Coastal wetlands act as nursery habitats for several commercially and recreationally exploited species of fish and crustaceans (Beck et al., 2001; Dahlgren et al., 2006).
Taylor et al. (2018) provide an established framework to estimate the value of coastal wetlands (e.g., mangroves, saltmarsh) on the basis of their contribution to the diet of exploited species via the following formula:
\[\begin{equation} GVP_{s,p} = C_{s,p}\cdot H_s\cdot M_s\cdot P_s \tag{2.1} \end{equation}\]
where GVPs, p is the gross value of production (AUD y-1) of species s derived from primary producer p, Cs, p is the proportional contribution of primary producer p for species s derived from stable isotope measurements and associated modelling, Hs is the annual harvest of species s (kg y-1), Ms is the market value for species s (AUD kg-1), and Ps is the spatial partitioning coefficient for species s (see Taylor et al. (2018) for further details).
Estimation of economic value is achieved by determining the gross value of production (GVP), based on market value at first-point-of-sale (FPS). GVP is then converted to total economic output (TOP) via an economic multiplier (m; derived from data presented in Voyer et al., 2016). The multiplier m is expressed using a normal distribution (i.e., \(m \sim N[\mu, \sigma]\)), derived from the statewide-GVP for New South Wales (PGV), and the minimum (Omin) and maximum (Omax) estimate of total economic output from commercial fishing (including GVP, and the value of retail processing etc.) reported in Voyer et al. (2016), using the two following equations:
\[\begin{equation} \sigma = \frac{\frac{O_{max}-O_{min}}{P_{GV}}}{6} \tag{2.2} \end{equation}\]
\[\begin{equation} \mu = \frac{O_{max}}{P_{GV}}-3\sigma \tag{2.3} \end{equation}\]
Enhancement (E) of the exploited species (s) by habitat (h) is calculated for each species using the following equation:
\[\begin{equation} E_{s,e} = (P_{s, h} - P_{s,u}) \tag{3.1} \end{equation}\]
where Ps, h is the abundance of juveniles (estimated to be 0.5 years old) of species s in habitat h (individuals ha-1), and Ps, u is the abundance of species s in unvegetated habitats u (Zu Ermgassen et al., 2016; Jänes et al., 2020).
Total average annual biomass production of each exploited species s supported by habitat h (kg ha-1 y-1) is estimated using the approach developed by Peterson et al. (2003) and extended by Zu Ermgassen et al. (2016). This approach incorporates species-specific natural mortality (M), but not fishing mortality, via the following equation:
\[\begin{equation} y_{s,i} = e^{-Mi} \tag{3.2} \end{equation}\]
where ys is the proportion of exploited species s surviving to age class i. Biomass enhancement (kg ha-1) for each age class (Bi) is then calculated by:
\[\begin{equation} B_i = E_{s,e}\cdot e^{-M\cdot(i-0.5)} \tag{3.3} \end{equation}\]
where Es,e is taken from Equation (3.1). For each age class i, the length of an average individual (total length [TL] for teleosts, carapace length [CL] for crustaceans) was calculated using the Lorenzen (2000) growth equation and subsequently converted to weight (biomass, kg) using length-weight relationships. The total annual biomass enhancement (kg ha-1) of species s was then calculated by summing the incremental increase in biomass for an average individual in each year class i by the number/density (ha-1) of species s (Bi) in each age class.
x <- rnorm(n = 100, mean = 0, sd = 1)
mean(x)
## [1] -0.01107776
hist(x)