Protecting Hemlock Trees from the Invasive Woolly Adelgid

By Lina Sorg

The hemlock woolly adelgid (Adelges tsugae) is an invasive insect pest from Japan that feeds on the sap of hemlocks in the eastern U.S., which sickens and ultimately kills the trees. Hemlocks are an essential part of the New England forest system, as they limit erosion along stream banks, provide a food source for deer and other wildlife, and offer shelter for animals in the winter. The eastern U.S. is home to two different species of hemlock. The eastern hemlock extends from the upper northeast down through the Appalachian Mountains to northern Georgia and Alabama, while the Carolina hemlock populates a much narrower region and is confined predominately to North Carolina. Hemlocks serve as a foundation species in areas that have not experienced recent disturbances. They grow slowly and do not often replace other hemlocks that have died; this makes them especially vulnerable to adelgid infestation, which can cause hemlock death in four to 15 years.

Adelgid populations fluctuate based on the health of the hemlocks on which they’re feeding. As the adelgid population increases, the ensuing damage to the trees causes the hemlocks to stop producing new growth. This lack of growth subsequently reduces the number of adelgids; fewer adelgids allow the hemlocks to recover, which prompts a subsequent recovery in the adelgid population and restarts the cycle. During a minisymposium presentation at the 2020 SIAM Annual Meeting, which took place virtually last week, Hannah Thompson of the University of Tennessee, Knoxville utilized several models to better understand and mitigate woolly adelgid damage to hemlock trees.

Thompson used data from Mountain Lake, Virginia, courtesy of Tom McAvoy, who collected the data between 2001 and 2013 at the tree-level scale. He recorded crown characteristics (pertaining to the above-ground parts of the trees) once a year, including the crown ratio and percentage of live branches, alive tips, new foliage, and crown density. McAvoy documented adelgid density twice a year because there are two generations of adelgids per year in the U.S. Winged females cannot reproduce in North America, but wingless females lay eggs and restart the life cycle.

Thompson created a model to reflect this data and represent hemlock health by the proportion tips alive, which is equivalent to 1 – the proportion of recent crown dieback. Her model, which includes seasonality, makes three major assumptions:

• Multiple mechanisms produce adelgid density dependence, and some are the result of interactions with hemlocks
• The proportion tips alive growth rate depends on adelgid density
• Adelgid mortality rate depends on proportion tips alive.

It consists of a system of ordinary differential equations (ODEs), with \(H\) signifying hemlock health (proportion tips alive) and \(A\) representing the adelgid population (the density of individuals per centimeter). 

Thompson exploited McAvoy’s data to conduct parameter estimation. She utilized 23 data points, each of which was the mean of 12 trees. She then took the model’s initial conditions directly from the data and estimated nine parameters with MultiStart and fmincon in MATLAB. Thompson selected the tenth parameter—the carrying capacity of proportion tips alive—from existing literature.

Next, she turned to biocontrol. Rather than completely eradicate the adelgid population, Thompson wanted to reduce it to a manageable level to limit hemlock damage. In their native environment, adelgids cause limited damage because of the resistance and tolerance of other hemlock species and a community of arthropod predators. Since this is not the case in the U.S., scientists have introduced biocontrol species in affected areas to manage the pests and bolster hemlock health. Thompson investigated two such species of predatory beetles: Laricobius nigrinus and Sasajiscymnus tsugae (see Figure 1). The former is native to the U.S. and was first released in 2003, while the latter originated in Japan and was first released in 1995.

This portion of the project utilized data from the Great Smoky Mountains National Park, which captured interactions of established populations of L. nigrinus and S. tsugae in the field after their dispersal from separate release sites; it was the first data set to record the two beetle species as established populations on the same tree. The data consisted of adelgid densities (adelgids per centimeter of twig) and larva and adult counts for L. nigrinus and S. tsugae. The study aimed to investigate the dynamics of the three interreacting species (adelgids, L. nigrinus, and S. tsugae), assess the joint impact of two predators on the adelgid population, and recognize the efficacy of biocontrol species to better manage hemlocks. “Ultimately, we want to help hemlock management by understanding what set of biocontrol species might be helpful,” Thompson said.

Her resulting model comprises systems of ODEs that represent populations of adelgids, L. nigrinus, and S. tsugae. The subdivides the populations into life stages and includes seasonality—produced by different systems of equations and time-dependent parameters—to reflect the active life stages at various times of year. It steadily models the adelgid population throughout the year.

To better explain the model, Thompson presented a diagram that breaks down the activity level of the three species’ life stages—adelgid eggs and adults; L. nigrinus eggs, larvae, and adults; and S. tsugae eggs, larvae, and adults—throughout the year (see Figure 2). In January and February, four life stages are active: adelgid eggs and adults, and L. nigrinus eggs and adults. From March through May, all classes of species are present in the system. During the summer months, L. nigrinus larvae burrow into the soil to mature into adults. Because they are not on trees and do not consume adelgids while underground, the model does not account for their population at this time. S. tsugae are no longer active in the fall, but L. nigrinus adults are active and the model reflects this.

Thompson then displayed a schematic that encompasses adelgids as both eggs and adults; their reproduction, maturation, and seasonal death; and predation of L. nigrinus and S. tsugae on both forms of adelgids (see Figure 3). L. nigrinus is a specialist predator that only preys on adelgids, but S. tsugae is a generalist predator and will eat both adelgids and other nearby species. They can survive in the absence of adelgids but reproduce in higher numbers if adelgids are present. 

Thompson’s model yielded preliminary results for populations of the three species over the course of a year. Seasonality is apparent, and the model yielded two peaks in the number of adelgid eggs that represent the two generations of adelgids, which occur in the spring and summer. Adelgid adults exist throughout the year, L. nigrinus are active in winter and spring when the population increases with larvae and adults, and S. tsugae are active in late spring into summer. 

This work is ongoing, and Thompson has further plans for both the hemlock-adelgid model and the adelgid-predator model. She hopes to include more parameters and finish parameter estimation for the hemlock-adelgid model, and prepare and perform parameter estimation for the adelgid-predator model. Ultimately, however, Thompson’s efforts lend clarity to the interactions between hemlock wooly adelgids, the trees upon which they prey, and two viable predatory beetle species.

Lina Sorg is the managing editor of SIAM News.