Area-weighted index standardization

class: center, middle, inverse, title-slide

.title[
# Area-weighted index standardization
]
.subtitle[
## DFO DSAF workshop
]
.author[
### 
]
.date[
### January 12–16 2026
]

---

# Why model-based index standardization?

* Design-based methods (e.g., stratified means) are straightforward but assume perfect survey implementation

* Model-based approaches can account for (some) aspects of imperfect implementation

* Model-based approaches can leverage spatial correlation to improve precision

* Model-based approaches can integrate additional data sources, multiple gear types, accounting for gear calibration, etc.

---

# Design- vs. model-based estimators

* Design-based: fish are homogenously distributed within strata; noise comes from sampling

* Model-based: fish are distributed according to a mathematical model; noise from uncertainty in fish distribution and sampling

---

# Calculating an area-weighted population index

1. Fit a sensible model: .blue[`sdmTMB()`]

2. Predict on a grid covering the survey domain: .blue[`predict(..., newdata = ...)`]

3. Sum up the density multiplied by cell area to calculate total abundance or biomass: .blue[`get_index()`] (a grid-based approximation of the integral)

---

# Fit a sensible model

``` r
mesh <- make_mesh(pcod, xy_cols = c("X", "Y"), cutoff = 10)
fit <- sdmTMB(
* density ~ 0 + as.factor(year),
  data = pcod,
  mesh = mesh,
  family = tweedie(link = "log"),
  spatial = "on",
  time = "year",
* spatiotemporal = "iid",
  silent = FALSE # show progress!
)
```

---

# Predict over the survey domain

.small[

``` r
pred <- predict(
  fit, 
* newdata = grid,
* return_tmb_object = TRUE
)
select(pred$data, year, X, Y, est) |> 
  head()
#>   year   X    Y      est
#> 1 2003 456 5636 1.639821
#> 2 2003 458 5636 1.682348
#> 3 2003 460 5636 1.724875
#> 4 2003 462 5636 1.767403
#> 5 2003 464 5636 1.889935
#> 6 2003 466 5636 2.361575
```
]

---

# Predict over the survey domain

---

# Sum up the density multiplied by cell area

(*and calculate standard errors)

``` r
index <- get_index(pred, area = 4, bias_correct = TRUE)
head(index)
#>   year       est       lwr       upr  log_est        se se_natural  type
#> 1 2003  936175.6  653699.1 1340715.9 13.74956 0.1832462   660600.7 index
#> 2 2004 1832130.4 1359020.1 2469942.7 14.42099 0.1524087  1352139.9 index
#> 3 2005 1757227.0 1224189.4 2522360.5 14.37925 0.1844208  1331654.2 index
#> 4 2007  452112.1  328785.5  621698.2 13.02169 0.1625155   317355.0 index
#> 5 2009  722981.6  518712.7 1007691.5 13.49114 0.1694080   499241.8 index
#> 6 2011 1357885.0 1028850.9 1792146.6 14.12144 0.1415770   992261.7 index
```

---

# The resulting standardized index

.xsmall[

``` r
ggplot(index, aes(year, est)) + geom_line() +
  geom_ribbon(aes(ymin = lwr, ymax = upr), alpha = 0.4) +
  xlab('Year') + ylab('Biomass estimate (kg)')
```

<img src="10-index-standardization_files/figure-html/pcod-st-index-plot-1.png" width="600px" style="display: block; margin: auto;" />
]

---

# Remember...

There is *one* design-based index.

A good model-based estimated depends on the modeller constructing a reasonable model!

There are *many* possible model-based indexes. Thankfully, results are often (but not always!) qualitatively similar across configurations.

.tiny[
Commander, C.J.C, L.A.K. Barnett, E.J. Ward, S.C. Anderson, T.E. Essington. 2022. The shadow model: how and why small choices in spatially explicit species distribution models affect predictions. PeerJ. 10: e12783. <https://doi.org/10.7717/peerj.12783>

Yalcin, S., Anderson, S.C., Regular, P.M., and English, P.A. 2023. Exploring the limits of spatiotemporal and design-based index standardization under reduced survey coverage. ICES Journal of Marine Science 80(9): 2368–2379. <https://doi.org/10.1093/icesjms/fsad155>
]