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Explaining the heterogeneous organization of vegetation across landscapes has proved both a puzzling and an inspiring concept as patterns have formed naturally across the world. One such pattern is the existence of treelines, i.e., the demarcation zone between forestland and vegetation without trees1,2. There is a large body of work with developed and competing theories for understanding the specific limits and drivers for the non-existence of trees beyond a treeline. Yet after decades of study, there is still debate among ecologists and biologists over the mechanisms that limit the presence of trees beyond treelines. Current explanations are rooted in, but not limited to, consideration of factors such as excessive light and wind, limited CO(_2), and low temperatures1,3,4,5,6,7.
With this in mind, we ask: Is there another perspective that could provide insights complementary to and beyond what has been developed through the prevailing mechanistic approach? While the existing explanations are based on ideas of structural stability (e.g., high winds above the treeline) and limited resources pertaining to water, energy, and nutrients1,3,4,5,6,7, we instead examine the question of what determines the existence of a treeline from the perspective of thermodynamic feasibility. Our premise is that the existence or non-existence of certain vegetation first and foremost has to be ascertained through thermodynamic feasibility or infeasibility, respectively. Therefore, we approach the question of the existence of treelines by asking: If certain vegetation does not exist at a given location, is there a role that the thermodynamic perspective can play in telling us that its existence is infeasible? By approaching the topic from the thermodynamic perspective, we seek to provide important complementary insight to the broad base of scientific understanding ecologists and biologists have developed to explain the existence of treelines. Further, this work lays out additional context for the discussion around the advance of treelines (e.g., why some treelines advance and others do not).For example, several theories assert that the stature of vegetation is limited by CO(_2) balance and photosynthetic requirements under harsh winter conditions1,6. Other hypotheses argue that plant life is instead limited by the atmospheric temperature and the local environments that the plants experience7,8. Is there a perspective that could unify both of these findings? Through this work, we demonstrate how thermodynamic infeasibility inferred from model simulations pertaining to counterfactual scenarios manifests through both of these physiological limits. This means that either of these limits, individually or together, could lead to the nonexistence of trees—which limiting factor is expressed first varies by location. Thus, the commonality among locations that have different limiting mechanisms can be found in the unifying concept of thermodynamic infeasibility. While CO(_2) limitation may prevail in one location and temperature-related constraints may be limiting in another, both lead to thermodynamic infeasibility, meaning that the thermal environment results in a mechanistic infeasibility, such as net CO(_2) loss. In the examples presented in this paper, thermodynamic infeasibility manifests through negative work associated with constraints arising from temperature gradients and net CO(_2) loss, demonstrating that both limitations can be encapsulated using the thermodynamic perspective.Ecosystem thermodynamicsIt is now generally accepted that observed patterns of vegetation composition and its organization are a result of self-organization, or the spontaneous emergence of pattern without external predetermination9,10. By framing ecosystems as open thermodynamic systems, we explore further the concept of thermodynamic feasibility and its role in the self-organization of vegetation structure. Vegetation structure consists of composition (i.e., the number and type of functional groups11) and organizational patterns on the landscape12. We focus on composition rather than the spatial pattern of vegetation organization. We utilize a one-dimensional ecohydrological model that incorporates representative functional groups with no lateral transport of energy or matter under the assumption that the vegetation composition and pattern remain spatially uniform at a given site. Thus, we are able to compare the vertical thermodynamic regimes of proximal ecosystems with varying vegetation composition. We present the case that observed organization reflected in the demarcation of differing vegetation structures on either side of a treeline is established in tandem with vertical thermodynamic gradients at a given location, driven by the incoming solar energy into an ecosystem. In other words, we hypothesize that beyond a treeline, the existence of trees is prevented by conditions of thermodynamic infeasibility.The application of thermodynamic theory to ecology has been studied for the better part of the last century through the introduction of theoretical thermodynamic properties, such as entropy and exergy, into environmental systems. This work asserts that open thermodynamic systems will evolve based on the strength of applied concentration gradients on the system and will undergo irreversible processes to dissipate energy and destroy these gradients through all means available13,14. In the context of ecosystems, fluxes of mass or energy from the external environment (i.e., above the canopy) result in concentration gradients within the system itself. State variables will transition along these gradients according to the second law of thermodynamics. When the magnitude of incoming energy and consequent spatial imbalance of energy becomes great enough, dissipative structures spontaneously emerge, or self-organize, and establish temperature gradients consistent with the dissipative need of the ecosystem13,15. In this paper we conceptualize the work performed by an ecosystem as its ability to dissipate these applied concentration gradients. Consequently, work is highly dependent upon the existence and composition of self-organized vegetation.In classical thermodynamics, work is performed due to a transfer, or physical movement, of heat15. In the context of ecosystems, work performed by an ecosystem is represented by the exchange of heat with the external environment outside the ecosystem control volume12. Work performed by an ecosystem is, therefore, estimated as the vertical transport of heat in the form of latent and sensible heat, driven by the vertical gradient in temperature within the control volume structured by both the incoming downward shortwave and longwave radiation and the vegetation structure. The bottom boundary of the ecosystem control volumes studied are significantly deep such that heat exchanges due to water infiltration at this interface are insignificant in magnitude relative to latent and sensible heat flux out of the top of the control volume above the canopy. Further, we ignore the substantially slower thermodynamic processes associated with geochemistry in the soil.The vertical temperature gradient creates a directionality of dissipation of incident radiation as heat leaves out of the ecosystem from higher surface temperatures to lower air temperatures. Throughout this paper, we measure work through the net sum of heat leaving the ecosystem as latent and sensible heat—which can either be positive or negative depending on the direction of the resultant temperature gradient (see “Thermodynamic Calculations” in the “Methods” section). This temperature gradient (Eq. 1) emerges as a result of self-organization through feedback between the incoming shortwave and longwave radiation, local environmental conditions, and the heat dissipation and work performed by the vegetation. The presence of ground cover, such as snow, is impacted by aboveground vegetation structure, which provides a physical buffer between the atmosphere and the ground, further influencing the thermal environment and temperature gradient.Although significant research has been conducted by studying plant response to snowpack7,16,17, including the physiological requirements for life under prolonged snowpack and alpine climatic conditions, the thermodynamic perspective provides further insight. In addition to the physiological/mechanistic response of plants to snowpack and other environmental conditions, the thermal regime of a column of land experiencing snowpack is fundamentally different when an ecosystem does or does not have plants with stature taller than the height of snowpack (e.g., trees). Presence of trees results in shading from solar radiation and a physical buffer between the earth/snow surface and the atmosphere. Thus, the thermal profile of an ecosystem reveals valuable information about ecosystem behavior, and there is a need to explore the thermodynamic relationship between solar radiation and vegetation composition under varying environmental conditions. Thus, through this paper we define the circumstances under which multiple functional groups that include trees are no longer feasible for the available solar radiation leading to demarcated zones identifiable as treelines.Work by Körner argues that the “climate [that] plants experience” is different than the ambient temperature7. By modeling the layers within the canopy of plants with differing stand heights and leaf distributions, we are able to characterize the thermal regime and the “climate [that] plants experience” throughout the course of a given year. This characterization helps us understand the fundamental changes in behavior under varying environmental conditions with and without trees.An ecosystem’s ability to perform work manifests into four distinct cases depending on the sign of the resultant temperature gradient and the net loss or gain of heat driven by the thermal environment derived from present ground cover, such as vegetation or snow: (1) First and most common during the day when photosynthesis is occurring, the temperature of the earth surface, which receives the solar radiation, is typically warmer than the air above the canopy, and heat leaves the ecosystem upward along the negative temperature gradient, corresponding to a positive work (Fig. 1a). (2) Even when the temperature of the earth surface is warmer than the air above the canopy, there can be situations when there is a net heat gain within the ecosystem, meaning that heat moves into the ecosystem against the direction of the temperature gradient. This case is rare and counterproductive to heat dissipation, corresponding to negative work. (3) Common during the night, temperature inversion emerges. In this case, the temperature gradient from the earth surface to the atmosphere can become positive, meaning that the temperature of the air above the canopy is greater than the temperature of the earth surface. As heat enters the ecosystem to warm the surface, positive work is performed since the heat is still moving along a negative temperature gradient into the ecosystem (Fig. 1b). (4) During snowmelt conditions during the day, particularly for Arctic and alpine ecosystems, temperature inversions also emerge18,19. When this occurs and the ecosystem experiences a net heat loss through latent and sensible heat from the canopy, the heat leaving the ecosystem travels opposite of the direction dictated by the temperature gradient. Thus, in this case, ecosystems perform negative work. Our findings demonstrate how extended periods of time in this last case of work lead to thermodynamic infeasibility for the alpine/Arctic ecosystem counterfactual vegetation scenarios; i.e., ecosystems with vegetation properties from below the treelines cannot be sustained under the environmental conditions above the treelines, and, hence, they do not occur in nature.A recent study concluded that at sites where multiple functional groups exist (e.g., forests), the vegetation structure in which all groups co-exist and interact is thermodynamically more advantageous and, thus, more likely to occur than any one of the individual functional groups that the forest comprises12. Thermodynamic advantage is defined by the production of larger fluxes of entropy, more work performed, and higher work efficiency – a quantity that captures how much of the incoming energy is converted into forms useful for actively dissipating heat. It is possible to envision that under certain environmental conditions, the thermodynamic advantage offered by the existence of multiple functional groups is not tenable, indicating a thermodynamic infeasibility. Thermodynamic infeasibility occurs when a particular vegetation structure is not supported by the thermal environment at a given location. The demarcation exhibited by treelines presents an ideal case to explore this scenario, in that there is a distinct transition from multiple functional groups below the treeline to a single functional group above.Research questionIn this paper, we examine vegetation above and below Arctic and alpine treelines to determine whether the absence of trees in ecosystems above treelines are a result of thermodynamic infeasibility. Simply speaking, we seek to answer the following research question: Is the non-existence of trees beyond the transition zone demarcated as a treeline a reflection of thermodynamic infeasibility associated with the presence of trees, and if so, how is this infeasibility exhibited?Figure 1Conceptual diagram of temperature gradients. The W+ arrow indicates the positive direction of work performed through heat transport. Although in different directions, in both cases (a) and (b), the work performed is positive because heat moves from high to low temperatures. (a) Typical summertime temperature gradients from the earth surface to the air above the canopy are negative for the two real scenarios: subalpine/sub-Arctic forest (left) and alpine tundra/Arctic meadow (right). (b) A conceptual temperature inversion, or positive temperature gradient, which arise when alpine/Arctic forest are simulated as counterfactuals.Full size imageTo address this question, we use an extensively validated multi-layer 1-D physics-based ecohydrological model, MLCan12,20,21,22,23,24,25,26, consisting of 20 above-ground layers, 1 ground surface layer, and 12 below-ground layers (see Supplementary Material). This model is chosen because of its ability to capture interactions among functional groups, such as the impact of shading on understory vegetation and the resulting thermal environment within the canopy23. To balance model performance and accuracy, standing plant species are aggregated into functional groups (i.e., evergreen needleleaf trees, shrubs, grasses; see Table 1) based on literature27,28,29,30. The model output is used to compare the thermodynamic work performed at paired sites above and below the respective treelines for three different locations: the Italian Alps (IT), the United States Rocky Mountains (US), and the Western Canadian Taiga-Tundra (CA) (Fig. 2; see Site Descriptions). For each site pair, four scenarios are performed (Table 1): (1) The subalpine/sub-Arctic forest ecosystems are modeled as they exist with multiple functional groups (Fig. 1a, left). (2) The alpine/Arctic ecosystems are modeled as they exist with one functional group (i.e., shrubs or grasses; Fig. 1a, right). (3) We construct counterfactual scenarios above the treeline in which the vegetation of the subalpine or sub-Arctic forest is simulated with the environmental conditions and parameters of the alpine meadow or Arctic tundra (i.e., adding hypothetical trees where none exist; Fig. 1b). (4) As a control, a final counterfactual scenario is constructed below the treeline in which we model the understory of the subalpine/sub-Arctic forest individually (i.e., removing trees from the existing ecosystem).Table 1 Simulation scenarios with observed and hypothetical vegetation.Full size tableThe simulation of these four scenarios facilitates comparison of the existing vegetation structure of each site with the corresponding counterfactual scenarios. By varying the model inputs of vegetation present at each site while holding the environmental conditions and site-specific parameters consistent, we are able to directly compare thermodynamic outcomes as a result of varying vegetation structure and determine whether the counterfactual scenario with the simulated forest is thermodynamically feasible. Model performance was judged based on comparison to observed heat fluxes, such as latent and sensible heat (see Supplementary Material, Figs. S1–S3). As detailed below, the analysis supports the conclusion that thermodynamic feasibility is an important and complementary condition to the usual considerations of resource availability, such as water and nutrients, which determines the organizing form and function of ecosystems. More

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