = the mortality associated with metamor¬ 
phosis and migration to the ocean. M met 
is poorly characterized (Hansen et al., 
2016) but, for our purposes, was desig¬ 
nated as 0.4 for individuals of all age 
classes. 
Juvenile demographics 
Juvenile sea lamprey typically spend 1-2 years at sea 
(Beamish, 1980). We calculated the number of juveniles 
spending a second year in the ocean as 
where J 2 
Ji 
Mjuv 
P 
£ mat 
J 2 - J\ (1 — Mj uv )( 1 — P m at)) 16) 
the number of juveniles recruited to a second 
year at sea; 
the number of juveniles that have completed 
a full year at sea; 
the estimated juvenile mortality; and 
the proportion of individuals recruiting to 
maturity and returning to freshwater to 
spawn. 
We calculated Mj uv to be 0.40, by averaging estimates 
of survivorship of juvenile to adult spawners in the 
Great Lakes (Eshenroder et al. 6 ; Jones et al., 2003; 
Howe et al. 5 ; Table 1). We designated probabilities as¬ 
sociated with juvenile P mat after 1 and 2 years at sea 
as 0.5 and 1.0, respectively. 
ductivity-mediated growth rate because is held con¬ 
stant. Therefore, higher values of K mean individuals 
reach their maximum length sooner. We hypothesized 
that a nutrient feedback mediated through additions 
to the value of K would have a peak effect (an inflec¬ 
tion point) followed by diminishing returns as the addi¬ 
tion of carcasses increased. This relationship has been 
postulated or shown for many ecological systems (Kefi 
et al., 2016) and effectively described with a logistic 
regression. During model simulations of populations 
receiving nutrient feedbacks, we assumed K values fol¬ 
lowed a logistic regression: 
K = 0.3 + l/(l + e^ +5TSt> ), (7) 
where y and 8 - parameters that influence how steeply 
the logistic function rises through a 
midpoint and the duration at which 
the midpoint occur, and 
TS t - the total number of adults returning to 
freshwater streams at year t. 
Calculated values from the logistic equation were added 
to the baseline K value of 0.3 to depict the adjustment 
in growth rate for larvae in subsidized populations. 
Model execution 
We initially populated each larval and juvenile age class 
with arbitrary values and ran the unsubsidized model 
for 200 years, which served as a burn-in period to allow 
the population to stabilize. We took the final numbers 
of each larval and juvenile age class and reseeded the 
starting model with those values. We estimated our un¬ 
subsidized population size at the point at which abun¬ 
dance remained constant over a 200-year period. We 
then reran the model with larval growth influenced by 
the number of returning adult spawners as reflected by 
varying values of K (Eq. 7) and examined the resulting 
changes in demographics for the subsidized population. 
Nutrient feedback model 
Model sensitivity 
Carcasses of postspawn sea lamprey deposit organic 
carbon and inorganic nitrogen and phosphorous in 
freshwater streams (Weaver et al., 2015), and such de¬ 
posits have been reported to influence stream produc¬ 
tivity (Weaver et al., 2016). To test the effect of a hypo¬ 
thetical influence of carcass nutrients on larval growth, 
we allowed the Brody growth coefficient K, to vary as a 
function of the number of carcasses deposited in fresh¬ 
water. This estimate of K served as a representation 
of the influence of organic and inorganic nutrients. Al¬ 
though A is a growth coefficient (which represents the 
rate at which growth slows as larvae approach L„) and 
not a growth rate per se, we used it as a proxy for pro- 
6 Eshenroder, R. L., R. A. Bergstedt, D. W. Cuddy, G. W. 
Fleischer, C. K. Minns, T. J. Morse, N. R. Payne, and R. 
G. Schorfhaar. 1987. Great Lakes Fishery Commission 
Report of the St. Marys River Sea Lamprey Task Force, 35 
p. [Available from website.] 
We gauged the local sensitivity of mortality, M larv , 
M met) Mjuv; the parameters a, (3, and K of unsubsidized 
populations; and the y and 8 logistic regression param¬ 
eters for manipulating K in subsidized populations. 
We applied a 1% increase in selected parameters on 
the number of total spawners in the stabilized popula¬ 
tion. Sensitivity ( S ) of parameters for number of total 
spawners was calculated as 
S = 
(R a -R n )/ R n 
(P a -P n )/P n ’ 
( 8 ) 
where R a = the result for the altered variable; 
R n - the result for the unaltered variable; 
P a = the altered parameter; and 
P n - the nominal parameter (Haefner, 2005; Bai¬ 
ley and Zydlewski, 2013). 
Model output was deemed “sensitive” to the parameter 
if IS I >1.00. 
