Hello,

My Project:

I'm analyzing beetle species at carcasses predated on by GPS collared pumas in the Greater Yellowstone Ecosystem. I have 12 fresh carcasses that I've sampled each week. Each carcass has a control site 20 meters away. At carcasses, I collected beetles via three barrier pitfall traps that surrounded the carcass. At controls, I have no carcass but set up the 3 barrier pitfall traps the same way as I did for the paired carcass. I have had all of my specimens identified to the level of species, ~24,000 beetles, 215 species. 86.1% of the total beetles were found at carcasses. The goal of this project is to demonstrate pumas as ecosystem engineers via creating habitat for beetle species that require this resources for crucial life history events (mating, food, habitat, etc.)

Questions to Address Statistically:

1) Is beetle abundance, richness, and diversity higher at carcasses compared to control sites.

2) How does beetle abundance, richness, and diversity change over time at carcasses and controls?

Statistics so far:

I've run a Two-Way Mixed ANOVA in SPSS to address beetle abundance across 16 time-periods for fresh carcasses vs. their controls. Data is horizontal. Sites ranged in time-periods, some longer than others. I had nineteen outliers, as assessed by boxplots. The data was not normally distributed, as assessed by Shapiro-Wilk’s test of normality (p > .05). There was no homogeneity of variances, as assessed by Levene’s test of homogeneity of variances (p > .05). Mauchly’s test of sphericity indicated that the assumption of sphericity was violated for the two-way interaction, X2 (119) = 720.789, p= .000. There was a statistically significant interaction between groups and time on beetle abundance, F (1.713, 30.832) = 9.869, p = .001, partial h2 = .354, e = .114. Data are mean ± standard error, unless otherwise stated. Beetle abundance was statistically significantly greater at carcasses (140.209 ± 25.376 beetles/collection period, p = .004) compared to controls (22.425 ± 25.376 beetles/collection). There was a statistically significant effect of time on beetle abundance for carcasses, F (1.680, 15.120) = 10.222, p = .002, partial h2 = .532. There was not a statistically significant effect of time on beetle abundance for controls, F (2.489, 22.404) = .903, p = .439, partial h2 = .091.

Overall, the data is messy with imputation (80% real values). I had to imputate values 20% of the time because some weeks I couldn't collect (bears taking carcass; horrible weather; coyotes messy with stuff, etc.) or a site was not sampled as long (i.e. ending at week 14, but analysis is to 16). Moving forward, I need to address species richness and diversity, as I have here, with abundance.

Help I'm asking for:

I think it's clear that my data is too messy to rely on a analysis of variance, therefore, I've started to pursue 'Mixed Models - Linear' in SPSS. I've read that Mixed Models are more robust and can deal with my data with different covariant structures, etc. I've reorganized my data into longitudinal form. However, I have little experience with Linear Mixed Models, fixed and random effects. I've read a few books, including ones that demonstrate data analysis in SPSS. Yet, I still can't figure LMM out, specifically, what procedure to take and how to organize the data. I do not use the syntax, rather, the command bar. Does anyone know how I can specifically input this data into a LMM in SPSS? This would help me out tremendously. It's so clear that carcasses have an effect on beetle species, but the analysis of variance I've done is violating a lot of assumptions and using imputation.