144 
Fishery Bulletin 11 6(2) 
Conceptual diagram of population model used in this study to estimate freshwater larval recruitment (R t ) growth, 
survival (S t ), metamorphosis (M t ) and migration to the ocean, parasitic juvenile phase, and juvenile recruitment to 
freshwater (R s ) for sea lamprey (Petromyzon marinus ). Ri~R t represent ages of larval recruitment. S^St represent 
survival to the next age for either larvae or juveniles. and J 2 represent the number of juvenile lamprey spending 
one or two years at sea. The nutrient influence depicts the proposed effects of nutrients from sea lamprey carcasses 
on the growth of larval conspecifics. 
Dawson, 2007; Dawson and Jones, 2009). We defined mass of 885.2 g (Beamish et al., 1979) and 233 eggs/g 
the recruitment relationship as of mass (Hardisty, 1971; Table 1). 
R t = aEe-P E , 
ID Freshwater larval growth 
where R t = recruitment of larvae at age class t; 
E = the total number of eggs from female 
spawners; 
a = the slope at the y-intercept of the stock re¬ 
cruitment relationship and describes sur¬ 
vival at very low levels of E\ and 
3 = the slope of the stock-recruitment relation¬ 
ship and describes the degree to which 
survival falls as E increases (i.e., carrying 
capacity). 
We adjusted the a and 3 terms to obtain a stabilized 
population on the basis of the survival parameters 
used in the model (Table 1) and the desire to model a 
realistic carrying-capacity of adult spawners in a small 
stream (Gardner et al., 2012). We derived a value of 3 
iteratively to obtain a stable population size of 4800 
spawning adult sea lamprey for an area of suitable 
spawning habitat of approximately 4.8 ha (1 individu¬ 
al/10 m 2 ; Nislow and Kynard, 2009), which represents 
a realistic density of sea lamprey spawners in a third- 
order stream that was not impounded. We assumed an 
unequal sex ratio of 1.00:1.36 females to males for the 
total number of spawning adults (Beamish and Potter, 
1975; Beamish et al., 1979). The value of E was cal¬ 
culated from the number of females with an average 
We permitted larvae to remain in freshwater for up to 
12 years, which is within the range of the reported de¬ 
velopment period (Manion and Smith 1 ; Beamish, 1980). 
We modeled growth of larval sea lamprey according to 
a von Bertalanffy (1938) function, defined as 
L t = LJl-e~ m - to) ), (2) 
where L t 
K 
h 
the length of the larvae at time t (years); 
the theoretical maximum (asymptotic) body 
length; 
the Brody growth rate coefficient per year 
that describes the decline in growth rate 
as individuals approach L„; and 
the theoretical age at which body length is 
zero (Guy and Brown, 2007). 
We adopted the Ford-Walford method for estimating 
parameters of the von Bertalanffy growth function 
(Ford, 1933; Walford, 1946; Isely and Grabowski, 2007) 
by plotting L t and L t+1) transforming the von Berta¬ 
lanffy growth model to follow a linear relation. 
We used the plot of L t and L t+1 to extract the inter¬ 
cept b from linear regressions with different K values 
ranging from 0.3 to 0.7, which were selected to repre¬ 
sent a range of growth trajectories along a gradient 
of hypothetical streams of varying productivity. At K 
