Bachillerato

odel Description
Only small numbers of Pterois miles have been documented along the Southeast United States [17] with no captures to date in The Bahamas [18]. Lionfish are hereafter referred to as inclusive of both P. miles and P. volitans. For the purpose of this modeling exercise, life history parameters were derived primarily from P. volitans. We assumed that given the taxonomic similaritybetween P. volitans and P. miles (two closely related sympatric species), there would be no substantial life history differences [see 19] between the two species that might affect the overall outcome of this study.
The population model structure was identical to that published previously [20], [21], and it predicted equilibrium recruitment and age-specific abundance under a variety of harvestrates. Survival schedules incorporated natural and harvest mortalities. Harvest was driven by a stated exploitation rate and length-based vulnerability to removal efforts. Fecundity was expressed as a function of fish weight and the collective fecundity for a given year was reduced by all mortality sources. The model included ages 1–20 and was constructed in Excel®.
Equilibrium recruitment wascalculated using a Botsford modification of a Beverton-Holt stock recruitment function [22], [23], [24] as described elsewhere [20]. This simple formulation predicts equilibrium recruitment as a function of the fishing mortality rate. The model predicted the equilibrium age-1 recruits (Req) of an exploited population and is summarized as [20]
(1)
where R0 is the number of age-1 recruits of the unfishedpopulation at equilibrium, and CR is the Goodyear compensation ratio [25]. It is unknown if the current population is near the asymptotic unfished abundance, however, because lionfish populations have been established for over ten years in the Atlantic coastal waters, we initiated the simulation at unfished equilibrium. This is supported by simulation runs initialized at very low population size,which reached equilibrium recruitment in four to six years depending upon the value for CR. The CR is defined as the ratio of the recruits per spawner at very low population abundance relative to the recruits per spawner in the unfished equilibrium condition [25]. The parameter R0 is the unfished age-1 recruitment at equilibrium and is simply a scaling parameter that does not influence modelpredictions.
The model used survivorship curves to calculate the survivors per recruit to each age. Survivorship to age a in the absence of fishing was found as
(2)
where Sa is the age-specific finite annual natural survival (i.e., e−M). Our survivorship schedules in the fished condition incorporated natural mortality and harvest as
(3)
where lfa is the survivorship in the fished condition, U isthe finite annual exploitation rate, and Va is the age-specific vulnerability to harvest. We specified the proportion of fish vulnerable to harvest as
(4)
where TL is the mean total length at age a as calculated from the von Bertalanffy growth model, Lvul is the total length at 50% vulnerability to capture, and SDvul is the standard deviation of the logistic distribution for Lvul. The term Vamodels increasing vulnerability with length, and SDvul specifies the steepness of the curve. Age-specific abundance (Na) was estimated as the product of the number of age-1 recruits (Req) and the age-specific survivorship schedule.
Mean fish weight-at-age was used as an index of fecundity (egg production) as fecundity is directly proportional to weight-at-age. The age-specific fecundity (fa) wasset to zero if weight-at-age was less than weight-at-maturity. To account for the cumulative effects of fishing on the reproductive capacity of the population, we used the incidence function for the unfished (Φ0) and fished (Φf) egg production per recruit [20]. These incidence functions were calculated as
(5)

(6)
where fa represents age-specific fecundity, and la and lfa are the survivorship...