Population Dynamics

The Shark Population Assessment Group is attempting to represent the population dynamics of sharks through demographic methods and assess the status of shark stocks through stock assessment methodology.

Demographic methods

Life tables utilize fecundity and mortality schedules to project the population infinitely into the future and obtain estimates of the per capita rate of population increase (r), the finite population growth rate (e^r), or the mean generation time (T). The Leslie-matrix approach also allows the estimation of population growth rates and the calculation of elasticities proportional matricies sensitivities of e^r to changes in vital rates.

Elasticities can be calculated analytically from the dominant eigenvalue of the Leslie matrix (e^r) and the stable age and reproductive value distributions. Elasticities measure the effect from a proportional change in a vital rate on e^r. Both the life table and Leslie-matrix approach assume density-independence and generally time-invariance of vital rates and that the population will grow steadily at a rate of e^r after it reaches a stable age distribution.

Because of the difficulty of ageing many species of sharks, stage-based matrix models have recently been used to describe the demography of some species (e.g., the sandbar shark Carcharhinus plumbeus). Most of the demographic analyses conducted so far for sharks, however, have been deterministic. Because of the uncertainty in estimates of vital rates as well as the natural variability in those rates, it is necessary to adopt a stochastic approach. Monte Carlo simulation and elasticity analysis are tools used to investigate the demography of a species under uncertainty.

The group hopes to answer the following questions:

1. How do elasmobranch uncertainty and natural variability in vital rates affect population growth rates and generation times?

2. What are the most vulnerable life stages?

3. How likely is it that density-dependent compensation can offset the effects of exploitation given the life-history constraints of a particular species?

Stock assessment methodology

Few stock assessments of shark resources have been conducted because catch and catch rate data series, as well as age data, are often very limited or completely lacking for shark species.

Biomass dynamic models (e.g. the Schaefer model) can be used when good series of catches and catch-per-unit-effort are available. Age-structured models (e.g. virtual population analysis, dynamic pool models, yield-per-recruit models, or delay difference models) require knowledge of the age and growth dynamics of the stock. Some of the age-structured models also allow incorporation of gear selectivity parameters, natural mortality rates, and weight-at-age estimates. Recently, both biomass dynamic models and age-structured population models have been applied within a Bayesian approach to stock assessment. Bayesian methods offer the advantage of being able to incorporate experience into both the modeling process and the evaluation of alternative management options.

The Shark Population Assessment Group is using the Bayesian framework with biomass dynamics and age-structured models to assess the status of a variety of shark stocks in waters off the southeastern US. Stochastic population rates of increase are obtained through demographic methods, age and growth studies, and gear selectivity experiments. Additionally, fishery-dependent and -independent catch rates are standardized through generalized linear modeling (GLM) procedures. Results from previous stock assessments can be found by clicking on the Publications link on the right.

To see information regarding the latest Large Coastal Shark Stock Assessment on the SEDAR website, please Click Here.