##1.Observation of American shad maturity schedules (ASMFC, 2020)
#Growth parameters from Stich et al, 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.
#Temperature relative values from growth optimization
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)
growParStich <- Stich2020_sel %>%
To estimate the age at maturity and identify previous spawning activity, two methods have been used: scales and otholiths.
filter(catchment %in% regional_metapop) %>%
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)
select(catchment, Linf, K, L0_theo) %>%
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.
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)
```{r test }
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.
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).
group_by(age) %>%
Both sexes begin to mature at 3 years,with males maturing on average in 4.64 years and females maturing on average in 5,28 years (ASMFC, 2020).
summarise(Lmin = min(L),
For a deeper explanation on how the mean age for male and female was computed, see the xls file "MaturityOgives".
L025 = quantile(L, .25),
L25 = quantile(L, .25),
Lmed = median(L),
```{r American shad maturity at-age- observed by region and sex using the mortality correction approach (ASMFC, 2020), include = TRUE }
L75 = quantile(L, .75),
L975 = quantile(L, .975),
#American shad maturity at-age- observed by region and sex using the mortality correction approach (ASMFC, 2020)
inner_join(ogiveObs, by = 'age', suffix = c(".pred", ".obs"))
##1.2. Defintion of growth curve
In GR3D, growth of individuals was modeled as a Von Bertalanffy growth function (Von Bertalanffy 1938).
To account for variability in individuals, the seasonal growth increment is computed based on the growth coefficient K that is linked to water temperature.
The effect of water temperature (T°) on the growth coefficient K was introduced through a dome-shape relationship similar to the one for reproduction.
```{r calibration K and lengthAtMaturity by gender with ogive, warning = "FALSE"}
##1.2. Temperature effect experienced by fish for growth
#par = res_D$par
#----------------------------------------------#
During their life at sea, shads travel together in the marine environment, and population mixing occurs in different places according to season, suggesting that all populations relied/experienced various temperature to growth.
After hatching, juveniles spent their first summer in their natal river before emigrated to coastal marine waters. Juveniles reach their ‘inshore basin’ located at the main entrance of the river when fall begins.
Nind = 1000, seasonSelected = 'spring',
At the end of fall, juveniles move seaward and reach the closest ‘wintering offshore basins’ to spend the winter months.
RNGseed =1) {
In early spring, juveniles and sub-adults then move to one of the three ‘summering offshore basin’ to grow according to the migration routes defined by Dadswell et al. (1987) and come back each year until they reach their size at maturity. After spending 4-5 years at sea, ripe individuals started their spawning migration and go back to the ‘inshore basin’ near to their natal river, and enter a ‘river basin’ to spawn.
fullPar <- enframe(c(par, fixedPar)) %>% pivot_wider() #full set of parameters
