## New website

We have a new website: chandlerlab.uga.edu. It’s still a work in progress, but eventually we’ll get it cleaned up, at which point we’ll shut down this old site. Thanks for keeping up with us, and please stay in touch.

## Hierarchical species distribution models and Maxent

John Drake kindly invited me to guest lecture in his graduate seminar on species distribution models earlier this week. I discussed the often overlooked fact that many popular species distribution models assume that observed locations represent a random sample from the population of interest, and I used a simple simulation exercise to demonstrate how violations of this assumption can yield extremely misleading results. The rest of the talk briefly covered various types of hierarchical models that can be used to relax the random sampling assumption while allowing for inference about spatial variation in density or occurrence probability.

## Slides from ESA 2015

Had a great time at the 100th ESA meeting in Baltimore last week. A big thanks to Dave Miller, Evan Grant, and Charles Yackulic for the invitation to present in their organized session on the use of dynamic models for predicting range shifts. I thought every presentation in the session was great, and if classes hadn’t started up already, I’d have a lot more to say about the topic and the meeting itself. But alas, I have to prepare for two lectures tomorrow! Here are my slides:

## Spatial capture-recapture workshop

Andy Royle, Jared Laufenberg, and I will be offering a workshop on spatial capture-recapture here at the University of Georgia. The workshop will take place March 9-12. Workshop details and registration information can be found here. Please contact me if you have any questions.

## Seminar at Auburn University

Conor MgGowan invited me to speak at Auburn yesterday. I had a great time meeting faculty and students, and was very impressed by the program and facilities. Conor, big thanks. Looking forward to having you over here next semester.

Here are the slides from my seminar.

(Unfortunately, the animation on slide 18 doesn’t seem to work when viewed through slideshare. Oh well.)

## PhD position announcement

Population dynamics of white-tailed deer in south Florida: implications for management of the endangered Florida panther

We are seeking a PhD candidate to participate in a study of white-tailed deer population dynamics within the range of the endangered Florida panther. Objectives of the research include determining the effects of changing hydrological conditions, predation pressure, and hunting regulations on deer populations, and developing a long-term deer monitoring program using non-invasive sampling methods such as camera traps. The monitoring program will be used to inform management actions aimed at maintaining the viability of both deer and panther populations.

Responsibilities will include intensive field work and statistical modeling. Field work will involve capture, collaring (GPS), and monitoring a large sample of white-tailed deer in Big Cypress National Preserve and the Florida Panther National Wildlife Refuge, as well as establishment of an extensive camera trapping array. Applicants must be prepared to work in remote, hot, and humid conditions where biting insects, venomous snakes, and large carnivores are common.

Applicants should have a solid foundation in population ecology, spatial ecology, mammalogy, and statistical modeling. Preference will be given to candidates with experience analyzing telemetry data and capture-recapture data. A positive attitude, strong work ethic, and the ability to work independently and as a team member are required.

The student will be jointly advised by Dr. Richard Chandler, Dr. Robert Warren, and Dr. Karl Miller at the University of Georgia’s Warnell School of Forestry and Natural Resources, and by Dr. Mike Conner at the Joseph W. Jones Ecological Research Center. The start date is January 2, 2015. Send statement of interest, CV, unofficial transcripts, GRE scores, and contact information for 3 references as a single PDF to Dr. Richard Chandler: rchandler@warnell.uga.edu. The application deadline is November 1, 2014.

## From mathematical models to statistical models

As is true in every branch of science, most ecological theories have been formalized as mathematical models. These models are often used to make predictions that are tested in the lab or sometimes in the field, and this is one way that the theoretical foundation of ecology develops.

As important as these mathematical models are, it seems to me that they are not routinely fitted to data and used for statistical inference, which is important in applied settings. In fact, I would guess that most theoretical models in ecology have never seen the light of day, in the sense that they have’t been fitted to data from field studies. This is a wild speculation and it may prove wrong, but the point of this post is to suggest that one of the most exciting trends in ecology these days is due to the emergence of statisticians that are providing the necessary tools to fit models from theoretical ecology to field data. As a result, applied ecologists like myself can make rigorous predictions about things like population viability under different environmental scenarios, without resorting to various forms of ad-hockery.1

I have already written about one example of the conversion of mathematical models to statistical models — the case of spatially explicit metapopulation models. Metapopulation models are great when populations occur in discrete patches, and the development of occupancy models has made it possible to fit these models to real data sets fraught with various forms of observation error. But what mathematical models are available when individuals are distributed continuously in space? One option came up in a great seminar that I attended yesterday by Tom Miller. He noted that, when time can be regarded as discrete, integrodifference equations are a powerful theoretical device, as has been demonstrated by mathematical ecologists such as Mark Kot. Integrodifference equations usually have the form:

$\displaystyle n_{t+1}(x) = \int_{\cal{S}} f(n_t(y))k(\|x-y\|) \mathrm{d}y$

where $n_t(x)$ denotes the number of individuals at location $x$ in some two-dimensional spatial region $\cal{S}$ during time $t$. The number of individuals in the next time step is governed by (1) a local population growth model, $f(n_t(y))$, parameterized in terms of birth and death rates (or perhaps just a growth rate), and (2) a dispersal kernel $k(\|x-y\|)$ that determines the probability of moving from $y$ to $x$ as a function of (usually Euclidean) distance $\|x-y\|$.

If you choose specific forms of $f$ and $k$, you can begin analyzing the spatial and temporal dynamics of a theoretical population under different parameter settings. But can you fit integrodifference models directly to data? It turns out that you can, and one of the earliest papers I know of that did this was Lele et al. (1998). Although I can’t say I fully understand the estimating equation approach they used, the estimation problem essentially boils down to replacing $n_t(x)$ with an expectation, say $\mu_t(x)$, and then modeling the realized values of abundance (i.e., the data) as normally distributed. That sounds easy, but it turns out to be pretty difficult, especially when dealing with random effects arising from environmental and demographic stochasticity.

Notwithstanding the estimation problem, I regard the Lele et al. paper as a major step forward in efforts to make theory from spatial ecology more relevant in applied settings. However, as mentioned by the authors, their model requires abundance data from all locations in area of interest. In practice, only a subset of the area will be surveyed and even in the surveyed areas, many individuals will not be detected. Dealing with these issues in a spatially explicit, statistical framework such that the parameters of $f$ and $k$ can be estimated is an exciting area of ongoing research that has been fueled by recent extensions of spatially implicit $N$-mixture models (see here and here).

A related class of models that can be used to describe and predict spatial and temporal population dynamics is spatiotemporal point process models. Interestingly, this seems to be a case where statistical ecologists have made more progress than mathematical ecologists, but that may be changing. More importantly, when these models are coupled with an observation model, they are extremely powerful tools for studying both population and individual-level processes, as discussed in our book. Computation issues still remain, but hopefully new methods will continue to be developed to resolve these problems and make the methods, and the theory behind them, more accessible to practitioners.

1. By ad-hockery, I’m referring to what Caughley (1994) called “games played with guesses” when he was speaking of way that some ecologists were approaching population viability analysis.