I am Distinguished Research Professor of Mathematical Biology, UCSC, Adjunct Professor in the Theoretical Ecology Group at the University of Bergen, Norway (Visit the TEG) and Affiliate Research Professor at the University of Washington, Tacoma. In my first job out of graduate school, I worked for the Operations Evaluation Group (OEG) of the Center for Naval Analyses doing operations research for the Navy. I moved to UC Davis in 1980 with the intention of doing OEG-style work, but with applications to fisheries and agriculture, and to UC Santa Cruz in 1996. I formally retired from UCSC in 2013 as Distinguished Professor, returning one month later to active service to conduct research (hence the title Distinguished Research Professor). I am broadly interested in using mathematical methods to solve problems that arise in biology (especially ecology, evolution, and behavior) and work in what Donald Stokes called Pasteur's Quadrant of use-inspired basic research, where a search for fundamental understanding is motivated by an important applied problem. Stokes's book Pasteur's Quadrant. Basic Science and Technological Innovation (Brookings Institution Press 1997) is well worth reading.

Current Research Projects

Combining Dynamic Energy Budget and State Dependent Life History Models: Supported by the office of Naval Research and in collaboration with Andre de Roos and Benjamin Martin (both at the University of Amsterdam) I an workng to find ways to unify Dynamic Energy Budget (DEB) models and Stochastic Dynamic Programming (SDP) models in order to predict the consquences of disturbance on marine mammals. We have decided to use a demand-style DEB model, as described by Andre in Chapter 12 of his wonderful book Population and Community Ecology of Ontogenetic Develop (A.M. de Roos and L Perrson. Princeton University Press, 2013). More detailed descriptions of the DEB approach can be found in these publications:

Detailed demand DEB model (unpublished)

Ungulate example (de Roos et al 2009)

And our publications:

2020 Pirotta, E., Hin, V., Mangel,M., New,L., Costa,D.P., de Roos, A.M. and J. Harwood. Propensity for risk in reproductive strategy affects susceptibility to anthropogenic disturbance. The American Naturalist, 196: doi: 10.1086/710150

Population Biology and Cybersecurity : Since July 2018, I have been working with colleagues at the Johns Hopkins University Applied Physics Laboratory with the intention of using models from population biology to inform various aspects of cyber-security. At this point, there are three sub-projects: i) using classical disease models (SIR, SIRS) to illuminate attack and defense of cyber networks, with application to the electric grid; ii) using metapopulation models to understand cyber system volatility; and iii) bringing notions of complex adaptive systems to the evolution of cyber law. In the last few months, I have also been helping colleagues at APL think about testing for covid-19, both at APL and in Howard County, MD (where APL is located) more generally. No publications yet.

The Role of Mesopelagic Fishes in Northeast Atlantic Marine Ecosystems . I am part of a project at the University of Bergen with Christian Jorgensen, Tom Langbehn, and Gabriella Ljungstrom on mesopelagic species in the Norwegian Sea. We have three objectives: i) to investigate the role of predation from mesopelagic fishes in driving latitudinal life history variation among calanoid copepods; ii) to identify the drivers of the unique migratory life history of Norwegian spring-spawning herring, with particular focus on a vacant niche directly and indirectly shaped by mesopelagic fishes; and iii) to predict changes in the Norwegian Sea ecosystem as a response to climate warming, with emphasis on the changed distribution of mesopelagic fishes. Here's a kind of precursor paper to this project:

2018 Ljungstrom, G., Francis, T.B., Mangel, M., and C. Jorgensen. Parent-offspring conflict over reproductive timing: ecological dynamics far away and at other times may explain spawning variability in Pacific herring. ICES Journal of Marine Science doi:10.1093/icesjms/fsy106

Mathematical Modelling of Biological Control Interaction to Support Agriculture and Conservation I am part of a research group) organized by Tamar Keasar, Michal Segoli, and Eric Wajnberg and supported by the Israel Institute of Advanced Studies.

Global crop losses due to arthropods amount to 18-26% of the annual production. Efficient and sustainable pest control strategies are needed to reduce these losses. Many tools for controlling insect pests are available. Among them, biological control by insect natural enemies (predators and parasitoids) has recently gained renewed interest because of environmental concerns and problems encountered with the use of pesticides. Biological control has a long history of use in pest management and has been outstandingly successful in many instances. Nevertheless, such successes remain limited in number and failures are often under-reported. Moreover, biological control programs are still widely practiced as trial-and-error enterprises, rather than being guided by theory-driven principles.

The deficiency in theory-based biological control practices is not only due to insufficient basic information. A wealth of knowledge exists on the behavioral mechanisms employed by insect natural enemies to find and exploit their hosts/prey, as well as on their population dynamics and evolutionary adaptations to their environments. Moreover, a variety of modeling approaches are available to describe these processes and to predict their long-term population-level effects. These include tools such as static and dynamic optimization, game theory, stochastic dynamic modeling, matrix models and genetic algorithms. However, theoretical and empirical knowledge are often being advanced independently, limiting the interplay between the two fields and hence the connection between theory and practice.

Our study group spans the continuum between theoretical approaches (behavioral, population and community ecology) and application (biological control) will meet formally in Jerusalem in the first half of 2022, but we are already working together remotely. Our main aim will be to bridge the existing gaps between the well-developed theory of interactions between insects and their natural enemies, and the optimization of the efficacy of biological control projects in agriculture and conservation.

I am particularly thrilled to be involved with this group of scientists that includes two of my students (George Heimpel and Asaf Sadeh), one of my post-docs (Tamar Keasar), and my long-time (since 1985!) collaborator Bernie Roitberg.

Recently Completed Projects

Population Consequences of Disturbance : Starting in 2016, I worked with Liz McHuron, Leslie New, Enrico Pirotta, and Lisa Schwartz to develop state dependent life history models of how anthropgenic disturbance of foraging habitats will affect marine mammals. We have thus far developed a general framework, and applied it to California sea lions, blue whales, and the western population of gray whales. Publications from thus far:

2016 Schwarz, L.K., McHuron, E., Mangel, M., Wells, R.S., and D.P. Costa Stochastic dynamic programming: An approach for modelling the population consequences of disturbance due to lost foraging opportunities. Fourth International Conference on the Effects of Noise on Aquatic Life Dublin, Ireland 10-16 July 2016. DOI: 10.1121/2.0000276

2017 McHuron, E.A., Costa, D.P., Schwarz, L., and M. Mangel. State-dependent behavioural theory for assessing the fitness consequences of anthropogenic disturbance on capital and income breeders. Methods in Ecology and Evolution doi: 10.1111/2041-210X.12701

2017 McHuron, E.A., Mangel, M., Schwarz, L.K., and D.P. Costa.Energy and prey requirements of California sea lions under variable environmental conditions. Marine Ecology Progress Series 567:235-247

2018 Pirotta, E., Mangel, M., Costa, D.P., Mate, B., Goldbogen, J.A., Palacios, D.M., Huckstadt, L.A., McHuron, E.A., Schwarz, L., and L. New. A dynamic state model of migratory behavior and physiology to assess the consequences of environmental variation and anthropogenic disturbance on marine vertebrates. American Naturalist 191: DOI: 10.1086/695135

2018 McHuron, E.A., Schwarz, L.K., Costa, D.P., and M. Mangel. A state-dependent model for assessing the population consequences of disturbance on income-breeding mammals. Ecological Modeling 385:133-144

2019 Pirotta, E., Mangel, M., Costa, D.P., Goldbogen, J., Harwood, J., Hin, V., Irvine, L.M, Mate, B.R., McHuron, E.A., Palacios, D.M., Schwarz, L., and L. New. Anthropogenic disturbance in a changing environment: modelling lifetime reproductive success to predict the consequences of multiple stressors on a migratory population Okios 00:1-18, doi: 10.1111/oik.06146

I also worked with colleagues at the University of Alberta on climate change and polar bears:

2019 Reimer, J.R., Mangel, M., Derocher, A.E., and M. A. Lewis. Modeling optimal responses and fitness consequences in a changing Arctic. Global Change Biology DOI: 10.1111/gcb.14681

Ecotherms in changing environments Supported by an OPUS (Opportunities for Understanding through Synthesis) grant from the Division of Environmental Biology at NSF (2015-18), I wrote a book synthesizing my work over the last 35+ years on salmonids, southern ocean krill, and insect parasitoids and tephritid fruit flies. My goal was to show how state dependent behavioral and life history theory, as implemented by stochastic dynamic programming intercollates with other methods (e.g. population dynamics or quantitative genetics models) used for studying organismal response to changing environments.

After receiving critical but very helpful comments from reviewers at Princeton University Press, I realized that the book had missed the mark. In retrospect, my goals were too ambitious -- I wanted to show how many of the different methods used to study response to environmental change inter-collate with state dependent life history. Since most readers would not be expert in most of the methods, I used simple models for purposes of illustration but now realize that doing so would leave most readers unsatisfied. But I simply did not have space or time to get into really detailed models of particular problems (unlike my other books).

I was knew this was the right decision when I read in Mark Nepo's wonderful book Seven Thousand Ways to Listen the following (on page 15 of the chapter called Beyond Our Awareness in the Kobo e-reader version): For me, it was listening to a fundamental uneasiness about being misunderstood that led me to pull a book from publication. I've worked with countless editors through the years and the tiger in my mind was roaring What are you doing?! Make it work!!...I couldn't know that listening to that uneasiness and following it would awaken the next phase of my authenticity.

The book had ten chapters, most of which can be converted to stand alone manuscripts, my current goal is to publish most of them and I will post them here as they are ready. (I am happy to share a copy of the submitted manuscript with anyone who asks, but you need to write to me.)

But to begin, there are two that will not work as stand alone journal articles and one that can be just as effective as an unpublished document, so I am leaving them permanently:

Homage to My Mentors

Potential Case Studies Using State Dependent Life History Theory

Informing population models with evolutionary theory to infer species' conservation status (NSF-NERC grant (2016-2019) with Holly Kindsvater (Rutgers), Jason Matthiopoulos (Glasgow), and Nick Dulvy (Simon Fraser)). We used a combination of evolutionary theory and Bayesian population modeling to make inferences about the status of data-poor stocks (we started with scombrids, sharks, rays, and groupers). My role was to use state dependent life history theory to produce scientifically based priors for use in the Bayesian analysis; I did this by solving the inverse problem -- observing life history traits and inferring the environment from them. Another overall goal of the project was to unify size spectra theory and Stochastic Dynamic Programming models for life histories. The first few papers:

2017 Mangel, M. The inverse life-history problem, size-dependent mortality and two extensions of results of Holt and Beverton. Fish and Fisheries. DOI: 10.1111/faf.12247

2018 Kindsvater, H.K., Dulvy, N., Horswill, C., Juan-Jorda, M-J, Mangel, M., and J. Matthiopoulos. Overcoming the data crisis in biodiversity conservation. Trends in Ecology and Evolution.

2019 Horswill, C., Kinsvater, H.K., Juan-Jorda M.J., Dulvy, N.K., Mangel, M. and J. Matthiopoulos. Global reconstruction of life-history strategies: A case study using tunas. Journal of Applied Ecology 56:855-865 DOI: 10.1111/1365-2664.13327

My Approach to Mathematical Biology I use models (differential equations, stochastic dynamic programming and Bayesian statistical methods), experiments (either here in Santa Cruz or in collaboration with colleagues elsewhere) and field observations. I apply these ideas to a variety of systems, currently including southern ocean krill, steelhead trout, Pacific rockfish, planaria). Although I worked for many years on insect parasitoids and tephritid fruit flies, I am not doing much with them just now except writing up a big field project that Bernie Roitberg and I did in the 1990s.