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The authors have declared that no competing interests exist.

Conceived and designed the experiments: WBL DMM CJ MNG JCP. Performed the experiments: WBL DMM CJ MNG JCP. Analyzed the data: RH ALR WBL DMM CJ MNG JCP. Contributed reagents/materials/analysis tools: RH ALR WBL DMM CJ MNG JCP. Wrote the paper: RH ALR WBL DMM CJ MNG JCP.

Current address: The Ohio State University, Department of Statistics, 1958 Neil Ave., Columbus, OH, 43210, United States of America

The McMurdo Dry Valleys constitute the largest ice free area of Antarctica. The area is a polar desert with an annual precipitation of ∼ 3 cm water equivalent, but contains several lakes fed by glacial melt water streams that flow from four to twelve weeks of the year. Over the past ∼20 years, data have been collected on the lakes located in Taylor Valley, Antarctica as part of the McMurdo Dry Valley Long-Term Ecological Research program (MCM-LTER). This work aims to understand the impact of climate variations on the biological processes in all the ecosystem types within Taylor Valley, including the lakes. These lakes are stratified, closed-basin systems and are perennially covered with ice. Each lake contains a variety of planktonic and benthic algae that require nutrients for photosynthesis and growth. The work presented here focuses on Lake Fryxell, one of the three main lakes of Taylor Valley; it is fed by thirteen melt-water streams. We use a functional regression approach to link the physical, chemical, and biological processes within the stream-lake system to evaluate the input of water and nutrients on the biological processes in the lakes. The technique has been shown previously to provide important insights into these Antarctic lacustrine systems where data acquisition is not temporally coherent. We use data on primary production (PPR) and chlorophyll-A (CHL)from Lake Fryxell as well as discharge observations from two streams flowing into the lake. Our findings show an association between both PPR, CHL and stream input.

The relationship between physiochemical variations and ecological processes is one that has been of primary interest to aquatic ecologists. Changes in climatic variables such as temperature, precipitation and sediment can lead to changes in hydrological processes that, in turn, affect nutrient fluxes, light penetration and other important ecological parameters in aquatic systems. The significance of these physical drivers on changing ecological conditions can only be established if both physical processes and ecological response can be linked. This needed linkage is made even more difficult in extreme environments where year around measurements of biological parameters cannot be obtained. In this paper we advance our previous work [

Image available at

Because the McMurdo Dry Valleys Long-Term Ecological Research (MCM-LTER,

The work presented here examines another of the Taylor Valley lakes, Lake Fryxell (see

The black line connects the average values for each season, marked with a black dot.

On each panel, we overlay the corresponding average daily temperature.

For each year, we consider the months of December and January, which are used in our analysis.

We begin by briefly describing the functional regression approach we pursue for this work. Abundant details and a comprehensive overview of the literature can be found in [_{1},_{2},…,_{n}). Departing from a classical linear regression approach, we consider several functional covariates _{j}(_{j}(^{th} covariate _{j}(⋅), where _{j}(⋅). When applied to the available data from Lake Fryxell, the role of _{i}(⋅) considered will be the discharge rates for the various streams that flow into Lake Fryxell.

Since functional spaces are infinite dimensional, estimation of the regression parameters _{j}(⋅) is typically done via a dimension reduction approach. The reason behind this is that one can always find functions _{j}(⋅) which will fit the _{j}(⋅) onto a finite dimensional space (ideally of dimension lower than the number of observations _{k}(_{j}(⋅) for _{k}(⋅), _{jk},

A straightforward approach to fitting the _{1}−_{0}. Since the basis functions _{k}(⋅) are known, this evaluation requires knowledge of the process _{ij}(⋅) at all time points {_{m}}. In our application, the functional covariates _{ij}(⋅) will be the discharge rates from Canada, Lost Seal and Von Guerard streams. Upon inspection of the discharge rate observations for Lake Fryxell, we note that there are some time intervals where discharge was not observed. Our methodology will account for this as we explain below.

In a preliminary step, we estimate the discharge profiles _{ij}(_{m}) for each season _{m}. It has been established that discharge rates in Taylor Valley are highly correlated to air temperature [

The discharge data set is plagued by many missing observations. In our approach to understand the uncertainty in the biological variables within Lake Fryxell we do require a _{ij} as required by ^{obs}^{(l)})represents a discharge observation at a time point ^{−1}, which is sparse. The role of DR^{obs}(·)is played by observations collected from the Canada, Lost Seal and Von Guerard streams. In each case,

In ^{obs}(·)(black dots, on a log-scale) as well as the corresponding fitted processes DR(·) (green curves), for the Canada, Lost Seal and Von Guerard streams, for four different austral summers months (December and January).

The green curves represent the predicted log-discharge for the four selected seasons. The horizontal blue line is at log(0.01) which represents zero discharge.

Once we have obtained estimates for the stream discharge profiles for both the three streams under consideration, at all time points _{m}, we used these as functional covariates in the regression model described above. The response variable

The vertical dashed lines represent predicted value ± 2 × standard errors for each season.

In this manuscript we present a statistical approach to modeling the association between stream discharge and the biological production in lake Fryxell, Antarctica. Our approach is based on a functional regression model, which requires complete (functional) observations of stream discharge over the period of interest (December-January of each austral summer, in this case). Although we have incomplete discharge observations, we are able to obtain functional estimates of the stream discharge (see

Annual variation of stream flow into a permanently ice-covered, closed-basin lake such as Lake Fryxell has a number of important ecological consequences. Increased stream flow introduces higher nutrient concentrations into the lake’s surface waters and it might also introduce high amounts of suspended matter into the lake as well. In the case of the former, this process should lead to potentially increased primary production in the surface portion of the euphotic zone [

The three streams under consideration have mean dissolved inorganic nitrogen (DIN) and soluble reactive phosphate (SRP) as summarized in

DIN | SRP | |
---|---|---|

Canada | 0.99 |
0.29 |

Lost Seal | 3.06 |
0.84 |

Von Guerard | 1.96 |
1.39 |

The significance of the year lag can be explained as follows. In the austral spring (October―November), after the sun rises, primary production begins. However, because glacier melt, and hence stream flow does not occur generally until late November, and the maximum flows until mid-late December into early January, the yearly pulse of primary production must be driven by nutrient input from the previous flow season, and, in some lakes via upward diffusion of nutrients [

We provide the temperature observations, the PPR and CHL observations, as well as the discharge rate data from the Canada, Lost Seal and Von Guerard streams.

(ZIP)

We would like to thank the two anonymous reviewers and the editorial board for their insightful comments. We are grateful to the long list of dedicated MCM-LTER limno- and stream team members over the years, who dutifully collected and analyzed the samples used in this study. We also thank Dr. Johanna Laybourn-Parry (University of Bristol, United Kingdom), who initially suggested this work.