RESILIENCE AND STABILITY OF PERMO-TRIASSIC KAROO BASIN COMMUNITIES

Tags

biodiversity, extinction, food webs, modeling, paleo-food web, paleontology, simulations, trophic guild

Late Permian community dynamics

This is the second presentation that I made at the Annual Conference of the Geological Society of America in Vancouver last month. The presentation was part of a special session, “Extreme Environmental Conditions and Biotic Responses during the Permian-Triassic Boundary Crisis and Early Triassic Recovery”, co-organized my myself, Tom Algeo, Hugo Bucher and Arne Winguth. The session, spanning two days, was excellent, outstanding, and a lot of fun! I came away with the firm conviction that we are beginning to really understand the massive Permo-Triassic mass extinction, from its causes to consequences to recovery. It truly was a watershed “moment” in the history of the biosphere. The full program for both days can be found here and here. And, here is the abstract. An online copy of the presentation is available here.

RESILIENCE AND STABILITY OF PERMO-TRIASSIC KAROO BASIN COMMUNITIES: THE IMPORTANCE OF SPECIES RICHNESS AND FUNCTIONAL DIVERSITY TO ECOLOGICAL STABILITY AND ECOSYSTEM RECOVERY

ROOPNARINE, Peter, Invertebrate Zoology and Geology, California Academy of Sciences, 55 Music Concourse Dr, Golden Gate Park, San Francisco, CA 94118, proopnarine@calacademy.org and ANGIELCZYK, Kenneth D., Department of Geology, The Field Museum, 1400 South Lake Shore Drive, Chicago, IL 60605

A central question of the P/Tr extinction is the manner in which Permian ecological communities collapsed and E. Triassic ones were built. The end Permian Dicynodon Assemblage Zone (DAZ) has recently been resolved into 3 phases of the extinction spanning ~120ky, followed by the E. Triassic (Induan) Lystrosaurus Assemblage Zone (LAZ), offering an opportunity to examine the ecological dynamics of extinction and recovery in enhanced detail. We do this with 2 modelling approaches.

The first model assumes that populations exist in an energetic balance between consumption and predation. Communities are modelled as stochastic variants sampled from a space defined by species richness and functional diversity. Paleoenvironmental data from the DAZ indicate an increasingly seasonal, arid and drought-prone environment. The models were perturbed by simulated reductions of primary productivity. Results show that DAZ Phase 0 (Ph0) was a robust community resistant to low-moderate levels of perturbation with a well-defined collapse threshold. DAZ Ph1 and Ph2, however, exhibit highly variable responses and are significantly less resistant. LAZ similarly exhibits highly variable responses across minor variation of model configurations.

The second model assumes that communities are locally stable, i.e. minor perturbations are followed by asymptotic returns to equilibrium. During this return, however, communities can exhibit transient behavior during which perturbations can be greatly amplified. Amplification is likely to be important in unstable environments when the frequency of perturbations is shorter than the return time to equilibrium. Applying this model to DAZ and LAZ communities shows that the Karoo ecosystem became more limited in its responses to perturbation as the P/Tr boundary was approached, with Ph1 and Ph2 communities exhibiting very little transient behavior. LAZ in contrast exhibits increased transience.

The energetics and stability models are reconcilable in a history where the Karoo ecosystem became more ecologically stable as the extinction unfolded, yet more sensitive to cascading effects of species extinction and reductions of productivity. The Induan ecosystem was an unrecovered one, sensitive to both extinction and minor ecological disturbances.

Modern and paleocommunity analogues

Tags

connectance, coral reef, food webs, marine communities, modeling, Network theory, networks, paleo-food web, paleontology, real world networks, Scientific models, trophic guild, trophic level

Last week I gave a keynote presentation at the annual conference of the Geological Society of America in Vancouver. Here is the abstract, and a link to the presentation (pdf file).

ANCIENT AND MODERN COMMUNITIES AS RECIPROCAL ANALOGUES OF PERSISTENCE AND STABILITY

ROOPNARINE, Peter, Invertebrate Zoology and Geology, California Academy of Sciences, 55 Music Concourse Dr, Golden Gate Park, San Francisco, CA 94118, proopnarine@calacademy.org
Paleocommunities are spatio-temporally averaged communities structured by biotic interactions and abiotic factors. The best data on paleocommunity structures are estimates of species richness, number of biotic interactions and the topology of interactions. These provide insights into paleoecological dynamics if modern communities are used as analogs; e.g., the recent lionfish invasion of the western Atlantic is the first modern invasion of a marine ecosystem by a high trophic-level predator and serves as an analog for the invasion of paleocommunities by new predators during the Mesozoic Marine Revolution. Despite the invader’s broad diet, it targets very specific parts of the invaded food web. This will lead to non-uniform escalation on evolutionary timescales.

Theoretical ecology provides a rich framework for exploring dynamics of community persistence. Persistence–the stability of species richness and composition on geological timescales–is central to paleoecology. Ecological stability, a community’s return to stability after perturbation, is not necessary for geological persistence. However, it does dictate a community’s response to perturbation, and thus a species’ persistence or extinction. What then is the relationship between paleoecological richness/composition and ecological stability? How do communities respond to losses of species richness or ecological function? Questions of stability and diversity loss are addressed with an examination of transient responses and species deletion stability analyses of end-Permian terrestrial paleocommunities of the Karoo Basin. Transience is measured as the degree to which a perturbation is amplified over ecological time, even as a community returns asymptotically to stability. Transience during times of frequent perturbation, as during times of environmental crises, decreases the likelihood of a persistently stable community. Species deletion stability measures the dynamic response of a community to the loss of single species. It is an open question whether communities become more vulnerable or more resistant during environmental crises. That process, which has occurred repeatedly in the geological past, is important to the fate of threatened modern communities.

PNAS: Late Cretaceous restructuring of terrestrial communities facilitated the End-Cretaceous mass extinction in North America

Tags

Cretaceous, dinosaurs, extinction, food webs, mass extinction, modeling, networks, paleo-food web, paleontology, Robustness, Scientific models, simulations, Tipping point, trophic guild

That’s the title of our new paper, hot off the PNAS press. This study was a lot of fun, because it combines my food web work with one of the best known events in the fossil record. The lead author is Jonathan Mitchell, a graduate student at the University of Chicago. Jon became familiar with the food web work via Ken Angielczyk at the Field Museum, also in Chicago, a former post-doctoral researcher in my lab and close collaborator.  Jon wondered what Late Cretaceous, dinosaur-bearing communities would look like when subjected to CEG perturbations (just search this blog for info. on CEG!), and presented his results two years ago at the Annual Meeting of the Geological Society of America. The results were so intriguing that we decided then to explore the question in much greater detail, and ask what sorts of community and ecosystem changes unfolded in the years before the Chicxulub impact, and what role they might have played in the subsequent extinctions. And here are the results! I will list the full reference below, and you can obtain a complete copy of the paper from PNAS (sorry, not open access). Also, here are links to some news websites that have covered the paper, as well as the paper’s abstract. Enjoy!

EurekAlert, Science Daily, Science Codex

Jonathan S. Mitchell, Peter D. Roopnarine, and Kenneth D. Angielczyk. Late Cretaceous restructuring of terrestrial communities facilitated the End-Cretaceous mass extinction in North America. PNAS, October 29, 2012

ABSTRACT

The sudden environmental catastrophe in the wake of the end-
Cretaceous asteroid impact had drastic effects that rippled through
animal communities. To explore how these effects may have been
exacerbated by prior ecological changes, we used a food-web
model to simulate the effects of primary productivity disruptions,
such as those predicted to result from an asteroid impact, on ten
Campanian and seven Maastrichtian terrestrial localities in North
America. Our analysis documents that a shift in trophic structure
between Campanian and Maastrichtian communities in North
America led Maastrichtian communities to experience more second-
ary extinction at lower levels of primary production shutdown and
possess a lower collapse threshold than Campanian communities.
Of particular note is the fact that changes in dinosaur richness had
a negative impact on the robustness of Maastrichtian ecosystems
against environmental perturbations. Therefore, earlier ecological
restructuring may have exacerbated the impact and severity of the
end-Cretaceous extinction, at least in North America.

Coral reef food webs are out!

Tags

biodiversity, coral reef, corals, food webs, marine communities, real world networks, trophic guild

The first paper dealing with our Caribbean coral reef work is finally out. This paper is really just a detailed account of the data and webs compilation, but the data are now available to all. Enjoy!

Roopnarine, Peter D. and Rachel Hertog. 2013. Detailed Food Web Networks of Three Greater Antillean Coral Reef Systems: The Cayman Islands, Cuba, and Jamaica. Dataset Papers in Ecology, Vol. 2013, Article ID 857470, 9 pages.

Abstract: Food webs represent one of the most complex aspects of community biotic interactions. Complex food webs are represented as networks of interspecific interactions, where nodes represent species or groups of species, and links are predator-prey interactions. This paper presents reconstructions of coral reef food webs in three Greater Antillean regions of the Caribbean: the Cayman Islands, Cuba, and Jamaica. Though not taxonomically comprehensive, each food web nevertheless comprises producers and consumers, single-celled and multicellular organisms, and species foraging on reefs and adjacent seagrass beds. Species are grouped into trophic guilds if their prey and predator links are indistinguishable. The data list guilds, taxonomic composition, prey guilds/species, and predators. Primary producer and invertebrate richness are regionally uniform, but vertebrate richness varies on the basis of more detailed occurrence data. Each region comprises 169 primary producers, 513 protistan and invertebrate consumer species, and 159, 178, and 170 vertebrate species in the Cayman Islands, Cuba, and Jamaica, respectively. Caribbean coral reefs are among the world’s most endangered by anthropogenic activities. The datasets presented here will facilitate comparisons of historical and regional variation, the assessment of impacts of species loss and invasion, and the application of food webs to ecosystem analyses.

A species’s tragedy of the commons

Tags

biodiversity, carrying capacity, cascades, competition, extinction, food webs, interaction strength, link distribution, link strength, modeling, networks, paleo-food web, paleontology, Robustness, Scientific models, simulations, Tipping point, trophic guild

My colleague Ken Angielczyk and I have a new paper out in the Royal Society‘s Biology Letters, entitled “The evolutionary palaeoecology of species and the tragedy of the commons“. If you have never read Garrett Hardin’s original paper on the tragedy of the commons, I strongly suggest that you do. It is a principle that I believe has broad application, and would well be worth a re-visit (first visit?!) by today’s leaders and economists. Our paper can be found here or here (first page only). And here is the abstract, as a little teaser!

Abstract

The fossil record presents palaeoecological pat-
terns of rise and fall on multiple scales of time
and biological organization. Here, we argue that
the rise and fall of species can result from a tragedy
of the commons, wherein the pursuit of self-inter-
ests by individual agents in a larger interactive
system is detrimental to the overall performance
or condition of the system. Species evolving
within particular communities may conform to
this situation, affecting the ecological robustness
of their communities. Results from a trophic
network model of Permian–Triassic terrestrial
communities suggest that community perform-
ance on geological timescales may in turn
constrain the evolutionary opportunities and
histories of the species within them.

New paper – Networks, extinction and paleocommunity food webs

Tags

connectance, extinction, food webs, graph, link distribution, metanetwork, Network theory, networks, nonlinear, paleo-food web, power law, probability, real world networks, Robustness, simulations, trophic guild

Roopnarine, P. D. 2010. Networks, extinction and paleocommunity food webs in J. Alroy and G. Hunt, eds., Quantitative Methods in Paleobiology, The Paleontological Society Papers, 16: 143-161. (available here).

The paper is part of a volume, Quantitative Methods in Paleobiology, sponsored by The Paleontological Society. Full details are available here. The volume is also available for sale. Purchase one and support the Society!

A space for species-level food webs

Tags

food webs, metanetwork, probability, trophic guild

Let’s begin the description of an ensemble space by recognizing that it is a probability space of all the species-level networks (SLNs) possible given a specific metanetwork. We will adopt a set of formal definitions of the space, namely as a probability space (S, F, P). The set S is the complete sample space of the metanetwork whose topology is U, F is the set of sets for which real-world SLNs exist (see below) and P is the probability of an element in F, that is, P(SLN). F is often taken to be the power set of S, or the set of all sets, but as shown below, many of those sets in S would contain SLNs that cannot exist in the real world.

Ensemble size.– The number of SLNs that can be derived from a metanetwork ensemble is finite, because there is a finite number of arrangements or graphs of the species. The number or ensemble size also defines the maximum variation possible for a real community, unless the taxon composition itself changes. The number of SLNs (the number of elements in S, or the cardinality of S) is designated |S|.

Examine the simple metanetwork in the figure. We will designate the metanetwork U, and the number of guilds as |U|. Guilds 1 and 2 (G1 and G2) comprise species that are preyed upon by species in G4. In order to construct a SLN, we must specify exactly which species in G1 and G2 are preyed upon by each species in G4. Let the presence of a metanetwork link be indicated by elements of the adjacency matrix, being one if a link exists, and zero otherwise. Then the maximum number of prey species (maximum in-degree) available to any species in G4, denoted is

since and equal zero. This can be generalized to a metanetwork of any complexity as

Since every species in G4 may have an in-degree range of one to , and every one of these possibilities or predatory states could be combined with every other state of the remaining species in G4, the maximum number of possible networks is simply . Moreover, the in-degree or number of predatory states of every species in the network may be combined regardless of guild membership, allowing us to generalize to metanetworks of all sizes and complexity. By this argument, the number of possible SLNs, |S|, is the product of the number of predatory states of species in every guild, that is,

This formula overestimates |S| because prey species in a guild are treated neutrally from a consumer’s point of view. Neutral is used here in the sense of ecological neutrality; the species are indistinguishable from each other on the basis of trophic properties. In other words, the above calculation of |S| does not specify which prey species are linked to when the predatory states of different predators are combined. Therefore, many of the combinations counted in the calculation will be isomorphic food webs, and they would not have unique ecological properties.

In order to resolve this problem, and gain a more accurate measure of |S|, we need to understand the number of different ways in which a consumer’s links can be distributed among it’s prey. This is a classic partitioning problem, where say we wish to determine the number of ways in which n fossils can be distributed among m museum drawers, with fossils in the first drawer, in the second, and so on. The fossils (links) are not distinct, and we do not care specifically to which drawer (prey species and guild) they are assigned. The trick is to first state the problem as: How many combinations of n fossils can I get if I have m drawers to select from? Or, how many combinations of r links can I get if there are g guilds to select from? We recognize that we are in fact permuting n fossils plus m-1 partitions among the drawers, yielding

Therefore in our sample food web, if a species in G4 has three in-links, then the problem is

The links can be partitioned between guilds G1 and G2 as {3,0}, {2,1}, {1,2} or {0,3}. None of these are isomorphic topologies.

The calculation of |S| can now be refined, where the topologies obtained for a particular in-degree are combined with those of other species, rather than simply combining the number of in-degrees possible. We proceed in several steps. First, determine the maximum number of in-links possible for a species in guild . Next, determine the number of in-link topologies possible for each in-degree (1 to ), given the set of prey guilds,

where is the number of topologies possible for species , which is a member of guild , is the in-degree of , and is the number of guilds upon which preys (sum of the row of the adjacency matrix). Note that this is calculated and summed over all possible in-degree values, one to . Following from the earlier calculation of |S|, the number of topological combinations among species in is . We therefore re-calculate |S| as

This calculation is still an overestimate, however, because the number of links between a consumer species and any prey guild is unconstrained. It represents all elements in the power set of S. In terms of the museum fossils analogy, we have assumed that the cabinet drawers are of infinite capacity (sadly, a curatorial fantasy). A more accurate measure of |S| is possible if we limit drawer capacity to some finite number of fossils, thereby limiting ourselves to the set F of real possibilities. The food web situation is more complicated because different prey guilds will most likely have different species-richnesses, and hence differing capacities for links. The situations would be analogous if drawers in the collection were of different sizes, indeed a curatorial nightmare! The solution would be to modify the above formula for , using only topologies where the number of links from a prey guild to is less than or equal to the species-richness of the prey guild. That is, the capacity of the prey guild is not exhausted. This solution, however, requires partitioning appropriately among the prey guilds so that this condition is met. The set of all such partitions that match the constraints of prey guild species-richnesses can be determined, but the solution is not straightforward and requires application of a partition function and partition theory. Both those topics are, unfortunately, beyond the scope of the current post. Therefore, the given calculation of |S| remains an overestimate at this point. It is possible, however, to determine the probability of any particular SLN being found in a metanetwork’s ensemble. I’ll follow this up in the next post.

Taxon aggregation

Tags

food webs, metanetwork, paleo-food web, paleontology, trohpic species, trophic guild

Metanetwork of a Late Permian terrestrial community from the Karoo Basin, South Africa

A key assertion of the CEG model is that a paleocommunity’s trophic network can never be specified by a single topology (Roopnarine, 2006; Roopnarine, 2009). There is uncertainty associated with the biotic interactions of a fossil species because no one was there to observe them. Preserved evidence of interactions such as bite marks, gut contents or leaf damage record a subset of the possible range of interactions. Moreover, the topology specified for a single community is expected to vary spatially and temporally. The strength and direction of interspecific interactions of extant species are known to vary according to physical conditions, the presence or absence of other species in the community, relative population sizes, and the incumbency of species when addition to the community is asynchronous. These uncertainties must be incorporated into any realistically complex model of a community food web. In the CEG model, species are therefore grouped into trophic guilds based on the most accurate trophic interpretations available, into trophic guilds. Trophic guilds are defined as the trophic habits and habitats of member species, for example, the “very small carnivorous amniotes” of a Late Permian terrestrial community.

The resulting guild structure represents a species aggregation scheme. The most common aggregation scheme is to assemble species into groups called “trophic species”. Trophic species group species that are assumed to have the same prey and predators. The motivation for this grouping is unclear in cases where link data are available at the species level. One advantage, however, may be to avoid biases introduced by an undersampling of poorly resolved links. Patterns of connection among trophic species may also illuminate patterns of energy and nutrient flow among major species ecotypes in the community. There is no guarantee, though, and in fact no expectation for the preservation of network topology in the conversion of species-level data to a trophic species network. It is always preferable to use species-level data to represent true community complexity. Furthermore, aggregation into trophic species is an inference the strength of which cannot be justified for fossil taxa, and the scheme should be avoided in paleo-food webs. Given that species-level data are rarely available for fossil species, however, and are basically never complete, aggregation is necessary. Dunne et al. (2008) therefore converted species-level data to trophic species in their study of Cambrian food webs. The CEG model aggregates species into trophic guilds, groups of species that cannot be distinguished trophically on the basis of available data. An example would be “epifaunal, seagrass-dwelling suspension feeding bivalves”. Those species, in a particular community, potentially share the same predators and prey. Trophic guilds are similar but not equivalent to trophic species, yet it is clear that if a trophic species is an accurate representation of the species which it comprises, then the composition of a similar trophic guild will approach the composition of the trophic species as the species data become more precise. A network of trophic guilds is termed a metanetwork, and is an hierarchically higher level representation of a species-level network. Two trophic guilds linked in a metanetwork contain species that are potentially trophic interactors. A metanetwork therefore summarizes the most accurate and precise data available for a paleocommunity’s food web.

The contrast between the two aggregation schemes is reduced to one of accuracy and precision. The trophic species scheme assumes a high level of precision, thereby justifying an assumption of trophic neutrality among species within the trophic species. This level of precision is unlikely to be available for fossil taxa, and in any case can never be tested. The metanetwork and trophic guild scheme assumes that the understanding of a species trophic habit is accurate, even though its precise interspecific interactions may be unknown or known incompletely. These uncertainties, stemming from incomplete data and temporal-spatial variance of the data, will be addressed in a future post by exploring the range of species-level food webs implied by the metanetwork.