Erin Conlisk

MAXIMUM ENTROPY AND THE STATE‐VARIABLE APPROACH TO MACROECOLOGY

The biodiversity scaling metrics widely studied in macroecology include the species-area relationship (SAR), the scale-dependent species-abundance distribution (SAD), the distribution of masses or metabolic energies of individuals within and across species, the abundance-energy or abundance-mass relationship across species, and the species-level occupancy distributions across space. We propose a theoretical framework for predicting the scaling forms of these and other metrics based on the state-variable concept and an analytical method derived from information theory. In statistical physics, a method of inference based on information entropy results in a complete macro-scale description of classical thermodynamic systems in terms of the state variables volume, temperature, and number of molecules. In analogy, we take the state variables of an ecosystem to be its total area, the total number of species within any specified taxonomic group in that area, the total number of individuals across those species, and the summed metabolic energy rate for all those individuals. In terms solely of ratios of those state variables, and without invoking any specific ecological mechanisms, we show that realistic functional forms for the macroecological metrics listed above are inferred based on information entropy. The Fisher log series SAD emerges naturally from the theory. The SAR is predicted to have negative curvature on a log-log plot, but as the ratio of the number of species to the number of individuals decreases, the SAR becomes better and better approximated by a power law, with the predicted slope z in the range of 0.14-0.20. Using the 3/4 power mass-metabolism scaling relation to relate energy requirements and measured body sizes, the Damuth scaling rule relating mass and abundance is also predicted by the theory. We argue that the predicted forms of the macroecological metrics are in reasonable agreement with the patterns observed from plant census data across habitats and spatial scales. While this is encouraging, given the absence of adjustable fitting parameters in the theory, we further argue that even small discrepancies between data and predictions can help identify ecological mechanisms that influence macroecological patterns.

A THEORY OF SPATIAL STRUCTURE IN ECOLOGICAL COMMUNITIES AT MULTIPLE SPATIAL SCALES

A theory of spatial structure in ecological communities is presented and tested. At the core of the theory is a simple allocation rule for the assembly of species in space. The theory leads, with no adjustable parameters, to nonrandom statistical predictions for the spatial distribution of species at multiple spatial scales. The distributions are such that the abundance of a species at the largest measured scale uniquely determines the spatial- abundance distribution of the individuals of that species at smaller spatial scales. The shape of the species-area relationship, the endemics-area relationship, a scale-dependent com- munity-level spatial-abundance distribution, the species-abundance distribution at small spatial scales, an index of intraspecific aggregation, the range-area relationship, and the dependence of species turnover on interpatch distance and on patch size are also uniquely predicted as a function solely of the list of abundances of the species at the largest spatial scale. We show that the spatial structure of three spatially explicit vegetation census data sets (i.e., a 64-m 2 serpentine grassland plot, a 50-ha moist tropical forest plot, and a 9.68- ha dry tropical forest plot) are generally consistent with the predictions of the theory, despite the very simple statistical assumption upon which the theory is based, and the absence of adjustable parameters. However, deviations between predicted and observed distributions do arise for the species with the highest abundances; the pattern of those deviations indicates that the theory, which currently contains no explicit description of interaction mechanisms among individuals within species, could be improved with the incorporation of intraspecific density dependence.

A NEW CLASS OF MODELS OF SPATIAL DISTRIBUTION

We analyze a new class of models of spatial distribution, developing mathematical properties and performing empirical tests. The models are based on a simple colonization rule operating on a rectangular grid. Two special cases within the class are traditional random placement and negative binomial models. Over three large data sets, these two cases are strongly outperformed by more flexible models within the class, in particular, models that allow more general patterns of aggregation. The models are simple and broadly applicable, with only one adjustable parameter, representing aggregation. Shortcomings of the colonization rule are studied, and extensions and applications of the models are discussed.

Warming and provenance limit tree recruitment across and beyond the elevation range of subalpine forest

Climate niche models project that subalpine forest ranges will extend upslope with climate warming. These projections assume that the climate suitable for adult trees will be adequate for forest regeneration, ignoring climate requirements for seedling recruitment, a potential demographic bottleneck. Moreover, local genetic adaptation is expected to facilitate range expansion, with tree populations at the upper forest edge providing the seed best adapted to the alpine. Here, we test these expectations using a novel combination of common gardens, seeded with two widely distributed subalpine conifers, and climate manipulations replicated at three elevations. Infrared heaters raised temperatures in heated plots, but raised temperatures more in the forest than at or above treeline because strong winds at high elevation reduced heating efficiency. Watering increased season-average soil moisture similarly across sites. Contrary to expectations, warming reduced Engelmann spruce recruitment at and above treeline, as well as in the forest. Warming reduced limber pine first-year recruitment in the forest, but had no net effect on fourth-year recruitment at any site. Watering during the snow-free season alleviated some negative effects of warming, indicating that warming exacerbated water limitations. Contrary to expectations of local adaptation, low-elevation seeds of both species initially recruited more strongly than high-elevation seeds across the elevation gradient, although the low-provenance advantage diminished by the fourth year for Engelmann spruce, likely due to small sample sizes. High- and low-elevation provenances responded similarly to warming across sites for Engelmann spruce, but differently for limber pine. In the context of increasing tree mortality, lower recruitment at all elevations with warming, combined with lower quality, high-provenance seed being most available for colonizing the alpine, portends range contraction for Engelmann spruce. The lower sensitivity of limber pine to warming indicates a potential for this species to become more important in subalpine forest communities in the coming centuries.

The impossibility of estimating a negative binomial clustering parameter from presence-absence data : A comment on he and gaston

An important problem is to infer the abundance of a species in an area from its presence or absence in the cells of a uniform grid. If the abundance is assumed to be distributed over cells according to a negative binomial model, a value of the clustering parameter k is needed to infer the abundance. It is shown that, despite a proposal in the literature, k cannot be estimated from presence‐absence data but must be given from outside information.

Declines in low‐elevation subalpine tree populations outpace growth in high‐elevation populations with warming

Author(s): Conlisk, Erin; Cristina Castanha; Matthew J. Germino; Thomas T. Veblen; Jeremy M. Smith; Lara M. Kueppers | Abstract: Species distribution shifts in response to climate change require that recruitment increase beyond current range boundaries. For trees with long life spans, the importance of climateâsensitive seedling establishment to the pace of range shifts has not been demonstrated quantitatively. Using spatially explicit, stochastic population models combined with data from longâterm forest surveys, we explored whether the climateâsensitivity of recruitment observed in climate manipulation experiments was sufficient to alter populations and elevation ranges of two widely distributed, highâelevation North American conifers. Empirically observed, warmingâdriven declines in recruitment led to rapid modelled population declines at the lowâelevation, âwarm edgeâ of subalpine forest and slow emergence of populations beyond the highâelevation, âcool edgeâ. Because population declines in the forest occurred much faster than population emergence in the alpine, we observed range contraction for both species. For Engelmann spruce, this contraction was permanent over the modelled time horizon, even in the presence of increased moisture. For limber pine, lower sensitivity to warming may facilitate persistence at low elevations â especially in the presence of increased moisture â and rapid establishment above tree line, and, ultimately, expansion into the alpine. Synthesis. Assuming 21st century warming and no additional moisture, population dynamics in highâelevation forests led to transient range contractions for limber pine and potentially permanent range contractions for Engelmann spruce. Thus, limitations to seedling recruitment with warming can constrain the pace of subalpine tree range shifts.