# 1. Estimation of American shad maturity schedules (ASMFC, 2020)
Maturity schedules or ogives were calculated by determining the proportion of mature and immature fish as a function of age for both male and female based on the capture of fish of a species.
When age data were not available, length was used as a surrogate.
In either case, this methods required satisfying the assumption of equal mixing of mature and immature fish and equal recruitment to gear.For most anadromous fish, this condition was not satisfied, and the assumption was then made for 'in-river' captures when all encountered fish were reproductively mature (ASMFC, 2020)
To estimate the age at maturity and identify previous spawning activity, two methods have been used: scales and otholiths.
However, Maki et al. (2001) developped a new approah to estimate maturity probability using scale-derived age in conjonction with the scale-derived patterns of spawning (Maki et al. 2001)
Consistent with this method, the ASMFC used at sea mortality estimates to inform a maturity ogive, by assuming that all fish observed returning to river system were reproductively mature.
## 1.1. Maturity ogives
Otholiths data were used as age informations and scales as a binary variable discriminating first time spawners from multiple spawners.
Following this, a matrix of age-at-capture and age_at first spawn was build for both male and female from each of the 3 regional metapopulations (semelparous, sourthern iteroparous, northern iteroparous)
Assuming a proportional capture of fish across years, and that all fish are susceptible to capture, the proportion of fish mature at age a (p_a) would then calculated as follow:
where p_a is the proportion of fish mature at age a, observed_a are mature fish observed at age a, with a assumed to be between years 1 and 9, and immature a are the immature fish observed each age.
As it was considered that returning fish were exclusively mature, there is no observations of immature fish at age.
Then, the proportion of immature fish was estimated based on all the returns greater than age a and the estimated mortality (M) at sea as below:
The natural mortality at sea (M) was calculated based on maximum ages following the method described in Then et al. (2015) for each region. Estimates of natural mortality by region and sex were provided in Table 10, and Table 27 from the ASMFC.
```{r echo = FALSE, fig.cap= "Table 1. Natural mortality estimates by region and sex. Maximum age data for the northern iteroparous (NI) region were borrowed from the sourthern iteroparous (SI) region due to more prevalent and long term impacts of man-made barriers in the NI region", out.width='100%'}
By considering both sex and the mortality correction approach, female have a later maturity-at-age than males in each region, as commonly observed in other shad groups(Taverny, 1991).
Both sexes begin to mature at 3 years,with males maturing on average in 4.3 years and females maturing on average in 4.6 years (ASMFC, 2020).
```{r echo = FALSE, fig.cap= "Table 2. American shad maturity-at-age by region and sex using the mortality correcion approach", out.width='100%'}
metapop == "southern iteroparous" & sex =="F" ~ 5.591,
metapop == "southern iteroparous" & sex =="M" ~ 5.065,
metapop == "northern iteroparous" & sex =="F" ~ 5.153,
metapop == "northern iteroparous" & sex =="M" ~ 4.611))
```
```{r echo = FALSE, fig.cap= "Table 3. American shad mean age at maturity by region and sex using the maturity schedule from the ASMFC report (2020)", out.width='100%' }
growthCurvesBySex %>%
distinct(metapop,sex,age_at_maturity) %>%
flextable() %>%
autofit()
```
```{r interpolation on age based on the mean length from Stich et al. (2020), echo = FALSE , include = TRUE, fig.cap= "Table 4. American shad mean age at maturity by region and sex based on the growth cruve from Stich et al. (2020)", out.width='100% }
Age-at-maturity derived from Stich growth curve are lowest than those estimates from the maturity ogive if we considered a mean size of approximately 38cm.
## 2.2. Length at maturity
In the GR3D model, females are mature for the first time at the length of 45cm (TL), and 40cm (TL) for males.
The mean length-at-age was computed for each river in the 3 region based on the VBF growth functions derived from Stich et al. (2020) described in "6-Growth_Calibration.Rmd".
geom_vline(aes(xintercept = age_at_maturity, color = sex)) +
labs(x = 'Age (year)', y = 'Fork length (cm)', color = "Metapopulation (Stich)") +
facet_wrap(.~ metapop, ncol =2)
```
```{r interpolation on size based on the mean age-at-maturity, echo = FALSE , include = TRUE, fig.cap= "Table 4. American shad mean age at maturity by region and sex based on the maturity ogives from the ASFCM report (2020)", out.width='100% }
