Author: Morgan Sparks, Bryan M. Maitland

# Non-fish examples

#### Morgan Sparks, Bryan M. Maitland

Because poikilotherms largely have a similar mechanistic relationship with ambient temperature and developmental rates, hatchR, may easily be applied to other non-fish species. Unlike many examples in other articles on this website, non-fish species will obviously rely exclusively on the `fit_model()` function for creating developmental models. An excellent starting place for potential model parameterization is the Model sources section below.

Here, we outline examples of how one can use developmental studies from peer-reviewed or grey literature to develop species- or population-specific models in a generalizeable format.

    #libraries
    library(hatchR)
    library(patchwork)
    library(ggplot2)
    library(tibble)
    library(dplyr)
    library(purrr)

# A simple example: coastal tailed frogs

Tailed frogs (Ascaphus spp.) are common amphibians in the Rocky and Cascade Mountain regions of the northern United States and southern Canada, generally occupying the cold and fast-flowing habitat of headwater streams of the region. Compared to many other frog species, tailed frogs are comparatively slow growing and occupy colder habitats.

Brown (1975) raised coastal tailed frogs (A. truei) at temperatures ranging from 5-20 °C. Using those data we can easily parameterize a developmental model for coastal tailed frogs to be used in similar situations we present with fish.

First we set up the raw data from the study and parameterize the model with `fit_model()`:

    ### parameterize mod
    ascaphus_data <- tibble(temp = c(7.6,9.8,11,13,14.5,15,18),
                            days = c(44,27.1,22.6,16.1,13.4,12.7,10.7))

    ascaphus_mod <- fit_model(temp = ascaphus_data$temp,
                              days = ascaphus_data$days,
                              species = "ascaphus",
                              development_type = "hatch")

To demonstrate the respective effective value at different daily temperatures we can evaluate our model across a vector of daily temperatures

    ### get effective values
    temps <- c(6:20) # daily temps

    #loop to calculate model expression at different temps
    ef_vals <- NULL
    for (x in temps) {
      ef <- eval(parse(text = ascaphus_mod$expression$expression)) # call model expression
      ef_vals <- rbind(ef_vals, ef)
    }

    # make data into plotable format
    ascaphus_ef <- matrix(NA, 15, 2) |> tibble::tibble()
    colnames(ascaphus_ef) <- c("temp", "ef")
    ascaphus_ef$temp <- temps
    ascaphus_ef$ef <- ef_vals[, 1]

We can then demonstrate our fit and the effective values for a daily temperature:

    ### plot

    fmt <- "~R^2 ==  %.4f" # format for R^2 val

    lab1 <- sprintf(fmt, ascaphus_mod$r_squared) # R^2 label

    # plot 1 of model fit
    p1 <- ascaphus_mod$pred_plot +
      labs(x = "Incubation Temperature (°C)", y = "Days to Hatch") +
      lims(y = c(0, 50)) +
      annotate("text", x = 10, y = c(35), label = c(lab1),  hjust = 0, parse = TRUE)

    # data table for 1 degree increase of temp for 0.01 increase in effective value for reference
    data_1 <- tibble(t = c(0:20), e = seq(0, 0.20, by = 0.01))

    #plot 2
    p2 <- ascaphus_ef |>
      ggplot() +
      geom_point(aes(x = temp, y = ef)) +
      geom_line(aes(x = temp, y = ef)) +
      geom_line(data = data_1, aes(x = t, y = e), linetype = "dashed") +
      # geom_abline(intercept = 0, slope = .01, linetype = "dashed") +
      labs(x = "Daily Average Temperature (°C)", y = "Effective Value") +
      theme_classic()

    p1 + p2

# Multiple populations: developmental rates of cabbage beetles

The application of hatchR need not be limited to aquatic species, though many such putative species source data are available. Here we demonstrate how data from a clinal study on cabbage beetles (Colaphellus bowringi) from Tang et al. (2017) can be leveraged to understand population specific developmental rates, by generating effective value models for five separate populations.

    # vector of experimental temps
    tang_temps <- c(16, 19, 22, 24, 26, 28)

    # vectors of population specific developmental rates at the above temperatures
    hb <- c(24.834, 19.481, 14.172, 11.205, 9.865, 8.570)

    sy <- c(23.822, 19.129, 13.644, 10.897, 9.645, 8.306)

    ta <- c(21.887, 18.381, 12.984, 10.809, 9.382, 8.130)

    xy <- c(21.623, 18.337, 12.589, 10.633, 9.205, 8.085)

    xs <- c(21.271, 16.666, 11.797, 9.929, 9.117, 6.942)

    # make a list of pops
    pop_list <- list(hb, sy, ta, xy, xs)

    # map fit_model() over our list of pops
    beetle_mods <- pop_list |>
      map(fit_model,
        temp = tang_temps,
        species = "cabbage beetle",
        development_type = "hatch"
      ) |>
      map("expression") |>
      map("expression") |>
      unlist()

Now we have our five beetle models stored as character strings (to be parsed and evaluated later on).

    beetle_mods
    #> [1] "1 / exp(5.17706892381201 - log(x + -9.0421606255981))"
    #> [2] "1 / exp(5.16085302046131 - log(x + -8.88858299500937))"
    #> [3] "1 / exp(5.17970628340703 - log(x + -8.15597145640711))"
    #> [4] "1 / exp(5.16007787793513 - log(x + -8.22714018896069))"
    #> [5] "1 / exp(5.03375638770247 - log(x + -8.94965470593722))"

To demonstrate the differences in developmental rates, we can turn each model into a reaction norm, much like we did in the second plot for the tailed frog example.

    # data set up
    temps <- c(12:30) # temps to iterate throug
    pops <- c( # pops to iterate through
      "Haerbin City",
      "Shenyang City",
      "Taian City",
      "Xinyang County",
      "Xiushui County"
    )

    ef_vals_pops <- NULL # NULL object to stor ef vals in

    # loop stepping over temps and populations to create
    # temperature and population specific ef values

    for (m in 1:length(beetle_mods)) {
      mod <- beetle_mods[m]
      pop <- pops[m]

      for (x in temps) {
        ef <- eval(parse(text = mod))
        temp_df <- data.frame(
          temperature = x,
          effective_value = ef,
          beetle_pops = pop
        )
        ef_vals_pops <- rbind(ef_vals_pops, temp_df)
      }
    }

After we run our loop to create population and temperature specific effective value estimates, we can plot each population’s effective value reaction norm.

    ef_vals_pops |>
      tibble() |>
      ggplot(aes(x = temperature, y = effective_value, color = beetle_pops)) +
      geom_line() +
      geom_point() +
      labs(x = "Daily Average Temperature (°C)", y = "Effective Value") +
      scale_color_brewer(palette = "Dark2", name = "Beetle Populations") +
      theme_classic() +
      theme(legend.position = c(0.25, 0.75))

# Model sources

The above examples are meant to inform how we can easily leverage the `fit_model()` function for paramereterizing developmental models for non-fish taxa. We recommend our other articles on this site for examples of how these models may be leveraged for applied and basic questions. We also stress that the assumptions made for fish (as well taxa-specific ones not outlined here) should be considered when applying these models. Here we provide a non-exhaustive list of putative model sources for parameterizing developmental models for non-fish organisms.

Class | Order | Genus | Species | Study
--- | --- | --- | --- | ---
Amphibia | Anura | Lithobates | L. sylvaticus | Moore (1939)
|  |  | L. pipiens |
|  |  | L. clamitans |
|  |  | L. palustris |
|  | Ascaphus | A. truei | Herbert A. Brown (1975)
| Urodela | Ambystoma | A. gracile | Herbert A. Brown (1976)
Reptilia | Squamata | Sceloporus | S. undulatus | Angilletta Jr., Winters, and Dunham (2000)
|  | Podarcis | P. muralis | Van Damme et al. (1992)
| Testudines | Mauremys | M. reevesii | Du et al. (2007)
|  |  | 181 species | 141 studies in While et al. (2018)
Insecta | Plecoptera | Nemurella | N. pictetii | John E. Brittain (1978) , Elliott (1984)
|  | Capnia | C. atra | John E. Brittain, Lillehammer, and Saltveit (1984)
|  | Capnia | C. bifrons | Elliott (1986)
|  | Mesocapnia | M. oenone | John E. Brittain, Lillehammer, and Saltveit (1984)
|  | Taeniopteryx | T. nebulosa | J. E. Brittain (1977)
| Coleoptera | Colaphellus | C. bowringi | Tang et al. (2017)
|  |  | 18 species | Developmental equations in Pritchard and Leggott (1987)
Malacostraca | Decapoda | Pontastacus | P. leptodactylus | Aydın and Dilek (2004)
Copepoda | Calanoida | 10 genera | 28 species | Forster, Hirst, and Woodward (2011)
| Cyclopoida | Limnoithona | L. tetraspina |
|  | Oithona | O. davisae |
| Harpacticoida | Microsetella | M. norvegica |
|  | Mesochra | M.lilljeborgi |
| Poecilostomatoida | Oncaea | O. venusta |
Cephalopoda | Octopoda | Octopus | O. vulgaris | Márquez, Larson, and Almansa (2021)
|  |  | O. mimus |
| Myopsida | Loligo | L. vulgaris |
|  |  | L. reynaudii |
| Oegopsida | Illex | I. coindetii |
|  |  | I. illecebrosus |
|  | Todarodes | T.pacificus |
|  | Ommastrephes | O. bartramii |
Asteroidea | Valvatida | Odontaster | O. meridionalis | HOEGH-GULDBERG and PEARSE (1995)
|  |  | O. validus |
|  | Asterina | A. miniata |
|  | Acanthaster | A. planci |

# References

Angilletta Jr., Michael J., R. Scott Winters, and Arthur E. Dunham. 2000. “Thermal Effects on the Energetics of Lizard Embryos: Implications for Hatchling Phenotypes.” Ecology 81 (11): 2957–68. https://doi.org/10.1890/0012-9658(2000)081[2957:TEOTEO]2.0.CO;2.
Aydın, Hamdi, and M. Kamil Dilek. 2004. “Effects of different water temperatures on the hatching time and survival rates of the freshwater crayfish (Astacus leptodactylus) (Esch., 1823) eggs.” Turkish Journal of Fisheries and Aquatic Sciences 4 (2): –. https://dergipark.org.tr/en/pub/trjfas-ayrildi/issue/13289/160618.
Brittain, J. E. 1977. “The Effect of Temperature on the Egg Incubation Period of Taeniopteryx Nebulosa (Plecoptera).” Oikos 29 (2): 302–5. https://doi.org/10.2307/3543618.
Brittain, John E. 1978. “Semivoltinism in Mountain Populations of Nemurella Pictetii (Plecoptera).” Oikos 30 (1): 1–6. https://doi.org/10.2307/3543518.
Brittain, John E., Albert Lillehammer, and Svein Jakob Saltveit. 1984. “The Effect of Temperature on Intraspecific Variation in Egg Biology and Nymphal Size in the Stonefly, Capnia Atra (Plecoptera).” Journal of Animal Ecology 53 (1): 161–69. https://doi.org/10.2307/4349.
Brown, Herbert A. 1975. “Temperature and Development of the Tailed Frog, Ascaphus Truei.” Comparative Biochemistry and Physiology Part A: Physiology 50 (2): 397–405. https://doi.org/10.1016/0300-9629(75)90033-X.
Brown, Herbert A. 1976. “The Timetemperature Relation of Embryonic Development in the Northwestern Salamander, Ambystoma Gracile.” Canadian Journal of Zoology 54 (4): 552–58. https://doi.org/10.1139/z76-063.
Du, Wei-Guo, Ling-Jun Hu, Jian-Lei Lu, and Ling-Jun Zhu. 2007. “Effects of Incubation Temperature on Embryonic Development Rate, Sex Ratio and Post-Hatching Growth in the Chinese Three-Keeled Pond Turtle, Chinemys Reevesii.” Aquaculture 272 (1): 747–53. https://doi.org/10.1016/j.aquaculture.2007.09.009.
Elliott, J. M. 1984. “Hatching Time and Growth of Nemurellapictetii (Plecoptera: Nemouridae) in the Laboratory and a Lake District Stream.” Freshwater Biology 14 (5): 491–99. https://doi.org/10.1111/j.1365-2427.1984.tb00169.x.
———. 1986. “The Effect of Temperature on the Egg Incubation Period of Capnia Bifrons (Plecoptera: Capniidae) from Windermere (English Lake District).” Holarctic Ecology 9 (2): 113–16. https://www.jstor.org/stable/3682086.
Forster, Jack, Andrew G. Hirst, and Guy Woodward. 2011. “Growth and Development Rates Have Different Thermal Responses.” The American Naturalist 178 (5): 668–78. https://doi.org/10.1086/662174.
HOEGH-GULDBERG, OVE, and JOHN S. PEARSE. 1995. “Temperature, Food Availability, and the Development of Marine Invertebrate Larvae1.” American Zoologist 35 (4): 415–25. https://doi.org/10.1093/icb/35.4.415.
Márquez, Lorenzo, Majorie Larson, and Eduardo Almansa. 2021. “Effects of Temperature on the Rate of Embryonic Development of Cephalopods in the Light of Thermal Time Applied to Aquaculture.” Reviews in Aquaculture 13 (1): 706–18. https://doi.org/10.1111/raq.12495.
Moore, John A. 1939. “Temperature Tolerance and Rates of Development in the Eggs of Amphibia.” Ecology 20 (4): 459–78. https://doi.org/10.2307/1930439.
Pritchard, G., and M. A. Leggott. 1987. “Temperature, Incubation Rates and Origins of Dragonflies.” Advances in Odonatology 3 (1): 121–26. https://natuurtijdschriften.nl/pub/593065.
Tang, Jianjun, Haimin He, Chao Chen, Shu Fu, and Fangsen Xue. 2017. “Latitudinal Cogradient Variation of Development Time and Growth Rate and a Negative Latitudinal Body Weight Cline in a Widely Distributed Cabbage Beetle.” PLOS ONE 12 (7): e0181030. https://doi.org/10.1371/journal.pone.0181030.
Van Damme, Raoul, Dirk Bauwens, Florentino Braña, and Rudolf F. Verheyen. 1992. “Incubation Temperature Differentially Affects Hatching Time, Egg Survival, and Hatchling Performance in the Lizard Podarcis Muralis.” Herpetologica 48 (2): 220–28. https://www.jstor.org/stable/3892675.
While, Geoffrey M., Daniel W. A. Noble, Tobias Uller, Daniel A. Warner, Julia L. Riley, Wei-Guo Du, and Lisa E. Schwanz. 2018. “Patterns of Developmental Plasticity in Response to Incubation Temperature in Reptiles.” Journal of Experimental Zoology Part A: Ecological and Integrative Physiology 329 (4-5): 162–76. https://doi.org/10.1002/jez.2181.