Handling times and saturating transmission functions in a snail–worm symbiosis

Abstract

All dynamic species interaction models contain an assumption that describes how contact rates scale with population density. Choosing an appropriate contact-density function is important, because different functions have different implications for population dynamics and stability. However, this choice can be challenging, because there are many possible functions, and most are phenomenological and thus difficult to relate to underlying ecological processes. Using one such phenomenological function, we described a nonlinear relationship between field transmission rates and host density in a common snail-oligochaete symbiosis. We then used a well-known contact function from predator-prey models, the Holling Type II functional response, to describe and predict host snail contact rates in the laboratory. The Holling Type II functional response accurately described both the nonlinear contact-density relationship and the average contact duration that we observed. Therefore, we suggest that contact rates saturate with host density in this system because each snail contact requires a non-instantaneous handling time, and additional possible contacts do not occur during that handling time. Handling times and nonlinear contact rates might also explain the nonlinear relationship between symbiont transmission and snail density that we observed in the field, which could be confirmed by future work that controls for other potential sources of seasonal variation in transmission rates. Because most animal contacts are not instantaneous, the Holling Type II functional response might be broadly relevant to diverse host-symbiont systems.

Systematic review of modelling assumptions and empirical evidence: Does parasite transmission increase nonlinearly with host density?

“…Many such nonlinear transmission functions have been proposed (McCallum et al, ), with unique formulations arising from different underlying mechanisms. For instance, there are nonlinear functions that describe contact handling times that cause host contact rates to saturate with host density (Antonovics et al, ; Holling, ; Hopkins, McGregor, Belden, & Wojdak, ) and that describe heterogeneity in host susceptibility or resistance to infection (Dwyer, Elkinton, & Buonaccorsi, ), which can lead to nonlinearities such as macroparasite aggregation among hosts (Anderson & May, ). There are also purely phenomenological nonlinear transmission functions with unitless density dependence parameters, which could represent many underlying mechanisms (Fenton et al, ; Hochberg, ; Smith et al, ; Figure ).…”

Host preferences inhibit transmission from potential superspreader host species

“…Individual focal hosts had anywhere from 0 to 16 interspecific contacts during a 45 min observation period, and interspecific contact rates increased nonlinearly with alternative host density (figure 4). When comparing 95% credible intervals, the interspecific (alternative–focal) encounter rate (0.012 encounters min −1 ) estimated by the Holling Type II functional response was no different from the intraspecific (focal–focal) encounter rate (0.014 encounters min −1 ) that was previously published (figure 3) [32]. Similarly, the contact handling time for interspecific (alternative–focal) contacts was estimated to be 3.25 min in the interspecific Holling Type II contact rate function, which was not statistically different from the intraspecific (focal–focal) contact handling time previously published (figure 3) [32].…”

“…When comparing 95% credible intervals, the interspecific (alternative–focal) encounter rate (0.012 encounters min −1 ) estimated by the Holling Type II functional response was no different from the intraspecific (focal–focal) encounter rate (0.014 encounters min −1 ) that was previously published (figure 3) [32]. Similarly, the contact handling time for interspecific (alternative–focal) contacts was estimated to be 3.25 min in the interspecific Holling Type II contact rate function, which was not statistically different from the intraspecific (focal–focal) contact handling time previously published (figure 3) [32]. Overall, the contact rate function describing how interspecific (alternative–focal) contact rates varied with alternative host density was indistinguishable from the contact rate function describing how intraspecific (focal–focal) contact rates varied with focal host density.…”

“…Note that following mathematical conventions, the FA subscript designates transmission from alternative hosts to focal hosts throughout. We assumed that normalFOIF=βnormalFFNFkFFfalse(IF/NFfalse)+βnormalFA NAkFAfalse(IA/NAfalse), where β FF and β FA (estimated from the statistical model) are the intra- and interspecific transmission rates, N F and N A are the focal host and alternative host densities, I F and I A are the infested focal host and infested alternative host densities, and k FF and k FA (estimated from the statistical model) are flexible, unitless density-dependent parameters that allow intraspecific and interspecific transmission to be linear increasing functions of host density ( k = 1, density-dependent transmission), nonlinear functions of host density (0 < k < 1) or independent of host density ( k = 0, frequency-dependent transmission) [13,32]. Comparing β FA to β FF allowed us to compare the relative roles of inter- and intraspecific transmission to net focal host infestation risk.…”

Density dependence and disease dynamics: moving towards a predictive framework

“…Most epidemiological models use phenomenological or mechanism-agnostic density-dependent interaction curves (Hopkins et al 2018(Hopkins et al , 2020, rather than empirically identifying how a given interaction rate increases with density. Where researchers know the specific behaviours that allow transmission (space sharing, den sharing, air sharing, direct contact, mating, fighting, etc.…”