Maternal effects on male weaponry: female dung beetles produce major sons with longer horns when they perceive higher population density

Table 4 Model selection statistics for the allometry between horn length and pronotum width in Onthophagus taurus

	Model			Pairwise model comparisons
	Parameters as functions of experimental groups	df	log Likelihood	Likelihood ratio	P-value
1	A, μ, λ, and v common across groups	6	524.65
	Pre-mating group (PM)
2	All parameters ~ PM	10	533.39	17.47	0.002
3	A ~ PM; μ, λ, and v common across groups	7	524.68	0.06	0.81
4	μ ~ PM; A, λ, and v common across groups	7	533.20	17.11	< 0.0001
5	λ ~ PM; A, μ, and v common across groups	7	533.04	16.78	< 0.0001
6	v ~ PM group; A, μ, vand λ common across groups	7	525.49	1.68	0.20
	Mating group (M)
7	All parameters ~ M	10	525.10	0.90	0.92
8	A ~ M; μ, λ, and v common across groups	7	524.75	0.21	0.65
9	μ ~ M; A, λ, and v common across groups	7	525.05	0.81	0.37
10	λ~ M; A, μ, and v common across groups	7	524.95	0.60	0.44
11	v ~ M; A, μ, and λ common across groups	7	524.79	0.29	0.59

All models were fitted using the Richards’ growth function (see Table 3). Individuals in the sample are the male offspring produced by females from experimental groups that differed in population density during the pre-mating period (PM), and in the number of possible mates during the mating period (M). The set of models being compared is composed of a full model with common parameters across experimental groups (Model 1), and models in which one (or all) of the parameters were allowed to have different values for each pre-mating or mating experimental groups (indicated by ~ PM or ~ M). The variance was modeled as an exponential function of the fitted values with an estimated parameter value of - 1.853 in the full model with common parameters across experimental groups (Model 1). Likelihood ratios were calculated as the absolute difference between the - 2 x log Likelihood of the two models being compared, and every model is being compared to the model in italic (Model 1). Comparing these models in terms of their AIC values returns qualitatively similar results.

ISSN: 2730-7182