Appendix for Civitello et al. “Resources, key traits, and the size of fungal epidemics in
Daphnia populations.”
Appendix S1. Considering Additional structural equation models
Here we examine three additional structural equation models (SEMs) to assess the robustness of
our conclusions that (1) resources drive key traits, (2) spore production and host density drive
variation in epidemic size, and (3) that resources and host body size have no additional direct
effects on epidemic size.
METHODS AND RESULTS
We fit and competed 3 additional SEM models with the focal SEM presented in the main
text (designated as “Model 1” here) to assess three alternative hypotheses (H2-4) relating
resources, traits, and epidemic size. We fit each model with the lavaan package in R as for Model
1, and then competed the models using the small sample size corrected Bayesian Information
Criterion (BICC).
H2: Resources directly affect epidemic size
First, we assessed the possibility that resource availability has additional direct effects on
epidemic size. Thus, Model 2 adds a direct link from the Resources latent variable to epidemic
size.
Model 2: Potential direct effects of resources on epidemic size
When fit to the field data, this model indicates that spore load and host density directly affect
epidemic size, but the significant direct link between resources and epidemic size is not
significant. Consequently, this model fits the data nearly identically to the focal Model 1. Given
its additional complexity, the model does not significantly outperform the focal model according
to BICC (Table S1).
H3: Resources promote large host size, then solely body size determines key traits
The focal Model 1 assumes that body size, host reproduction, and parasite production are
linked because they are all jointly driven by resources. In other words, it assumes no causal
relationship among the traits themselves. Alternatively, resource availability may promote large
host size, and then large host size on its own could drive increases in host and parasite
reproduction. We built and fit an SEM (Model 3) that reflects this hypothesis:
Model 3: Host body size as the sole direct driver of host and parasite reproduction
Here, as before, resources significantly increase body size of host. Body size, itself, is
significantly linked with parasite production. However, on its own, it does not have a significant
direct link with host reproduction. As in the other models, host density and spore load have direct
effects on epidemic size. In addition, there is no evidence for an additional direct effect of body
size on epidemic size. Relative to the other models, Model 3 fits the data poorly (Table S1),
partly due to the non-significant link between host body size and reproduction.
H4: Resources promote large host size, and then size and resources jointly drive key traits
The focal Model 1 assumes that body size, host reproduction, and parasite production are
all driven by resources. In contrast, Model 3 assumes that host size is the sole driver of host and
parasite reproduction. Another alternative is to hypothesize that resources drive body size, and
then resources and size jointly drive the other traits. Thus, we built and fit an SEM (Model 4)
that reflects this hypothesis:
Model 4: Host body size and resources jointly drive of host and parasite reproduction
This SEM indicates that resource availability significantly directly drives increased host
body size and reproduction. However, resources do not directly drive spore production. Instead,
the influence of resources on spore load is indirect, and it is mediated through significant links
through body size. As in all other models, there is strong support for direct links from host
density and spore production to epidemic size. Again, there is no evidence for an additional
direct effect of body size on epidemic size. This model performs very similarly to Model 1
(Table S1). Despite this similar performance, biological reasoning and previous experimental
and theoretical results suggest that body size per se cannot be the sole driver of parasite
production in Daphnia. For example, even when large Daphnia are experimentally infected, they
produce many more parasite spores when provided with more algal resources (Hall et al. 2009).
Thus, resource acquisition (which can increase with body size), rather than larger physical space
is likely the central constraint on spore production in Daphnia (Hall et al. 2009).
After fitting these alternative models, we can compare their performance using
information criteria. We computed ΔBICC scores for each model by subtracting the BICC of the
best performing model from the BICC of each model. Next, we determined the Akaike model
weight for each model from these ΔBICC scores (Burnham and Anderson 2002). By definition,
the best performing model has ΔBICC = 0. In general, models with ΔBICC < 4 have similar
support and ΔBICC > 10 indicate very poor relative performance. Model weights index the
relative evidence that one model is the best model in the set under comparison. Model weights
approaching 1 indicate complete support and weights near zero indicate essentially no support.
Table 1. Model comparison statistics for the four competing SEMs
Model 1
Model 2
Model 3
Model 4
DISCUSSION
Parameters
21
22
19
21
BICC
153.90
152.52
158.69
153.90
ΔBICC
1.38
0
6.71
1.38
Model weight
0.246
0.491
0.017
0.246
In our analysis, Models 1, 2, and 4 all performed similarly well (Table S1). These models
were statistically indistinguishable (ΔBICC < 2 for Models 1 and 4). In contrast, Model 3
performed somewhat poorly. Overall, this analysis reinforces three conclusions from the analysis
of Model 1. First, all models indicate that resources drive host and parasite reproduction.
Although there was some evidence in Model 4 for an indirect resources-spore production link
mediated by host size, this model did not outperform any of the alternative SEMs. Second, all
models similarly indicate direct links from host density and parasite production to epidemic size.
However, no model found significant evidence for additional direct links from body size or
resources to epidemic size. In summary, this analysis supports the conclusion that resources and
host body size can drive epidemics indirectly by modulating key traits of hosts and parasites, but
that these factors do not have additional direct effects on epidemic size.
REFERENCES
Hall, S.R., Simonis, J.L., Nisbet, R.M., Tessier, A.J., & Cáceres, C.E. 2009. Resource ecology of
virulence in a planktonic host-parasite system: An explanation using dynamic energy
budgets. American Naturalist, 174:149-162.