Why am I receiving "non-numeric argument to binary operator" error when running a zero-inflated negative binomial mixed model?

I am attempting to a run a zero-inflated negative binomial mixed model. I ran an experiment where I gave adult snails a phosphorus-enriched diet and a phosphorous-depleted diets (P). These snails all come from different families; there are 10 families (Lineages). We also have 3 ploidy levels (diploid, triploid, tetraploid). Lineage is a random factor and will always be nested underneath a ploidy level. For example, Lineage A can only be diploid. It can never be triploid nor tetraploid. My dependent variable is embryo count, which is zero-inflated and the highest embryo number is 49. We measured adult length (Length) since it has a significant linear relationship with embryo number.

This is my code:

model5 <- zeroinfl(Embryonumber ~ (Ploidy/1|Lineage) + P:Ploidy + Length,
  data = x, dist = "negbin")
summary(model5)

What I think I have asked R to run is a zero-inflated negative binomial mixed model. Dependent is embryo number. Ploidy and P are fixed factors and I have included them as stand-alone factors and their interaction. Length is a covariate. Lineage is random and nested in Ploidy - Lineage cannot and should not be stand alone.

But I receive this error:

Error in Ploidy/1 : non-numeric argument to binary operator

I have 2 ideas here: 1) the format of my data is wrong or 2) coded a random factor nested in a fixed factor wrong.

When I run summary of my data (summary (data)) I receive:

     Lineage             Ploidy               P             SnailLetterSymbol      Length       Embryonumber   
 Length:99          Length:99          Length:99          Length:99          Min.   :3.500   Min.   : 0.000  
 Class :character   Class :character   Class :character   Class :character   1st Qu.:4.000   1st Qu.: 2.000  
 Mode  :character   Mode  :character   Mode  :character   Mode  :character   Median :4.100   Median : 6.000  
                                                                             Mean   :4.219   Mean   : 9.364  
                                                                             3rd Qu.:4.500   3rd Qu.:14.000  
                                                                             Max.   :5.000   Max.   :49.000  
    Presence      Standardized residuals
 Min.   :0.0000   Min.   :-1.405440     
 1st Qu.:1.0000   1st Qu.:-0.706935     
 Median :1.0000   Median :-0.299980     
 Mean   :0.7879   Mean   :-0.000001     
 3rd Qu.:1.0000   3rd Qu.: 0.593960     
 Max.   :1.0000   Max.   : 3.461570

Do I need to recode my Ploidy or Lineage as a vector?

Here are the two columns in question, but let me know if you need more:

I am unsure if I used the correct syntax for nesting and random factors. I see most vignettes that random and nested factors always have the (1 | in front of both factors. I have not done this, because Ploidy is not random only Lineage is. I have taken advice on how to nest a random factor from: 1) https://stats.stackexchange.com/questions/228800/crossed-vs-nested-random-effects-how-do-they-differ-and-how-are-they-specified?noredirect=1&lq=1 2) https://www.muscardinus.be/statistics/nested.html 3) https://rdoodles.rbind.io/2019/11/nested-random-factors-in-mixed-multilevel-or-hierarchical-models/ 4) https://ourcodingclub.github.io/tutorials/mixed-models/#nested

I then attempted to use long-hand syntax (as described in link 2) but I receive an error. Code:

model5 <- zeroinfl(Embryonumber ~ (Ploidy:1|Lineage) + P:Ploidy + Length,
  data = x, dist = "negbin")
summary(model5)

Error: Error in Ploidy:1 : NA/NaN argument

Do you all have any advice? Thank you!

An update: I have attempted the below code and I still receive the Error in Ploidy/Lineage : non-numeric argument to binary operator.

 model4 <- zeroinfl(Embryonumber ~ (1 | Ploidy / Lineage) + P:Ploidy + Length| Presence,
  data = x, dist = "negbin")
summary(model4)

As s commenter suggested I removed the nested factor, which is not an appropriate model for my data, but I wanted to at least test that the function works. Code:

model4 <- zeroinfl(Embryonumber ~ (1 | Lineage) + (1 | Ploidy) + P:Ploidy + Length| Presence,
  data = x, dist = "negbin")
summary(model4)

Error:

Error in 1 | Lineage : 
  operations are possible only for numeric, logical or complex types

Solution

zeroinfl doesn't handle random effects, so the only bar (|) in your formula should be the one splitting the conditional from the zero-inflation model, e.g.

Embryonumber ~ Lineage + P*Ploidy + Length| Presence

if you do want to incorporate random effect in a ZINB model, you could try glmmTMB, e.g.

library(glmmTMB)
glmmTMB(Embryonumber ~ P*Ploidy + Length + (1|Lineage),
    ziformula = ~ Presence,
  data = x, family = "nbinom2")

I would not recommend using Ploidy as a random effect grouping variable; for a random effect grouping variable, you need (1) enough levels to estimate an among-group variance (≥ 5 is a typical rule of thumb) and (2) you need the levels to be exchangeable, i.e. the labels of the levels could be switched without changing the meaning of the model, which I suspect is not true for ploidy.
you don't need to worry about the nesting of lineages within ploidy levels, that gets handled automatically