On Leslie matrices and ceviche

In the introductory ecology class I TA'd for last spring, the Leslie matrix is the bane of many students' lives. Many students come in expecting more saving the earth and/or charismatic megafauna and less mathematical models. About a month into the class, they are introduced to this:
which can be understood a little better by this, where each circle is one size class (1 is the smallest, 4 the biggest). P1, P2 and P3 are the probabilities of advancing (growing up) into the next class over a set time period and F1, F2, F3 and F4 are the probabilities of reproducing (making more little class 1's) for each respective size class. The number of individuals in each class after the time period is dependent on the number of individuals before the time period and all these probabilities - that relationship is described by the matrix equation.


So what does this look like in real life?

Let's say you have a snail about the size of your palm that is known to be a key predator of barnacles - this is important because barnacles act an 'entry point' of energy from the open-ocean (pelagic) to the ecological community that lives on/around the rocks and ledges (benthic). Barnacles eat plankton from the water column and use that energy to grow, making that energy available to predators like Hexaplex snails, which in turn get eaten by fish, etc. So there is a transfer of energy from the pelagic plankton to animals like fish which wouldn't happen without barnacles and their predators.

Hexaplex feeding on Megabalanus barnacles at about 8m depth.

At some sites in the Galapagos archipelago, Hexaplex is also fished to make the local dish ceviche. Presumably, the bigger snails are fished (this can be confirmed using fishing records and/or data from shell piles). How does that affect the way the population changes (grows/shrinks) at different sites? And from a bigger-picture view, how could fishing impact the flow of energy into subtidal Galapagos communities? If you can estimate the parameters of the model accurately enough, you can use the model to answer these questions. You could also model changes in the intensity of fishing to predict how the population would respond - information that can be useful if you'd like to set fishing limits or decide which population(s) are more worth protecting.

Leslie (who is very appropriately named for this research project) has been setting up to estimate class-specific Hexaplex growth rates (the P's) by measuring, tagging and releasing them at our study site. When we get back in January, we'll be looking out for these tagged snails and re-measuring them to track their growth.

Photographic record of size and shell morphology.

Newly freed Hexaplex at Isla Baltra. The bright green rock is the release point.

January is also supposed to be the reproductive season for Hexaplex, so we'll also be looking out for egg masses and laying Hexaplex in order to estimate reproductive outputs (the F's).

Hexaplex egg mass from last January, photo by JW.

Somewhat encouragingly, we recovered one of the Hexaplex that we did some preliminary tagging on in mid-June with 8-year old Z-spar epoxy. I think we only tagged 8 or 9 individuals then, so a return of one is pretty good news. We'll see what happens when we return to Baltra in 6 months.

Happy Leslie with the recaptured Hexaplex.

Sharing space

Working on a sheer subtidal wall can be interesting, especially when the wall has exactly two (2) ledges that you can put cameras and research equipment on, and exactly one (1) of them is occupied by a sleepy sea turtle that doesn't want to move.

I have seen and swum with many turtles before, but this is the first time I have ever looked one straight in the (sleepy blue) eye. It is a little bit surreal to be stared at by a turtle.

I see you too.

We wrapped up our last Galapagos dive yesterday, making a total of 48 for this trip. The next week and a half will be some data analysis and a side trip to the western island of Isabela for Leslie and me, then it's back to Nahant and more algae work. The summer goes by quickly.

Something missing

My brain works in funny ways. Yesterday, out of the blue, it occurred to me that I haven't seen or heard a kingfisher in a really long time, and I started missing them. When I lived next to the Sungei Serangoon in Singapore, I used to be able to sit at my window with a pair of binoculars and watch several different species of kingfisher in action (along with herons, egrets, white-bellied sea eagle and Brahminy kite).

The very common white-throated kingfisher. Picture by Manjith Kainikara, used under a CC license.

Kingfishers are found almost globally but are very species-poor in the New World. I definitely haven't come across the single (?) species from North America. Even South America with its insanely diverse birdlife only has 5 or 6 species, and unlike the finches, none of them ever made it out to the land of the tortoises.

The Galapagos islands are full of amazing birdlife, and the seabirds are particularly spectacular. But when little things like this nag at me, I remember that my home is where there are kingfishers and bird's nest ferns*.


*I spent a good part of my first year in New England missing heavily epiphytised trees, particularly the ones with big bird's nest ferns between the branches (e.g. this one)

Cages and friends

Over the past few days, we have been working hard to get everything ready for our big trip up to Isla Baltra, where we'll be working on multiple big experiments. I am going to be setting up my Pentaceraster cages this week, so I've been pulling together all the necessary materials and tools, and compacting them for transport.

Rolled-up cage sides and a stack of cage tops in the corner.

Someone has been busy in the week since I last worked on the caging material.

Rebar as cage anchors. I bought 6m of it at the construction store for $3.50 and asked them to cut it into 30cm pieces. They must have been very confused - I don't think they have ever cut rebar this small.

At the same time, we'll be setting up concrete bases for a large-scale sea urchin predation experiment that the lab will be running for the next couple of years. The bases will be put in the water this trip to accumulate a mat of turf algae for the urchins to graze on when the experiment actually gets going next summer. We moved them from the hardware/construction store to the loading dock yesterday. I'm excited to start putting them down using lift bags.

Jon on the station dock with his concrete bases.

The marine iguanas really liked them too.

We leave for Baltra tomorrow morning, so we loaded all our equipment into the boat today - there is a lot of it. We piled up all our stuff into a water taxi and it took two trips to get all of it on board our boat, the Pirata (probably the most adorable boat I have ever seen, complete with little pirate flag).

A very full water taxi at the loading dock. You can see: about half my cages, concrete bases, green oxygen box, GoPro camera stands, plenty of rope, quadrat, containers for Hexaplex snails. All our dive gear is in there as well, under the cages and rope.

Loading the concrete bases onto the boat. We were getting stared at by everyone in the passing boats and water taxis.

Will be hard at work for the next few days. There will eventually be photos.

Terrestrial invasion

Last week we put aside our stinky wetsuits and scuba gear to explore terrestrial Galapagos for a few days. We went out into the highlands of Santa Cruz with Heinke, a postdoc at Brown, and her two Ecuadorian field assistants. Heinke studies the impacts of an tree species (Cinchona pubescens, the quinine tree) that was introduced to Galapagos from mainland Ecuador, and has been doing research here for many years.

Introduced/invasive species are a particularly big concern in island ecosystems like the Galapagos. In the Galapagos National Park, there have been huge efforts to control the spread of invasive species and protect native Galapagos species. The results of these control efforts can be clearly seen where the national park borders private/agricultural land.

National park land on the left, agricultural land on the right. The plot on the left is full of the native Galapagos miconia plant, while you can see plenty of non-native elephant grass on the right.

Miconia robinsoniana, an endemic shrub that grows at high elevations. The 'miconia zone' at ~600m is named for it.

We had a beautiful, mostly clear day at Media Luna, which is unusual - the highlands have been rainy even when the coastal areas are clear and sunny. But when they are not shrouded in clouds, the view from the highlands is incredible - 180º of ocean - and you can see all the way to Puerto Ayora!

A clear view all the way to the ocean, with Puerto Ayora and Tortuga Bay in the south.

The Cinchona trees are very conspicuous against the native shrubs of the highland 'miconia zone' - they tower over everything else. Equally conspicuous is the park management's aggressive attempts to control it - around the Media Luna crater itself, they have cut most of the Cinchonas and locally applied chemical herbicides, leaving behind bare trunks.

Cinchona trunks as far as the eye can see.

One of the big questions that people tend to ask when looking at an invasive species is: what effects does it have on the ecological community? It is a question I have been asking as well, with respect to my own algal invader. Because Cinchona is a tree in a community that previously had no trees, it has the potential to shade out other plants and limit the light available to them for photosynthesis. Heinke's experimental set-up aims to figure out exactly what the effects of Cinchona shading are, using artificial shades to control the amount of light available to the native shrubs. It will be cool to see how this affects the species diversity and composition of the plant community.

Two different shade treatments: total shade in the centre and partial shade on the left. On the right you can see a Cinchona forest that hasn't been managed by the national park - a really different-looking plant community compared to the short, shrubby one in the foreground.

For the past year, I've thought of invasive species mostly in terms of the marine algal species I study. It was interesting to look at it in a terrestrial system, particularly an island one. It gives me a slightly broader perspective on things before I return to the invasion happening in the shallow subtidal zone of New England.

Cross-system exchange?

Intertidal finches eating intertidal algae. I am intrigued.

Grazing finch.

This one has Ulva ("sea lettuce") in its beak.

The quiet beauty of mangroves

Tortuga Bay is a beautiful site about an hour's walk from town - it has a long stretch of shore that surfers go to (="the surfers beach") and a protected bay with calm water (="the swimmers beach"), as well as plenty of rocky intertidal zone, a small forest of Opuntia cactus-trees. It's a popular spot with both the tourists and locals (and with Leslie and me who do not fall into either group).

The first time we visited, it was low tide (which we planned for so we could do some intertidal exploration). But when I noticed that the swimmers' beach was surrounded by red mangroves, I was determined to come back and explore it by snorkel at high tide. So we did, and this series of photos is the result. I have gone snorkelling in mangroves before, though I have explored them above water many times back in Singapore. So this was a bit of an adventure.

Red mangroves in the foreground, Opuntias in the back. I love the Galapagos.

Above the water, the roots form a tangled network. The water is still enough to see them reflected on the surface.

Beneath the surface, the sounds of people from the beach fade away and you can almost hear the trees breathing. The visibility is poor in this soft sediment habitat but if you are still and patient (and keep your fins off the bottom!) it clears out enough to make out the somewhat eerie shapes of the submerged roots, and of the fishes hiding in this silent, flooded forest.

A tiny sergeant major emerges, dwarfed by the submerged mangrove roots.

A little bullseye pufferfish peers outward.

Mangroves are known as important 'nursery' habitat - a relatively benign place with calm water and fewer predators for juvenile fish to grow up (including commercially fished food species like snapper - see below). There is definitely a high abundance of little fish here. But there are also bigger shapes lurking in the shadows of the underwater forest. They fade in and out of the murky water and occasionally emerge from among the roots to say hello and to feed in the carbon-rich sediments of the surrounding water.

Dog snappers play hide and seek with me.

Two diamond rays lurk under the shadows of the overhanging mangrove roots. These guys dig about in the sediment and feed on invertebrates living there - check out a video of that here. In the foreground is another bullseye puffer and a young snapper.

Moving out further from the swimmers' beach, the water gets clearer and you can see just how busy the mangroves are.

A buzz of activity.

Further outside of town, El Garrapatero on the southeast side of Santa Cruz has its own mangrove thickets as well - some were growing through/on the basalt (!)

Lone tree on the rocks. There are Opuntias in the background as well.

Pneumatophore roots coming up through the muddy basalt rubble