A perturbation approach to explore stock recruitment relationships

Screen Shot 2014-08-24 at 7.26.52 PMWe recently published a paper in ‘Theoretical Ecology’ where we use Generalized Modeling to explore stock recruitment relationships in fisheries. Models of stock recruitment are fundamental to fish population dynamics, describing how reproduction (in terms of the biomass of new recruits) changes as a function of the density of the current stock. In many resource-limited populations, recruitment increases for lower levels of stock biomass until it levels off at higher levels of stock biomass (described by the Beverton-Holt functional response). In others, particularly when there is cannibalism or nest predation, recruitment increases, reaches a peak, and then decreases for higher levels of stock biomass (described by the Ricker functional response). In open populations, where resources are not necessarily limiting, recruitment may continue to increase with stock biomass (the Cushing functional response).

Being able to distinguish between stock recruitment relationships (SRRs) is vital for predicting the long-term dynamics of a fish population. Traditionally, SRRs are distinguished using statistical methods of best fit. In this manuscript, we present an alternative method of distinguishing between SRRs based on the response of a population to an external disturbance. The timing and degree of a population’s reaction can be used to distinguish between SRRs and is strongly resilient to observational error. The method relies on ‘generalizing’ the functional response, where we do not assume to know the specific architecture of the SRR. This approach relies on ‘Generalized Modeling’, which we review here, and is based on techniques developed by Thilo Gross et al., illustrated with respect to some really neat examples here. We extend some of these ideas by introducing generalized modeling techniques with respect to discrete-time rather than continuous time systems.

We hope that this method illustrates a different way of looking at an old problem, and think that it has particular relevance to relatively new fisheries where long-term time-series data do not exist. It offers a way to explore different aspects of fish reproduction, while remaining in a modeling framework rooted in biological mechanisms. I think the most interesting parts of these ideas are illustrated with respect to age-structured models, where the dynamics become complex.

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New paper in J. Animal Ecology on population stability and Steelhead

Populations of animals can be quite complex… they can be composed of many different age classes with individuals seeking out different strategies with the common goal of maximizing reproductive fitness over a variable environment. An excellent example of an organism with such complex age-structured populations are Steelhead salmon.

In this paper that I co-authored with my post-doc advisor Jon Moore as well as Doug Peard, Jeff Lough and Mark Beere, we took advantage of an incredible dataset of life history information compiled from growth information in fish scales for two Steelhead populations in British Columbia watersheds. These scales tell us whether an individual fish was living in fresh vs. ocean water while the scale was growing, and permit reconstruction of individual life-histories. In other words, the scale data gives us an idea of the sequence of freshwater to ocean vs. ocean to freshwater transitions, and how many times individual Steelhead returned to their natal freshwater rivers to spawn.

We found that the complex and variable life histories exhibited by Steelhead salmon can protect their populations from environmental variability. In fact, populations that have a large percentage of individuals coming back to their natal streams to spawn multiple times lowers the Coefficient of Variation of their population sizes over time (the Standard Deviation of the population trajectory divided by the mean), thus stabilizing population fluctuations. This has important conservation implications because fish hatcheries, the building of dams, and other human-induced disturbances within river systems tend to ‘homogenize’  the life histories of fish populations, thus eroding the stabilizing influence of life-history diversity.

So the moral of the story is: it’s good to be different.

Check out the full paper here:

Moore JW, Yeakel JD, Peard D, Lough J, Beere M. Life-history diversity and its importance to population stability and persistence of a migratory fish: steelhead in two large North American watersheds. Journal of Animal Ecology. DOI: 10.1111/1365-2656.12212 [link]

New paper in Ecology Letters on the synchronization of river metapopulation networks

graphs075The immigration and emigration of individuals to and from populations within a metapopulation allows abundant populations to rescue those nearing extinction. This is an important trait of metapopulation dynamics, however this ‘rescue effect’ is destroyed if the populations are synchronized: if all populations are at low abundance at the same time, they cannot rescue each other. Moreover, the structure of interactions within a metapopulation (which controls how individuals can flow from one population to another) has a large impact on the dynamics of the whole system. The structure of a metapopulation may be influenced by any feature on the landscape that influences how an animal moves, including geological features such as mountains, the occurrence of water sources, or the distribution of forests, grasslands, or deserts. In aquatic populations that inhabit rivers, the geological constraints of watersheds dictate which populations interact.

In a paper that we just published in Ecology Letters [1], we explore how the specialized structure of river networks impacts both the sizes of fluctuations within populations, as well as the extent to which river populations can become synchronized as the result of river network structure. We show that river networks confer dual stability by both decreasing the fluctuations of riverine metapopulations, and providing a natural buffering against synchronization. We also show that altering river structure – for example by linking otherwise separated river branches with canals – has a large effect on dynamics, increasing the potential that populations can become synchronized. We finish by discussing the idea that the size of the organism (and by extension its mobility) changes the structure of the metapopulation that is distributed within a given watershed. This has a large impact on synchronization, and poses some exciting unanswered questions in metapopulation theory. Check out the paper on the website here.

Appendices: The Appendices were not posted on the official website. Until that is resolved, please find them here.

[1] Yeakel, J. D., Moore, J. W., Guimarães, P. R., Jr, & de Aguiar, M. A. M. (2013). Synchronisation and stability in river metapopulation networks. Ecology Letters. doi:10.1111/ele.12228 Link

New paper in Evolution on hominin foraging behaviors

Fig_EnamelVol

Many hominin species are distinguished by their large teeth. Notably, the genus Paranthropus had enormous bunodont molars covered in thick enamel. The evolution of the suite of traits collectively referred to as ‘megadontia’ was doubtless in response to the foods that these animals were consuming. We have just published a paper in the journal Evolution [1, link] where we explore how such traits may have influenced the foraging behaviors of human ancestors using a process-based state-dependent foraging model. The primary assumption in our model is that foraging decisions depend on both the energetic state of the organism (is the organism hungry or not), as well as its enamel volume (what is the state of the organism’s teeth). The attached figure shows a cartoon depiction of the enamel layer on a hominin molar tooth, as well as the simple method we use to approximate enamel volume (which, in terms of total volume across all molar teeth is quite an accurate approximation!).  As we consume foods over our lives, our enamel slowly erodes away. Generally this enamel loss is unnoticeable, and sometimes it is disastrous (for example, if you chip or lose a tooth). If you are a hunter or gatherer living in the wild, such enamel loss will have an impact on what foods you can eat – particularly if the foods that are being sought after have different mechanical properties with different demands on enamel.

Interestingly, there has long been a ‘disquieting discrepancy’ between the morphology of hominin species and their molar microwear [2]. The patterns of scratches and pits on the surfaces of molar teeth can be used to reconstruct the types of foods the animal consumed prior to its death. Many hominins have a microwear fabric that suggest softer, pliable foods. However, their robust morphology suggests a diet based on harder foods, particularly for hominins with megadont traits. Moreover, analysis of stable isotope ratios among hominin species indicates a diet that is based on the consumption of C-4 photosynthetic foods [3]. These foods include tropical grasses and sedges, and tend to be more fracture-resistent, or ‘hard’.

We use our modeling framework to investigate these seemingly disparate conclusions. We find that the predicted fitness-maximizing foraging behaviors bring consilience to morphological, isotopic, and microwear-based lines of evidence. We also show that our model correctly predicts the observed range of isotopic values for hominin species such as Paranthropus robustus. Of course, it is just a model, and to quote a reviewer ‘hominins cannot eat theory’. We heartily agree, but suggest that such process-based models are well-suited for exploring the important physical and behavioral constraints that are expected to impact the actual foraging behaviors of organisms in the wild. We also explore how body size is expected to interact with energetic reserves and tooth wear, how this has an impact on when foods become preferred vs. fallback resources (eaten only in times of stress), and to what extent very tough but common foods such as tropical grasses are likely to be major components of diet. Despite much emphasis on grass leaves as likely hominin foods in recent literature [4,5], our model predictions suggest that grass leaves are unlikely to maximize fitness except in extreme circumstances.

Literature cited

1. Yeakel, J. D., Dominy, N. J., Koch, P. L., & Mangel, M. (2013). Functional morphology, stable isotopes, and human evolution: a model of consilience. Evolution. doi:10.1111/evo.12240      [link]

2. Ungar, P. S., Grine, F. E., & Teaford, M. F. (2008). Dental microwear and diet of the Plio-Pleistocene hominin Paranthropus boisei. PLoS ONE, 3(4), e2044.

3. Ungar, P. S., & Sponheimer, M. (2011). The diets of early hominins. Science, 334(6053), 190–193. doi:10.1126/science.1207701

4. Lee-Thorp, J. (2011). The demise of “Nutcracker Man”. Proceedings of the National Academy of Sciences of the USA, 108(23), 9319–9320. doi:10.1073/pnas.1105808108

5. Rabenold, D., & Pearson, O. M. (2011). Abrasive, silica phytoliths and the evolution of thick molar enamel in primates, with implications for the diet of Paranthropus boisei. PLoS ONE, 6(12), e28379. doi:10.1371/journal.pone.0028379.t002

Science… Sort Of, and why the Beverton-Holt cannot be observed in nature

A few exciting bits of news this June:

First, we put a draft of a new paper in ArXive: “Compensatory dynamics, functional elasticities, and why the Beverton-Holt Stock Recruitment Relationship cannot exist in nature”. Check it out: [PDF]. Some friends argue the title of this paper is a bit provocative… but it did convince them to read it, so….

Second, I was invited back to the podcast I helped cofound [Science… Sort Of] and from which I was eventually kicked out after a tumultuous board meeting (for my stock options), to chat about networks, which you can hear [here].

Third, I have started to BBQ a lot, and that is exciting. Chicken rub recipe to follow.

Dietary flexibility, food webs, and the Last Glacial Maximum

mammoth-tusks-375

We just had a paper published in the Proceedings of the Royal Society B: Biological Sciences. [link]

The paper is on the structure of food webs before, during, and after the Last Glacial Maximum – a global scale climatic event that impacted mammalian communities across the world. We look at spatial and temporal variation in diet on both species-specific and community-level scales. We show that dietary flexibility distinguished bears and wolves, while large cats had relatively inflexible diets over space. We also show that trophic interactions among species in the mammoth steppe (ranging from Europe to the Yukon) were structured differently in western Europe than Alaska, however these structures were relatively unchanged across the Last Glacial Maximum.  Check out the press release [link]

Photo Caption: Mammoth tusks are still found in the arctic landscape, remnants of the mammoth steppe ecosystem that supported a diverse assemblage of large-bodied mammals. (Photo by Daniel Fisher, Museum of Paleontology and Department of Earth and Environmental Sciences, University of Michigan)

Recent Papers, November 2012

We just had a paper published recently in the Journal of the Royal Society Interface on the weighted structure of mammalian food webs using ratios of stable isotopes: Link

Also, we placed two recent papers in ArXiv (soon to be submitted for publication):

1) The impact of climate change on Pleistocene food webs: Link

2) Stable isotopes, functional morphology, and human evolution: a model of consilience: Link