for given spawning locations and hatching rates, 

 will be supplied by NU. Once MIT has validated 

 its model, the computer code will be installed in 

 our own computer system to run additional sim- 

 ulations as new or better input data become avail- 

 able. ITie MIT model is expected to be completed 

 before the end of 1988. 



Population dynamics model 



A problem central to modeling the dynamics 

 of fish populations is the difficulty of finding an 

 adequate formulation for describing the recruit- 

 ment process. Because egg and larval survival is 

 more dependent on environmental factors than 

 adult fish survival, a prominent feature of recruit- 

 ment data for many fisheries is the large amount 

 of variability present that cannot be attributed to 

 changes in parental stock size. Despite this well- 

 documented fact, past deterministic population 

 models (Christensen et al. 1977; Saila and Lorda 

 1977) have included in their formulations recruit- 

 ment equations whose parameters describe only 

 variation in parental stock and assume populations 

 at equilibrium. By contrast, our modeling ap- 

 proach recognizes that the very great temporal 

 variation in recruitment nullifies the concept of 

 "equilibrium" conditions and this mandates 

 stochastic models that account for this variability. 

 This is important because, for commercially ex- 

 ploited species like the winter flounder, the higher 

 the fishing effort, which reduces the average life- 

 time of the fish and their reproductive potential, 

 the greater is the significance of year-to-year vari- 

 ability. 



Our population model for the Niantic River 

 winter flounder will use a temperature-dependent 

 stock-recruitment relationship to generate year- 

 classes whose size depend upon both the water 

 temperature during larval development and the 

 size of the spawning population. This particular 

 representation of the recruitment process includes 

 compensatory mortality (based on the stock- 

 recruit model previously described) and will permit 

 the mtroduction of realistic environmental vari- 

 ability related to the water temperature in Febru- 

 ary. Although the temperature variability will be 



simulated stochastically, this will be done using 

 an empirical distribution derived from actual 

 records of annual mean water temperatures in 

 February. Because an earlier version of our 

 stochastic population dynamics model was already 

 described by Lxjrda et al. (1987), only the basic 

 features of the updated version now under devel- 

 opment are presented here. 



The final model will describe the dynamics of 

 an age-structured population of winter flounder 

 with stochastic recruitment and compensatory 

 mortality that occurs during the first year of the 

 life of the fish. ITie model makes no assumptions 

 about the stability of the population or its age 

 structure, which can vary as a result of environ- 

 mental variability introduced via the recruitment 

 equations. Adult fish are subject to annual natural 

 and fishing mortalities, and mature sundvors 

 spawn according to fecundity rates that depend 

 on the age of the fish. Although a Leslie matrix 

 formulation is used to carry the computations 

 corresponding to these annual processes, its func- 

 tion is simply one of book-keeping. This is so 

 because the size of each year-class is determined 

 by the stochastic recruitment, and the I^slie ma- 

 trix is only used to update the number of fish in 

 each age-class at the end of each year. A box- 

 and-arrow diagram of the underlying life-cycle 

 simulation scheme is shown in Figure 37. The 

 impact of larval entrainment is represented in this 

 diagram as additional density-independent mor- 

 tality in age-class 0. This mortality can be varied 

 annually and the actual value will be based on 

 estimates provided by the MIT larval dispersal 

 and entrainment model. A sample of graphical 

 model output corresponding to a simulation that 

 assumes a 10% larval mortahty due to entrainment 

 is shown, for illustrative purposes only, in Figure 

 38. The vertical line at 35 years, represents the 

 point in the simulation at which larval entrainment 

 ceases and the population size begins its climb 

 back to its initial level. This pattern of slow 

 population decline while entrainment takes place, 

 followed by a faster return to initial levels, is 

 typical of populations in which compensatory 

 mortality operates. 



210 



