Matt Michalska-Smith

Matt Michalska-Smith
Liz Sander
Stefano Allesina
Mercedes Pascual

Acknowledgements


Liz Sander	Stefano Allesina	Mercedes Pascual

Gyuri Barabás	Jacopo Grilli
Amy Henry	Joe Mihaljevic
Orissa Moulton	Molly Gallagher

“Science is knowledge arranged and classified according to truth, facts, and the general laws of nature.” — Luther Burbank

Scientists often seek to classify observable phenomena into categories based on similarity. Sometimes these categories are spurious and later revised or rejected, while other times a more in-depth analysis reveals a concrete foundation for what was originally little more than an intuition.

In the study of food-webs, ecologists have come up with categories to classify species according to the details of thier interactions with what they eat: herbivores, omnivores, carnivores, as well by trophic considerations: primary producers, top predators. In some cases, the definitions can be non-rigorous, allowing for a degree of interpretation.
next slide

What are parasites?

Prey/predator body size ratio (?)
Intimate, durable interactions (?)
Number of hosts or prey attacked during a particular life-history stage

Lafferty 2008

Take parasites, for example:
Lafferty, in his contribution to the Encyclopedia of Ecology, explains some of the many complications that arise when trying to systematically differentiate parasites from other life-cycles we observe in nature He discounts the first option since many predators consume prey that are larger than themselves (e.g. wolves eating moose) and the second with a similar argument: lions spend weeks consuming a single antelope.

Though he settles on the number of hosts/prey attacked in a particular life-history stage as a good indicator, with parasites attacking fewer (usually only one), this is difficult to measure quickly and precisely using the sampling methods that are common when collecting food-web data.
next slide

When the additional information of ecological classifications is unavailable, e.g. with a previously unobserved species, parasites and consumers look much more similar.

This project started as a question of whether or not we can identify species roles based just on this information, that is, the network structure.

Put another way, can we max-width:7.5em;do what an ecologist does when observing species extensively in the field by just looking at the binary network of interactions?

By approaching this problem in a more statistical way, we can more explicitly identify the important, distinguishing characteristics, and provide justification (or not) for the characteristics that are thought to be important.
next slide


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	1	1	1	0	0
0	0	0	1	1	1	0	0

Also known as the stochastic blockmodel

A generalized form of Modularity

Seeks to find groups of strongly connecting species

Allesina & Pascual 2009

Ecological classifications, such as herbivore or parasite, are assigned by ecologists following a detailed investigation of the species life history and, in particular, its interactions with other species. Another approach to group species is to look at the overall network structure and to group species that eat or are eaten by the same or similar prey or predators.

In 2009, Allesina & Pascual introduced the group model to ecology to make this concept statistically rigorous. The model had been used previously in the social sciences under a different name -- the stochastic blockmodel. This model works by re-arranging the rows/columns of the matrix in order to form blocks of species with similar interactions.
next slide


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	1	0	0	0
0	1	1	0	1	0	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	1	0	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


0	0	1	1	1	1	0	0
0	0	0	0	0	0	0	0
0	0	0	1	1	1	0	0
0	0	0	0	0	0	0	0
1	1	0	1	0	0	1	1
0	1	0	0	0	0	0	1
1	0	0	1	0	0	1	1
0	0	0	1	0	0	0	1
1	1	0	1	0	0	0	1
0	0	0	0	0	0	0	0

	ψ	p-value
Parasites	0.667	0.089
Predators	0.533	0.644
Herbivores	0.8	0.048
Primary Producers	1.0	0.022
Overall	0.533	0.005

Parasites	0.25	1.0
Predators	0.25	1.0
Herbivores	0.25	0.619
Primary Producers	0.25	1.0
Overall	0.063	0.695

Once we have these statistical groupings, we want to know how well these groupings correspond to ecological classifications.

Put another way, if we look at which species are parasites,
next slide
we want to calculate how "imbalanced" the groupings are with respect to the provided groupings. Are all of the parasites in a group by themselves? or are they evenly spaced between the groups? Finally, using a permutation test, we can calculate explicitly
next slide
how likely it is for such a level of imbalance to arise by chance.

We can apply this proceedure for each ecological classification (as well as look at all of them at once).
next slide
In this case, we see that the top grouping does well for producers and parasites, while the bottom grouping is more evenly spread (i.e. nonsignificant). Note that even though one of the degree-corrected groups is made up of entirely herbivores, the p-value is still quite high because it is not very unlikely for such a configuration to occur given this number of herbivores and groups.
next slide

7 Large, well-resolved, marine/estuarine food-webs

With/without Concomitant predation

Each species categorized:

Primary Producer
Herbivore
Parasite
Predators

Dunne et al. 2013

We can summarize this data by looking at the in- and out- degree distributions for each of our four categories. Recall that in-degree is the number of prey/hosts and out-degree the number of predators/parasites. Thus, primary producers are made obvious by their lack of in-degree and the top-predators (in the consumer class) have no out-degree.

Note this figure only depicts members of one web -- that of the Punta Banda Estuary, but other webs show similar trends. To see the values for other webs, tap Spc, , PgDn, or n.

Differences in degree distribution between classes are significant in all four cases (ANOVA p-value < 0.0001) and Tukey's Highly Significant Difference labels on the plot. Parasites fall in their own class in 3/4 of the cases for this web.
next slide

Concomitant Links	Degree Corrected	g	Primary Producers	Herbivores	Consumers	Parasites	Overall
No	No	2	0.895***	0.737***	0.491***	0.421	0.246***
		3	0.826**	0.589	0.331***	0.260	0.120***
		5	0.757***	0.551***	0.628***	0.430***	0.307***
		10	0.585*	0.448***	0.439***	0.445***	0.214***
	Yes	2	0.874	0.692	0.660***	0.449***	0.397***
		3	0.815	0.565	0.381***	0.521***	0.250***
		5	0.689	0.350	0.289***	0.559***	0.109***
		10	0.487	0.145	0.244***	0.138***	0.027***
Yes	No	2	0.898**	0.745***	0.912***	0.555***	0.555***
		3	0.839**	0.598	0.835***	0.603***	0.370***
		5	0.731	0.440*	0.702***	0.710***	0.327***
		10	0.702***	0.284***	0.582***	0.343***	0.164***
	Yes	2	0.874	0.709***	0.812***	0.609***	0.537***
		3	0.833**	0.609***	0.564***	0.515***	0.282***
		5	0.716	0.360	0.365***	0.506***	0.173***
		10	0.451	0.198***	0.364***	0.445***	0.114***

Concomitant Links	Degree Corrected	g	Primary Producers	Herbivores	Consumers	Parasites	Overall
No	No	2	0.895***	0.737***	0.491***	0.421	0.246***
		3	0.826**	0.589	0.331***	0.260	0.120***
		5	0.757***	0.551***	0.628***	0.430***	0.307***
		10	0.585*	0.448***	0.439***	0.445***	0.214***
	Yes	2	0.874	0.692	0.660***	0.449***	0.397***
		3	0.815	0.565	0.381***	0.521***	0.250***
		5	0.689	0.350	0.289***	0.559***	0.109***
		10	0.487	0.145	0.244***	0.138***	0.027***
Yes	No	2	0.898**	0.745***	0.912***	0.555***	0.555***
		3	0.839**	0.598	0.835***	0.603***	0.370***
		5	0.731	0.440*	0.702***	0.710***	0.327***
		10	0.702***	0.284***	0.582***	0.343***	0.164***
	Yes	2	0.874	0.709***	0.812***	0.609***	0.537***
		3	0.833**	0.609***	0.564***	0.515***	0.282***
		5	0.716	0.360	0.365***	0.506***	0.173***
		10	0.451	0.198***	0.364***	0.445***	0.114***

Red corresponds to an alpha value of one tenth of one percent.

Note that, despite the difference in degree we saw in the previous figure, the degree-corrected group model produced significantly more imbalanced groups, regardless of concomitant predation (paired t-test, estimated difference: .12, p < .001 and .067, p < .001, when including/excluding concomitant predation, respectively). This suggests that degree is not an essential distinguishing factor for parasites.

Including concomitant links also produced more imbalanced groups, under both the degree-corrected (paired t-test, estimated difference: .034, p = .0049) and uncorrected (estimated difference: 203 .085, p < .001) models.

For the following images, we will be looking at the case of including concomitant predation links, but not correcting for degree.
next slide

Ecological classifications have statistical meaning

Especially for Consumers and Parasites
(beyond simple degree distribution)

But this is not always the strongest source of variance

Further structure to be found

Concomitant links important
Next step: Identify the most explanatory properties of homogenous groups

So what can we take away from this?

Well, it is comforting to know that the classifications that ecologists use in the field have statistical meaning with regards to network structure, and that these differences extend beyond simple degree distribution (the degree-corrected model produced more imbalanced partitions, suggesting that discounting the effect of degree in fact improved the ability to distinguish ecological categorizations).

Interestingly, the intra-category differences were stronger than the inter-category differences in some cases, suggesting there might be more informative classifications than the one we used here.

Concomitant links are useful, but not the end-all in distinguishing parasites and consumers.

Finally, we can use these groupings (especially the homogenous ones) to identify the properties that differ between categorizations. These differences can then be used to produce more rigorous definitions and provide insight into the important distinctions between species roles in nature.
next slide

Questions?

Thanks for viewing this presentation, if you have any feedback or questions, please Email me!

Slides available on Michalska-Smith.com

Background and food-web animals ( 1, 2, 3, 4, 5 ) modified from images designed by Freepik and Snap2Objects.

Matt Michalska-Smith

Acknowledgements

introduction

introduction

What are parasites?

introduction: Food-Webs

introduction: Food-Webs

methods: Food-Webs

methods: Concomitant Predation

methods: Group Model

methods: Group Model

methods: Group Model

methods: Group Model (Degree Corrected)

methods: Imbalance

methods: Data

methods: Data

results: Imbalance

results: Imbalance

results: Condensed Graphs

results: Condensed Graphs

results: Condensed Graphs

results: Condensed Graphs

conclusions

Questions?

Thanks for viewing this presentation, if you have any feedback or questions, please Email me!


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	1	1	1	0	0
0	0	0	1	1	1	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	1	0	0	0
0	1	1	0	1	0	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	1	0	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


0	0	1	1	1	1	0	0
0	0	0	0	0	0	0	0
0	0	0	1	1	1	0	0
0	0	0	0	0	0	0	0
1	1	0	1	0	0	1	1
0	1	0	0	0	0	0	1
1	0	0	1	0	0	1	1
0	0	0	1	0	0	0	1
1	1	0	1	0	0	0	1
0	0	0	0	0	0	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	1	1	1	0	0
0	0	0	1	1	1	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	1	0	0	0
0	1	1	0	1	0	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	1	0	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


0	0	1	1	1	1	0	0
0	0	0	0	0	0	0	0
0	0	0	1	1	1	0	0
0	0	0	0	0	0	0	0
1	1	0	1	0	0	1	1
0	1	0	0	0	0	0	1
1	0	0	1	0	0	1	1
0	0	0	1	0	0	0	1
1	1	0	1	0	0	0	1
0	0	0	0	0	0	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	1	1	1	0	0
0	0	0	1	1	1	0	0


1	1	1	0	0	1	0	0
0	1	1	0	0	1	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	0	1	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


1	1	1	0	1	0	0	0
0	1	1	0	1	0	0	0
0	0	0	1	1	1	1	1
0	0	0	1	1	1	0	1
0	0	0	0	1	0	0	1
0	0	0	0	1	1	1	1
0	0	0	0	0	0	1	1
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0


0	0	1	1	1	1	0	0
0	0	0	0	0	0	0	0
0	0	0	1	1	1	0	0
0	0	0	0	0	0	0	0
1	1	0	1	0	0	1	1
0	1	0	0	0	0	0	1
1	0	0	1	0	0	1	1
0	0	0	1	0	0	0	1
1	1	0	1	0	0	0	1
0	0	0	0	0	0	0	0