Initial Population Abundance

The initial population abundance vector \(\underline{N}(1)\) represents the number of fish alive on January 1 of the first projection year. This vector defines the starting condition for all forward simulations in AGEPRO.

AGEPRO provides two methods for initializing the population:

  1. Stochastic Initialization – A set of \(B\) initial population vectors \(\underline{N}(1)^{(b)}\) are sampled from the estimated distribution of \(\underline{N}(1)\). This approach explicitly incorporates uncertainty in the initial population estimate and propagates that uncertainty through the projection. The sampling distribution of \(\underline{N}(1)\), denoted by \(\underline{N}^{(*)}(1) = \left\{ \underline{N}^{(1)}(1), \underline{N}^{(2)}(1), \dots , \underline{N}^{(B)}(1) \right\}\), can be derived using frequentist (bootstrapping), Bayesian (Markov Chain Monte Carlo), or other methods.

  2. Deterministic Initialization – A single point estimate of \(\underline{N}(1)\) is used, ignoring uncertainty. The deterministic option uses a single best estimate for \(\underline{N}(1)\). This approach assumes the initial population size is known exactly and only other stochastic elements (e.g., recruitment or process error) contribute to variability.

If the initial population vectors are expressed in relative units (e.g., thousands of fish), they must be converted to absolute numbers using a scaling coefficient \(k_N\). For each replicate \(b\),

\[ \underline{N}^{(b)}(1) = k_{N} \cdot \underline{n}^{(b)}(1) = {\Bigl(k_N \cdot n_1^{(b)}(1),\ ...,\ k_N \cdot n_A^{(b)}(1) \Bigr)} \]

where \(\underline{n}^{(b)}(1)\) is the relative abundance vector and \(\underline{N}^{(b)}(1)\) is the corresponding absolute abundance vector.