We don’t only care about prevalence

  • Prevalence : fraction of the population infected (infection is binary here)

  • Intensity : the number of parasites within an infected host (how infected is the host?)

But prevalence and intensity are interesting to look at together

  • Prevalence and intensity are driven by potentially different forces

  • Prevalence is more about encounter (\(c\)) and intensity is more about host susceptibility (\(a\))

  • We’ll consider both until next lecture

Why do we care about intensity in particular?

  • outcomes (death is more likely if you have more parasites)

  • transmission potential (transmission is more likely when you have more parasites)

  • mitigation targets (who do we treat?)

Outcomes (Ebola)

Faye et al. 2015 PLoS Medicine

Transmission potential

  • supershedders: high infection burden can lead to shedding lots of pathogen in the environment (increases transmission rate)

  • Supershedding is different than superspreading

  • Transmission potential increases for both external parasites and internal parasites

  • Even for sexually-transmitted infections (so transmission goes up, even though contact does not change; \(\beta = c*a\)

An example of HIV

Higher viremia means higher transmission potential

Fraser et al. 2007 PNAS

But once symptoms start, contact goes down

There is nuance here, as transmission depends on contact and infectivity

Fraser et al. 2007 PNAS

Timeline of infection

Arzt et al. 2019 Scientific Reports

Monogean ectoparasites of guppies

Saturating transmission potential (there’s only so many parasites you can have before transmission potential saturates)

Walsman et al. 2022 Nature E&E

Mitigation

If we can identify phenotypes of heavily infected individuals, we can target treatment

Target high-risk individuals

  • could estimate social contact network (variation in contact rate \(c\))

  • or could use measures associated with burden (and subsequently probability of infection)

    • so vaccinate based on which individuals you think are either highest risk or would have the highest burden if infected

Targeted vaccinations of highly central individuals

  • Knowing social network structure helps vaccination

  • Even using traits to target vaccination still works better than random

Rushmore et al. 2014 Interface

What causes variation in parasite burden within a host population?

  • host sex

  • time of exposure

  • superinfection

  • home range size

  • immune function

Sex-biased parasitism

  • Generally, males tend to have higher parasite prevalence and intensity than females

  • At least two main drivers:

    • ecological (males have different traits)
    • physiological (different hormone profiles)

Ecological drivers of sex-biased parasitism

  • sexual size dimorphism : difference in body size between sexes

  • males tend to (but not always) be larger than females

  • However, differences in size are also related to differences in other things which influence parasite encounter (home range size, territoriality, etc.).

  • Really tough to disentangle differences in size from differences in behavior.

How would we test if sex-biased parasitism was driven by size differences versus other behavioral or trait differences?

Zuk & McKean 1996 Int J of Parasitology

Physiological

  • Hormonal differences between the sexes may also play a role in at least two ways
    • hormones may alter immune function
    • hormones may influence behavior

Hormones may alter immune function

  • testosterone suppresses the immune system, increasing susceptibility to infection

  • note that this does not increase contact rate (which is important for prevalence), but does increase the parasite’s ability to increase within the host (which is important for intensity)

Hormones may influence behavior

  • Testosterone associated with risk-taking behavior, home range size, and movement

  • This serves to increase encounter rates (which is important for prevalence), but does not increase the parasite’s ability to increase within the host (which is important for intensity)

What does this all mean?

  • If parasite prevalence and intensity is higher in males, then there are likely multiple forces at work

  • If parasite prevalence is higher, but intensity is not, then it boils down to variation in contact rate, not within-host physiological differences

  • If parasite intensity is higher, but prevalence is not, then it boils down to variation in physiology/hormones/immune/energy budget, not contact rate

A fun example of sex-biased parasitism

Swislocka et al. 2020 _Int J Parasitol Parasites Wildlife

Evidence in rodents and bats

Krasnov et al. 2012 Mammalia

Sex-biased parasitism

Krasnov et al. 2012 Mammalia

Time of exposure

  • If all host individuals were equal, there could still be aggregated parasite burdens

Timeline of infection

Arzt et al. 2019 Scientific Reports

Simulated data to show how this matters

What happens if all hosts are equivalent and timing of exposure is the same?

Does not really happen though

Tinsley et al. 2020 Parasitology

Superinfection

Superinfection is when an infected individual is exposed again to a parasite, and it infects.

  • This serves to increase pathogen burden in infected hosts, as it disrupts the infection timeline by adding more parasites to an individual.

  • This effect is pronounced when hosts vary in their exposure probability, such that some individuals just have a higher risk of exposure and resulting superinfection.

Home range size

  • Species with larger home ranges, or home ranges with more overlap with other species, lead to greater encounter of parasites

  • The potential energetic cost of having a large home range could lead to higher infection intensity

Godfrey 2013 _Int J Parasitol: Parasites and Wildlife

Immune function

  • We talked about immune function as related to sex differences, but there could also be standing variation in immune function across the population.

  • We focus here on innate immunity

Immune function

  • Variation in immune function will influence infection intensity, but not prevalence

  • Often tough to disentangle, as it requires immune information before and after parasite infection (or at least before)

  • Studies tend to look at how parasites influence immune regulation

    • e.g., some helminth parasites can downregulate immune function of hosts (McSorley and Maizels 2012 Clin Microbiol Rev)




End of lecture 1

What have we learned so far?

  • There is variation in parasite infection prevalence and intensity within a population

  • This variation is related to host traits, physiology, etc.

  • Some things affect infection prevalence, some intensity, some both

Parasite aggregation

  • Now we’ll focus almost entirely on infection intensity

  • This variation in infection intensity (aka parasite burden) gets at the fundamental idea that parasites are aggregated within host populations

  • Let’s dive into some of the terminology and how intensity is measured

What does infection intensity mean for microparasites and macroparasites?

  • Viremia (viral load)

    • Infectious copies per ml (blood) or g (host tissue)

  • Ectoparasite burdens

    • Count of individual parasites (sometimes standardized by host weight)

Issues that we’re still struggling with

  • Do we need to account for host body mass in estimates of infection intensity?

Issues that we’re still struggling with

  • Do we need to account for parasite size or impact?

Lambden & Johnson 2013 Ecology & Evolution

What does the distribution of intensity look like?

Webber & Willis 2020 Royal Society Open Science

What does the distribution of intensity look like?

Buhat et al. 2021 Modeling Earth Systems and Env

Tradeoffs in infection intensity

  • Taking too many host resources (e.g., when intensity is high) can kill the host, or reduce parasite fitness

  • There should be a sweet spot of intensity

  • But this spot is super dependent on amount of host resources, host lifespan, parasite transmission mode, parasite survival in the environment, etc. etc. etc.

How do we measure parasite aggregation?

  • Variance-mean ratio

  • Negative binomial fit (\(k\))

  • Mean crowding

  • Patchiness

  • Poulin’s \(D\)

  • Hoover’s index

Morill et al. 2023 _Int J for Parasitology

Variance-mean ratio

  • Basically a test of dispersion

  • Values greater than 1 mean variance is larger than the mean (overdispersed)

  • So there’s more aggregation when VMR is high

\[ VMR = \dfrac{\sigma^2}{\mu} \]

Negative binomial distribution

  • By fitting a known distribution, we get a single measure of aggregation based on the distribution of parasite infection intensity values

  • As aggregation increases, \(k\) decreases

  • As infection intensity becomes random, \(k\) goes to infinity

\[ k = \dfrac{(\mu^2 - \sigma^2)/N}{(\sigma^2 - \mu^2)} \]

Negative binomial distribution

Mean crowding

  • Basically, the average number of parasites infecting host (but not quite)

\[ m* = \dfrac{\sum x^2_j}{\sum x_j} - 1 \]

Patchiness

  • Mean crowding divided by the sample mean

  • Crowding on single host from the perspective of any one parasite, in units of the mean abundance.

  • Could be considered as how many times more crowded an average parasite is, compared with if the same parasites were distributed randomly among hosts

\[ P = \dfrac{m*}{\mu} \]

Poulin’s D (discrepancy)

  • Compares observed aggregation with the case of all the sampled parasites being on a single host

  • Based around the Lorenz curve (not unique to this measure)

  • This measure is also called the Gini index in economics

\[ D = 1 - \dfrac{2\sum^N_{i=1} \sum^i_{j=1} x_j}{\mu N(N+1)} \]

Lorenz curve

  • Developed in economics to describe wealth inequality

McVinish & Lester 2020 Interface

A note about Poulin’s D (the Gini index)

  • So the Gini index, based on the Lorenz curve, is an attempt to get at inequality

  • The overall goal is to say something about super heavy-tailed distributions

  • But the Gini index does not get at these heavy tails as good as it could

  • And we will stop before we go down this statistics rabbit hole

Hoover’s index

  • proportion of parasites that would need to be redistributed to achieve an even distribution among hosts

  • e.g., value of 0.7 indicates that 70% of the parasites would need to be redistributed in the sample to achieve evenness

\[ H = \dfrac{\sum^N_{i=1} |x_i - \mu | }{2\sum^N_{i=1} x_i} \]

Collinearity among aggregation indices

Morill et al. 2023 _Int J for Parasitology

This is not good

Why is this a problem?

What causes variation in infection intensity between host species for the same parasite?

  • host immune profiles

  • trait distributions of hosts

  • parasite specificity

  • shared habitat use

Evidence for differential host use

Fenton et al. 2015 Am Nat

host immune profiles

  • Differences among host immune response could mean some host species have higher (lower) infection intensities

  • Variable host condition (ability to mount immune response) could drive variation in infection intensity (Beldomenico & Begon2010 TREE)

Bats are weirdos

trait distributions of hosts

  • Host traits influence both prevalence and intensity

  • So different distributions of host traits will influence encounter (\(c\)) and susceptibility (\(a\))

trait distributions of hosts

Greenberg et al. 2017 Evolutionary Applications

parasite specificity

  • Parasites are better at infecting some hosts than others

Dallas et al. 2019 PRSB

parasite specificity

  • This could be for a number of reasons

    • parasites infecting fewer host species might be better suited to infect those particular host species

    • distantly related host species may be harder to infect for a given parasite (phylogenetic distance is important!)

shared habitat use

  • intensity could increase when contact increases (provided superinfection possible)

  • e.g., if host prefers same microclimate as parasite, could lead to higher intensities for that species, and potentially shifts in distribution of infection intensity

A fun side note

  • Mean-variance scaling relationships in infection intensity

  • Mean burden is related to the variation in burden

Johnson & Hoverman 2014 J Animal Ecology

What causes variation in infection intensity for the same host species across parasites?

  • It’s not just about host differences

  • Parasites differ in their transmission, ecology, habitat preferences, tissue infected, etc. etc. etc.

  • All of these things influence the resulting infection intensity possible for a given parasite

  • Even if it’s infecting the same host

But this is pretty obvious

  • If this is a shock, it shouldn’t really be

  • More similar parasite species should have similar infection intensities in the same host though

A holistic view of prevalence and intensity

Holian & Dallas 2023 in prep

Hosts are less variable in their parasite intensities

Holian & Dallas 2023 in prep

Standing questions for thought



Are aggregated burdens comparable across host species?

Are aggregated burdens comparable across parasite species?

Are aggregated burdens a property of the host, the parasite, or the location?