Weaver et al.: Influence of nutrients from carcasses of Petromyzon marinus on growth of larval conspecifics 
145 
Table t 
Settings for recruitment and life-history variables for a model that represents a population 
of anadromous sea lamprey (Petromyzon marinus). 
Variable 
Value 
Source 
Recruitment 
a 
0.0014 
Derived from this study 
P 
2.84 x 10- 9 
Derived from this study 
K 
0.3-0.7 
Modified from Quintella et al. (2003) 
Eggs (p-g-mass -1 ) 
233 
Hardisty (1971) 
Female adult mass (g) 
885.2 
Beamish et al. (1979) 
Proportion of females 
0.44 
Beamish and Potter (1975), 
Mortality 
Larval mortality (Mi arv ) 
Age 1 
0.70 
Beamish et al. (1979) 
Age 2 
0.20 
Age 3 
0.10 
Adopted from Zerrenner (2001), 
Age 4 
0.10 
Howe et al. 5 
Age 5 
0.10 
Ages 6-12 
0.10 
Metamorphosis (M met ) 
0.40 
Best guess estimate 
Juvenile ( M )av ) 
0.40 
Eshenroder et al. 6 , 
Jones et al. (2003); Howe et al. 5 
values <0.3, simulated larval populations did not reach 
within the designated age structure. We capped 
the range of K at 0.7, which was observed in larval 
populations by Quintella et al. (2003) in the Mondego 
River, Portugal, where larvae grew relatively quickly 
and achieved metamorphosis at age 4 or younger. We 
plotted K and h values and then extracted the linear 
equation to use as an intercept (fe w ) to estimate the 
length of larvae. We then estimated the body length of 
an individual at t +1 as 
Lt+i - L t e~ K + hvi . (3) 
This method allowed us to manipulate K as a way of 
representing the influence of nutrient subsidies on lar¬ 
val growth. Estimated values of K obtained from the 
Ford-Walford plot were calculated as the inverse natu¬ 
ral log of the slope. This method approximates but is 
not identical to those directly derived from the von Ber- 
talanffy growth function (Isely and Grabowski, 2007). 
To define the von Bertalanffy growth curve, we used 
an initial hatching length of 10 mm, a size adopted 
from 51-d posthatch larvae of Pacific lamprey (Ento- 
sphenus tridentatus) (Barron et al., 2016). We found 
reported total lengths (TLs) of larval sea lamprey be¬ 
fore metamorphosis in a range from 120 to 200 mm 
(Manion and McLain 4 ; Potter et al., 1978; Quintella et 
al., 2003), and we used a length of 200 mm TL as the 
value for L„. We defined a minimum K value of 0.3, 
which served as a baseline value for simulated unsub¬ 
sidized populations. Subsidized populations had aug¬ 
mented K values that were calculated as a function of 
the number of returning adult spawners (see Eq. 7 in 
the Nutrient feedback model section). 
We adopted the pattern of estimated annual inter¬ 
val larval mortality at age from Zerrenner (2001), Zer- 
renner and Marsden, 2005, and Howe et al. 5 (Table 1) 
for larval ages 1-12. We calculated larval survival to 
the next age class with the following equation: 
W t+ i = W t (l-M larv )(l-P met ), (4) 
where iV t+1 
N t 
■M] a rv 
p 
1 met 
the number of larvae that are recruited to 
the f+l age class; 
the number in the current age class; 
the estimated larval mortality; and 
the proportion of larvae that underwent 
metamorphosis and migrated out of 
freshwater. 
Probability of metamorphosis 
We modeled larval metamorphosis into the macropthal- 
mic stage by using length and growth data from the 
4 Manion, P. J., and A. L. McLain. 1971. Biology of larval 
sea lampreys (Petromyzon marinus) of the 1960 year class, 
isolated in the Big Garlic River, Michigan, 1960-65. Great 
Lakes Fish. Comm., Tech. Rep. 16, 33 p. [Available from 
website.] 
5 Howe, E. A., E. Marsden, and T. M. Donovan. 2004. Stage 
based population viability model for sea lamprey ( Petromy¬ 
zon marnius). Lake Champlain Basin. Prog., Tech. Rep. 43, 
37 p. [Available from website.] 
