##Default assumption:

If HandlingTime_sec is not NA and > 0, it was a completed capture event.

## 
## ---- Fish summary quick view ----
## # A tibble: 3 × 5
##   Sp.x          n_fish mean_size mean_attacks mean_consumed
##   <fct>          <int>     <dbl>        <dbl>         <dbl>
## 1 P. reticulata     11      27.6         23.3          11.4
## 2 P. harpagos       12      26.6         24.3          15.9
## 3 P. vivipara       12      31.0         20.4          19.7

Differences in Total Intake

Question: Do species differ in total prey intake during a standardized 10-minute assay, after controlling for individual body size?

Given 10 minutes and identical prey availability, do species differ in how many larvae they can convert into intake?

##  Family: nbinom2  ( log )
## Formula:          n_consumed_10min ~ SL + Sp.x
## Data: fish_sum2
## 
##       AIC       BIC    logLik -2*log(L)  df.resid 
##     216.0     223.8    -103.0     206.0        30 
## 
## 
## Dispersion parameter for nbinom2 family ():  410 
## 
## Conditional model:
##                  Estimate Std. Error z value Pr(>|z|)    
## (Intercept)      2.489732   0.300912   8.274  < 2e-16 ***
## SL              -0.002154   0.010426  -0.207  0.83631    
## Sp.xP. harpagos  0.335030   0.117240   2.858  0.00427 ** 
## Sp.xP. vivipara  0.555802   0.117898   4.714 2.43e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Species differed significantly in feeding efficiency, measured as the total number of larvae consumed during a 10-min assay (negative binomial GLM). After controlling for body size, P. harpagos consumed approximately 40% more larvae than P. reticulata (p = 0.004), whereas P. vivipara exhibited a substantially higher intake, consuming ~74% more larvae than P. reticulata (p < 10⁻⁵). Standard length had no detectable effect on intake (p = 0.84), indicating that species differences in feeding efficiency were independent of body size. Together, these results reveal a clear ranking in feeding efficiency, with P. vivipara outperforming P. harpagos and P. reticulata under standardized prey availability.

Differences in prey-capture speed through time

Quation: Are species different in capture tempo, after controlling for size and repeated events?

To answer this question, we fitted a Cox proportional hazards mixed-effects model (frailty model), including fish identity as a random effect, to test for species differences in prey-capture speed. These models are well suited for time-to-event data with censoring and repeated capture events. Hazard ratios provide an intuitive measure of relative capture tempo among species, independent of assay duration and body size.

## Mixed effects coxme model
##  Formula: Surv(event_sec) ~ Standard_length_mm + Sp + (1 | ID) 
##     Data: cons_events 
## 
##   events, n = 33, 33 (519 observations deleted due to missingness)
## 
## Random effects:
##   group  variable        sd  variance
## 1    ID Intercept 0.6432996 0.4138343
##                   Chisq   df        p  AIC   BIC
## Integrated loglik 11.58 4.00 0.020735 3.58 -2.40
##  Penalized loglik 28.80 9.74 0.001139 9.32 -5.25
## 
## Fixed effects:
##                       coef exp(coef) se(coef)    z       p
## Standard_length_mm 0.04724   1.04838  0.05010 0.94 0.34573
## SpP. harpagos      0.57462   1.77646  0.59473 0.97 0.33395
## SpP. vivipara      1.85518   6.39288  0.60498 3.07 0.00217

Species differed markedly in prey-capture speed through time. Event-time mixed-effects models that controlled for body size revealed that P. vivipara captured prey at a substantially higher rate than P. reticulata, exhibiting an estimated 6.4-fold increase in instantaneous capture probability (hazard ratio = 6.39, p = 0.002). In contrast, prey-capture rates of P. harpagos did not differ significantly from those of P. reticulata after accounting for size (hazard ratio = 1.78, p = 0.33). Standard length had no detectable effect on capture rate (p = 0.35), indicating that species differences in prey-capture speed are independent of body size. Together, these results demonstrate that pronounced differences in capture tempo—rather than body size variation—drive interspecific differences in feeding efficiency.

We generated predicted survival curves from a marginal Cox model with clustered standard errors for visualization.