Population Dynamics

I have used Bayesian statistical models to detect lag phases (delays in growth) and population collapses (spontaneous and severe declines in abundance) in biological invasions. I exploited the large and freely available Audubon Christmas Bird Count database to construct the models, and I employed a variety of data management methods (e.g., correcting for observer error and variable effort). These efforts required me to develop new models to quantify the presence and length of lag phases and the degree and magnitude of collapses. These models can be extended beyond biological invasions and used for resource allocation prioritization by identifying the most at-risk populations for eradication (if exotic), or for conservation (if native).

Lags:

Exotic species often show periods of very slow population growth, followed by more rapid increases in growth rates. We refer to these as 'lag phases' and 'increase phases', respectively. Lag phases can be inherent properties of population growth (as in exponential, e.g., t₀ to t_exp in the graph below), or true lags composed of two different functions (as in the two piece model, e.g., from t₀ to t_lag below).

In terms of management, it is crucial to understand the dynamics of these processes. If management officials prescribe a certain plan of action based on the expectation that a populations is following exponential population growth, they are likely to find themselves dealing with higher abundances of the target population sooner than they had anticipated. Conversely, they may come to the point at which the management action is scheduled to be implemented and find virtually no difference in the population abundance because its experiencing a long-lasting lag phase; the temptation to save money and delay action can lead to massive issues down the road when the target population does finally exit its lag phase and begin to increase more rapidly than expected.

I used Christmas Bird Count data to detect lags in several exotic bird populations on Hawaii, using statistical models. I found that lags are very common in these species. Mathematical models aimed at simulating and predicting lag phases can allow for more informed management decisions and help anticipate lags. Developing these models is a future goal of mine. Read more in Diversity and Distributions.

Collapses:

Exotic Species

Similar to the lags that occur in biological invasions, collapses are also relatively common and even less well understood. We can see them pretty clearly, as in this time series for the Cattle Egret:

The difficulty is in distinguishing between a population that has overshot its carrying capacity and one that has truly collapsed. While we can do the math to detect a population settling down around its carrying capacity, we require knowledge of what the carrying capacity is to begin with, which is not an easy characteristic to determine. For our purposes, we concern ourselves only with the maximum observed abundance, using IUCN red list criteria for a collapse from this point. This point is also difficult to determine, as there may be some error in the reported abundance.

I used a series of statistical models in a Bayesian framework to try to overcome these complications and qualitatively determine the apparent decrease of time series like the one shown above, and determine just how much of a population decrease is required to define it as a collapse. This work is out in Biological Invasions.

Native Species

While population collapses are seen in boom-bust dynamics in biological invasions, many native species experience collapses as well. Thus, I used the same dataset from which I obtained information about exotic species to assess population collapses in native species. My findings indicate that perhaps collapses are not inherent to biological invasions, but a fundamental part of many species population dynamics influenced by some mechanism other than introduction events. This work is out in Ecological Modelling.