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The steady increase in white-tailed deer populations and largely unnoticed invasion of earthworms are changing some of the important underlying processes that support North American forest understory communities (Greiner 2012, MAERZ 2009, NUZZO 2009, Rooney 2003).

Amidst a rapidly-changing set of ecological drivers, earthworm invasion and increased browse pressure from white tailed deer are two of the most important stressors to forest plant populations (Fisichelli 2013). Northern forests in North America have developed in the absence of earthworms, at least as far back as the last glaciation (Bohlen 2004). Human activity has facilitated the introduction and dispersion of earthworms to even remote forested areas through logging roads, dumping of fishing bait, and the relocation of fill or horticultural materials (Frelich 2006). Whereas uninvaded forest soils often build up a thick leaf-fermenting-humus (LFH) layer through slow, localized decomposition of organic material, earthworm-dominated forests are characterized by bare mineral soil, and can completely lack a stratified soil profile (Bohlen 2004). Many native plants require the unique habitat that the forest floor provides for protection of slowly germinating seedlings, nutrient and water retention, access to mycorrhizal symbionts and temperature buffering (Fisk 2004, Hale 2008, Lawrence 2003).

Drivers of change in understory plant communities are also occurring above-ground. In much of North eastern North America, browse pressure from rapidly growing white-tailed deer (Odocoileus virginianus) populations is dramatically altering forest understory communities, restricting regeneration and causing extinction of native plants at the local level (Anderson 1994, ALVERSON 1988, Rooney 2003). Long-term datasets show that overall species diversity decreases with high deer browse pressure, and selective browsing disproportionately affects palatable species, while releasing unpalatable plants competition (Rooney 2003). Deer browse impacts are compounded in slow-growing perennials, as they preferentially browse the largest individual plants that maintain growth rates of the plant population (McGraw 2005).

To look at the combined and individual effects of deer and earthworms, I set up experimental plantings of a large number of native forest understory species (n=15) in spring 2012. Because earthworm and deer impacts on seedlings are the net effect of a myriad of factors, I selected species with many different traits that could conceivably respond to these factors. Thus far I have been recording seedling survival, and have been surprised to find earthworms decrease seedling survival in 11 of 15 species, and had no effect on 4 species. This is surprising, because field surveys have found several plant species included in my study are associated with earthworm-invaded environments (Hale 2008). However, these snapshots of plant communities do not provide information on the impacts of deer and earthworms on plant population growth rates. As my seedlings become reproductive, I can build a stage-structured model to determine how deer and earthworms impact native plant population growth, both individually and together. I expected that, 1) most plants growing in earthworm-invaded areas will be slower to progress through the vegetative stages 2) plant species that appear to benefit from earthworm invasion (sedges, etc.) will have higher seed set (theta will be large) 3) unfenced plots will see more regressions to smaller stages due to deer browse 4) deer and earthworms will have a synergistic effect on decreasing population growth.

We developped stage-structured population models to predict growth rates of Tiarella cordifolia. Because T. cordifolia has discrete life stages, Leslie matrix models are useful to investigate their demography. The loop diagram (Figure 1) shows all lifestages of T. cordifolia (seed, rosette and reproductive adult). Lowercase letters $$s$$, $$r$$ and $$a$$ represent respective life stages. The number of indviduals in each life stage is represented by the vectors $$n_s$$, $$n_r$$ and $$n_a$$.

$\label{eq:dSdt} \frac{dS}{dt}=\gamma A -\theta S$

$%\label{eq:dRdt} \frac{dR}{dt}=\beta A +\theta S -\alpha R$

here we use eq. \ref{eq:dSdt}

$%\label{eq:dSdt} \frac{dA}{dt}=\alpha R -(\beta+\gamma) A$

$\frac{d}{dt} \left( \begin{matrix} S \\ R \\ A \end{matrix}\right) = \left( \begin{matrix} -\theta & 0 & \gamma \\ \theta & -\alpha & \beta\\ 0 & \alpha & -(\beta+\gamma) \end{matrix}\right) \left( \begin{matrix} S \\ R \\ A \end{matrix}\right)$

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$%\label{eq:dAlldt} \begin{array}{rl} \frac{dR}{dt} =&\beta A +\theta S -\alpha R \\ \frac{dS}{dt} =&\gamma A -\theta S \\ \frac{dA}{dt} =&\alpha R -(\beta+\gamma) A \\ \end{array}$