Simplified SEMs

This chapter will build on the insight gained from the previous chapter to build the final SEMs for our manuscript. In total, there will be three SEMs. The first SEM is a “full” model that explores all components of our proposed model (mouse traits and behaviors, mouse interactions with disease vectors, mouse gene expression, environment, and infection status). To ensure maximum power, this full model utilizes data for both P leucopus (PELE) and P maniculatus (PEMA). The two remaining SEMs will explore the specific differences in disease dynamics between PELE and PEMA. These models will have identical structure and will only differ by the species with which they are fitted. In order to make comparisons between two identically-structured SEMs, some variables from the full SEM are excluded from these species-specific models. This simplification is necessitated by low representation of PEMA for some combinations of variables. By structuring the analysis in this way, with one overarching model and smaller species-specific models, we are able to holistically explore the factors of disease dynamics in this system while also acknowledging and quantifying differences among species where possible.

Species identification

Because we are interested in species-specific effects and because field assignments are known to be error-prone, we re-assessed species identification prior to this chapter. Specifically, we used the following algorithm to assign species:

1. First, any individuals for which genetic information are available were assigned to the species indicated by genetic markers.

2. For individuals not covered by step 1, discriminant analysis (trained on individuals with genetic assignments) was used to assign observations for which ear length, hind foot length, and weight were available. These 3 variables had the highest assignment accuracy for both species (90% for PELE, 86% for PEMA). Individuals were assigned by averaging the predicted species across observations.

3. For individuals not covered by steps 1-2, discriminant analysis was used to assign observations for which ear length and weight were available. These two variables also had a high assignment accuracy for both species (90% for PELE, 84% for PEMA). Individuals were assigned by averaging the predicted species across observations.

4. Individuals not covered by steps 1-3 that were captured at BLAN, HARV, SERC, or ORNL were assigned PELE. This was done because genetic assessment identified no PEMA at any of these sites. Note: HARV specifically had extremely poor field identification, with the vast majority of individuals being labeled as Peromyscus spp. and about half of the individuals identified to species were (incorrectly) labeled as PEMA.

5. Any remaining individuals were given the field assignment that occurred most commonly across their full capture record.

Full SEM

The full SEM exploring relationships between mice characteristics and behaviors, environmental variation, gene expression, and Borrelia infection was fitted to all available data and is visualized by Figure 27. The model hypothesizes that 1) individual traits covary and influence individual behavior, contact with disease vectors (tick parasitism), expression of immunity genes, and infection status; 2) behaviors covary and influence contact with vectors and infection status; 3) tick parasitism influences immunity expression and infection status; 4) expression of immunity-associated genes are associated with infection status (influenced by resistance and influencing tolerance); and 5) environmental factors influence all other factors.

Our results show that these hypothesis are largely met:

1. Mouse phenotype is significantly and directly associated with behavior (sex, weight), parasitism rates (sex), resistance expression (sex, weight), tolerance expression (reproductive maturity), and infection rates (weight, reproductive maturity).

2. Mouse behavior is significantly and directly associated with parasitism rates (shift in capture time), but is only indirectly associated with infection rates (through its influence on tick parasitism).

3. Tick parasitism is significantly and directly associated with resistance expression and infection status, but is only indirectly associated with tolerance expression (through its effect on infection status).

4. Tolerance expression is significantly and directly associated with with infection status, but resistance expression is not.

5. Weather is significantly and directly associated with mouse phenotype ( reproductive maturity), behavior (capture timing), parasitism rates, immunity expression (resistance), and infection status. Longer-term climate also has significant impacts on parasitism rates, likely through its influence on tick populations.

Figure 27: PATH diagram for the full SEM of Peromyscus-Borrelia dynamics. Orange vectors represent negative effects, blue vectors represent positive effects, solid lines are statistically significant (P ≤ 0.1), and dashed lines are not. Line widths are proportional to the magnitude of the standardized coefficient estimates. Boxes are colored according to variable groupings (blue: phenotype; turquoise: envrionment; pink: behavior; green: parasitism; yellow: gene expression; brown: infection. Each component model used to build the SEM included species, site, and year as random effects to accout for covariation of observations within and among these groups. Table 16 shows full model parameters and Table 17 contains more information about the individual component models.

Table 16: Full SEM parameter estimates.

Response	R2.marg	R2.cond	Predictor	Estimate	DF	SE	P	Std.Estimate
Cap. time (Behavior)	0.02	0.10	Weather (Environment)	-0.05	2948	0.02	0.021	-0.04
Cap. time (Behavior)	0.02	0.10	Sex (Phenotype)	0.04	2980	0.01	<0.001	0.08
Cap. time (Behavior)	0.02	0.10	Reproductive (Phenotype)	-0.02	2984	0.01	0.111	-0.03
Cap. time (Behavior)	0.02	0.10	Weight (Phenotype)	0.01	2981	0.00	<0.001	0.12
Cap. time Δ (Behavior)	0.27	0.31	Cap. time (Behavior)	0.53	2753	0.02	<0.001	0.52
Cap. time Δ (Behavior)	0.27	0.31	Sex (Phenotype)	0.00	2758	0.01	0.677	-0.01
Cap. time Δ (Behavior)	0.27	0.31	Reproductive (Phenotype)	-0.01	2763	0.01	0.232	-0.02
Cap. time Δ (Behavior)	0.27	0.31	Weight (Phenotype)	0.00	2740	0.00	0.811	0.00
Resistance (Expression)	0.04	0.31	Weather (Environment)	0.17	436	0.07	0.011	0.12
Resistance (Expression)	0.04	0.31	Parasitism (Parasitism)	-0.05	436	0.03	0.084	-0.08
Resistance (Expression)	0.04	0.31	Sex (Phenotype)	0.05	431	0.03	0.067	0.08
Resistance (Expression)	0.04	0.31	Reproductive (Phenotype)	-0.02	431	0.03	0.554	-0.03
Resistance (Expression)	0.04	0.31	Weight (Phenotype)	0.01	422	0.00	<0.001	0.17
Tolerance (Expression)	0.03	0.24	Infection (Infection)	0.07	249	0.04	0.099	0.11
Tolerance (Expression)	0.03	0.24	Parasitism (Parasitism)	0.03	256	0.04	0.433	0.04
Tolerance (Expression)	0.03	0.24	Reproductive (Phenotype)	0.06	253	0.04	0.072	0.10
Infection (Infection)	0.13	0.58	Cap. time Δ (Behavior)	2.24	234	1.79	0.212	0.23
Infection (Infection)	0.13	0.58	Weather (Environment)	1.89	234	0.88	0.032	0.17
Infection (Infection)	0.13	0.58	Resistance (Expression)	0.00	234	0.60	1.000	0.00
Infection (Infection)	0.13	0.58	Parasitism (Parasitism)	0.85	234	0.37	0.021	0.17
Infection (Infection)	0.13	0.58	Sex (Phenotype)	0.25	234	0.36	0.479	0.05
Infection (Infection)	0.13	0.58	Reproductive (Phenotype)	0.93	234	0.41	0.022	0.17
Infection (Infection)	0.13	0.58	Weight (Phenotype)	0.09	234	0.05	0.083	0.15
Parasitism (Parasitism)	0.13	0.29	Cap. time Δ (Behavior)	-0.34	2140	0.20	0.079	-0.04
Parasitism (Parasitism)	0.13	0.29	Climate (Environment)	0.60	2140	0.31	0.056	0.24
Parasitism (Parasitism)	0.13	0.29	Weather (Environment)	1.68	2140	0.24	<0.001	0.17
Parasitism (Parasitism)	0.13	0.29	Sex (Phenotype)	0.46	2140	0.10	<0.001	0.10
Parasitism (Parasitism)	0.13	0.29	Reproductive (Phenotype)	0.15	2140	0.12	0.195	0.03
Parasitism (Parasitism)	0.13	0.29	Weight (Phenotype)	-0.01	2140	0.01	0.663	-0.01
Reproductive (Phenotype)	0.01	0.12	Climate (Environment)	0.13	23500	0.08	0.118	0.06
Reproductive (Phenotype)	0.01	0.12	Weather (Environment)	0.52	23500	0.07	<0.001	0.06
Reproductive (Phenotype)	0.01	0.12	Sex (Phenotype)	0.21	23500	0.03	<0.001	0.05
Weight (Phenotype)	0.20	0.31	Weather (Environment)	-1.74	18480	0.15	<0.001	-0.08
Weight (Phenotype)	0.20	0.31	Sex (Phenotype)	-0.27	19175	0.06	<0.001	-0.03
Weight (Phenotype)	0.20	0.31	Reproductive (Phenotype)	4.40	19182	0.06	<0.001	0.45

In addition to the direct effects outlined above, it is also possible to quantify cumulative (direct and indirect) effects from the SEM. The cumulative effects on parasitism rates, immunity expression, and infection status are given in Figure 28.

Figure 28: Cumulative effects on parasitism (Ticks), immunity expression (Resistance, Tolerance), and Borrelia infection. These effects are derived from the full SEM (Figure 27). Dashed borders around blue bars indicate non-significant direct effects.

Table 17: Full SEM component model fit. Columns represent model response, distribution family, marginal R\(^{2}\) (fixed effects only), and conditional R\(^{2}\). For binomial models, R\(^{2}\) values are theoretical.

Response	Model family	Marginal R\(^{2}\)	Conditional R\(^{2}\)
Tolerance expression	gaussian	0.03	0.24
Infection status	binomial	0.13	0.58
Resistance expression	gaussian	0.04	0.31
Parasitism (ticks)	binomial	0.13	0.29
Capture time Δ	gaussian	0.27	0.31
Capture time	gaussian	0.02	0.10
Weight	gaussian	0.20	0.31
Reproductive maturity	binomial	0.01	0.12

Conceptual model path diagram

In attempts to reduce the noise of the PATH diagram depicting our full SEM (Figure 27), I will attempt to further simplify its presentation by combining variables into groups. Sex, reproductive status, and weight will be combined into “traits” (perhaps this should be “morphology”?); resistance and tolerance expression will be combined into “expression”, weather and climate will be combined into “environment”, and activity timing and change in activity timing will be combined into “behavior”. This should reduce the visual clutter and double as our conceptual model, since we can label which paths met our assumptions (blue), and which didn’t (grey).

Figure 29: Factors contributing to infection of Peromyscus with Borrelia. Black solid vectors represent effects that matched our hypothesis and grey dashed vectors represent effects we hypothesized that were not supported, Widths of vectors are proportional to average observed direct effect sizes. For full model results, please see Table 16

Species comparison

## # A tibble: 2 × 4
##   Species     n P_infected successes
##   <chr>   <int>      <dbl>     <dbl>
## 1 PELE      469      0.539       253
## 2 PEMA       70      0.4          28

##    prop 1    prop 2 X-squared        df         P 
##     0.539     0.400     4.204     1.000     0.040

## # A tibble: 3 × 4
##   Species     n P_parasitized successes
##   <chr>   <int>         <dbl>     <dbl>
## 1 PELE    17076        0.420       7175
## 2 PEMA     4159        0.0991       412
## 3 <NA>        5        0.6            3

##    prop 1    prop 2    prop 3 X-squared        df         P 
##    0.4202    0.0991    0.6000 1502.9954    2.0000    0.0000

Figure 30: Path diagram comparing a simplified SEM between P. leucopus and P. maniculatus. Solid lines represent paths that are significant for at least one species, dotted lines represent paths that are not significant for either species. Purple paths are statistically different between species and black vectors are not. Vector widths are proportional to the difference in effect size between the species. Path labels represent standardized effect sizes for both species, with P. maniculatus in parentheses. See Table ?? for more model differences and Figure 31 for the cumulative effects on infection for each species.

Because relatively few P. maniculatus were observed with a combination of genetic, behavioral, and infection information, to compare PELE and PEMA with identical models required simplification. Specificially, we removed behavior and immunity expression for the comparative SEM.

With this comparison, we found that the model differed significantly between PELE and PEMA (Figure 30) and our general assumptions were only met for PELE and not PEMA due to no strong link between parasitism and infection among PEMA.

Specific hypotheses:

1. Mouse phenotype is significantly associated with parasitism via sex among PELE but not PEMA and via weight and reproductive maturity among PEMA but not PELE. Phenotype is also linked to infection status via reproductive maturity and weight in both species (though, PEMA’s weight effects are opposite PELE’s) and via Sex among PEMA only.

2. NA - behavior not assessed

3. Tick parasitism is directly associated with infection status only among PELE: Though it is not entirely clear through the figure, the effect of parasitism on infection status was significant for PELE (P = 0.003) but not for PEMA (P = 0.95). This path is not purple in the figure because their unadjusted 90% confidence levels overlap (0.847 ± 0.47 and -0.096 ± 2.29 respectively) - but PELE is different from 0 (effect) while PEMA is not (no effect).

4. NA - immunity not assessed

5. Weather significantly impacted phenotype, parasistism, and infection whereas long-term climate only impacted parasitism rates directly, as in the full model.

This means that, while both species exhibit intraspecific variation in disease competence, interaction with ticks is less important for PEMA than for PELE. This is likely because PEMA is more arboreal, meaning they are less likely to move through tick habitat (e.g., grassy areas).

Additionally all but one path (direct and indirect) from phenotypic traits through to infection differed between P. leucopus and P. maniculatus whereas none of the environmental effects differed.

Figure 31: Cumulative standardized effects on infection status for P. leucopus PELE and P. maniculatus (PEMA).

Predictions

NOTE: USE semEff PACKAGE!!