Parasitic Castrators: A Model

Last week, I introduced you guys to the wonderful world of parasites that castrate their hosts.  This week, I want to talk about the mechanisms behind parasitic castration – both how and why castration happens – and how the wacky responses (e.g., gigantism) of castrated hosts emerge naturally from these mechanisms.  So, enter, from stage left, a beeeeeeeautiful paper by Hall et al. (2007).

Pattern Oriented Modeling:

The Hall et al. (2007) paper is a wonderful example of pattern oriented modeling. Actually, pattern oriented modeling – as championed by Grimm, Railsback, and colleagues – is an approach used to make agent based models more rigorous and more ‘applied.’  For ABMs, using just one predicted pattern isn’t a very useful way to build a mechanistic model, because many different agent behaviors might result in the emergence of the same pattern.  How would you figure out which behaviors were mechanistically appropriate?  If you instead have several expected patterns, it is unlikely that just any agent behaviors will cause all of the patterns to emerge.  So, you can determine which mechanisms are biologically appropriate by determining which agent behaviors lead to your patterns.  Anyways, Hall et al. (2007) used differential equation models, instead of ABMs, but they still used a pattern oriented modeling approach that was very powerful.  Specifically, they knew that any model with parasitic castrators in it should produce the following patterns:

1. Gigantism.  At any given host age, hosts that are parasitized by castrators should be bigger than unparasitized hosts and hosts parasitized by noncastrating parasites.
2. Life span.  Hosts that are parasitized by castrators should live longer than hosts parasitized by noncastrating parasites.
3. Fecundity compensation.  Hosts that are parasitized by castrators should begin reproducing sooner than hosts parasitized by noncastrating parasites.
4. Reproductive rates.  Hosts that are parasitized by castrators should have lower mean reproductive rates than hosts parasitized by noncastrating parasites because castrated hosts are sterilized, either partially or completely.
5. Parasite reproduction.  Hosts that are parasitized by castrators should produce more new parasites than hosts parasitized by noncastrating parasites.
6. [There’s a sixth one in the paper, but I’m going to let you guys go check it out.]

Not only are these patterns predicted from theory, but they had also been demonstrated empirically in a system where bacterial parasites castrate Daphnia hosts.  So, Hall et al.’s (2007) model is based on that Daphnia-bacteria system.

The Kooijman DEB model

Before thinking about parasites, Hall et al. (2007) adapted a dynamic energy budget model to the Daphnia-bacteria system (or a similar system).  In a nutshell, hosts acquire, assimilate, and store energy from their food, and then they can use that energy for maintenance of their current state, growth, development, or reproduction.  Specifically, hosts devote a fixed proportion (k) of their energy reserves to growth and ‘structural maintenance.’  They spend the other fraction of their energy (1-k) on other stuff.  If they aren’t reproductively mature yet, they spend the (1-k) on development, and if they are mature, they spend the (1-k) on reproduction and ‘maturity maintenance.’  The two maintenance things are a bit confusing, I know, but just remember that there are two types of maintenance, and organisms need to spend some energy maintaining their current condition before they can spend any energy on other things.

Host Starvation:

Using this dynamic energy budget model, if the host starts to experience ‘moderate’ starvation conditions, its reserve energy stores will decline. Eventually, the reserves will be low enough that the proportion of energy available for growth and maintenance (k) will only be enough to cover ‘structural maintenance.’  The host doesn’t have any energy left in the ‘k’ part of the budget to devote to growth.  The host still divides up the (1-k) part of the budget to development or reproduction and ‘maturity maintenance,’ depending on whether the host is reproductively mature or not.  So, at this point, the host is still reproducing or developing.

However, if starvation conditions become severe, the host might not have enough energy to devote to reproduction and development.  The host might just spend all of its k and (1-k) energy budgets on maintenance.  And if reserves get so low that the energy stores don’t even cover the maintenance costs, the host dies.

Consumer Parasite:

Now let’s add a parasite to the model!  First, let’s add a noncastrating parasite, which Hall et al. (2007) called a ‘consumer’ parasite.  The parasite takes energy from the reserve energy stores of the host.  In that way, the host and parasite are competing – they’re both using and budgeting that energy pie.

Importantly, consumer parasites can affect how hosts allocate energy, but only indirectly.  That is, if the parasite uses enough of the reserve energy that the host finds itself in moderate starvation conditions, the host stops growing.  It devotes all of the k fraction of the energy to structural maintenance.  And if the parasite uses up enough of the reserve energy that the host finds itself in severe starvation conditions, the host stops developing or reproducing.

Hall et al. (2007) also added one more assumption – if the parasite takes up more than a certain proportion of the host’s total volume (p), the host dies.  Otherwise, very efficient parasites can reach unrealistically huge population sizes.

Ok, sooooo – what happens when we run the consumer model?  After several days of normal growth and reproduction rates, the hosts stop growing because the parasites have reduced the energy stores to moderate starvation conditions.  The hosts keep reproducing for a few more days, but reproductive rates start to decline because the (1-k) piece of pie gets smaller and smaller as the parasite populations grow bigger and bigger.  Finally, the parasites cross that critical volumetric proportion (p) and the hosts die.

Parasitic Castrators:

Now let’s add a parasitic castrator to the model, instead of a consumer parasite.  To do this, Hall et al. (2007) changed just one model assumption.  Instead of leaving k as the constant proportion of energy devoted to growth and reproduction, now k is a dynamic variable.  Specifically, k is a function of the number of parasites per host.  Whereas consumer parasites could only indirectly affect host’s allocation of resources, castrating parasites can directly manipulate host’s allocation of resources by directly affecting k.  (They can also indirectly affect host resource allocation, just like consumer parasites.)  When there are no parasites, the fraction of energy devoted to growth and maintenance (k(0)) is regular old k, from the baseline model.  But as the number of parasites increases, k also increases monotonically – the host spends more and more of the energy budget on growth because castrating parasites directly cause the hosts to budget energy differently.  And because k increases with parasite density, the energy available for development or reproduction (1-k) decline with parasite density.  So, the host is castrated.  [Insert “ooooooohs” and “ahhhhhhhs” of wonder here.]

Ok, sooooo – what happens when we run the castrator model?!  For just a few days, host growth and reproduction rates are normal because parasite populations are still too small to be consuming a lot of host energy.  Then, as parasite density increases, k starts increasing, and host growth rates increase dramatically.  In fact, castrated hosts get much bigger than uninfected hosts and hosts infected by consumer parasites.  After just a few more days, hosts stop reproducing because (1-k) is so low.  Hosts keep growing until just before they die, and host death occurs later than it did when the parasite was a consumer instead of a castrator.

Some Cool Notes:

As we expected, hosts infected by castrating parasites ended up having lower reproductive rates (Prediction 4).  But did they see fecundity compensation (Prediction 3)?  It’s hard to tell from the graphs, but Hall et al. (2007) said that hosts infected by castrating parasites started reproducing sooner than snails infected by consumer parasites and uninfected hosts.  The really cool thing is that the earlier reproduction was completely emergent – it wasn’t “programmed” into the model.  Because castrating parasites increased the growth rates of the hosts, the hosts reached the reproductive maturity threshold size sooner, and thus switched from spending their (1-k) energy budget on development to spending it on reproduction earlier than other hosts did.   Super cool!

Under these conditions, being a parasitic castrator was a better strategy than being a consumer parasite because castrators ended up producing more new parasites than consumers. Consumers rapidly used up all of the available host energy reserves, while castrators kind of “stocked up” energy by getting hosts to grow bigger.  (Bigger hosts can acquire and assimilate more energy.)

Back to Patterns:

Let’s go back and see if all of the predicted patterns emerged from these models.

1. Gigantism.  CHECK!
2. Life span.  CHECK!
3. Fecundity compensation.  CHECK!
4. Reproductive rates.  CHECK!
5. Parasite reproduction.  CHECK!
6. NOT check! In the discussion, Hall et al. (2007) note that their sixth pattern didn’t emerge from the model.  So, there’s some future work to be had there.  It doesn’t mean that this model is bad, but there is some interesting biology and math that needs to be considered further.

So… that was flipping awesome.  In case you’re wondering, the correct thing for you do right now, if you haven’t yet, is to follow this link to the PDF of the paper.  Happy reading!

Reference:

Hall, S.R., C. Becker, C.E. Caceres. 2007. Parasitic castration: a perspective from a model of dynamic energy budgets. Integrative and Comparative Biology 47(2): 295-309.