REVIEW AND
SYNTHESIS
Ecology under lake ice
Stephanie E. Hampton,
1
* Aaron W.
E. Galloway,
2
Stephen M. Powers,
1
Ted Ozersky,
3
Kara H. Woo,
1
Ryan
D. Batt,
4
Stephanie G. Labou,
1
Catherine M. O’Reilly,
5
Sapna
Sharma,
6
Noah R. Lottig,
7
Emily H.
Stanley,
8
Rebecca L. North,
9
Jason
D. Stockwell,
10
Rita Adrian,
11
Gesa
A. Weyhenmeyer,
12
Lauri Arvola,
13
Helen M. Baulch,
9,14
Isabella
Bertani,
15
Larry L. Bowman, Jr.,
16
Cayelan C. Carey,
17
Jordi
Catalan,
18
William Colom-
Montero,
12
Leah M. Domine,
19
Marisol Felip,
20
Ignacio
Granados,
21
Corinna Gries,
8
Hans-Peter Grossart,
22,23
Juta
Haberman,
24
Marina Haldna,
24
Brian Hayden,
25
Scott N. Higgins,
26
Jeff C. Jolley,
27
Kimmo K.
Kahilainen,
28
Enn Kaup,
29
Michael
J. Kehoe,
9,14
Sally MacIntyre,
30
Anson W. Mackay,
31
Heather L.
Mariash,
32
Robert M. McKay,
33
Brigitte Nixdorf,
34
Peeter N
~
oges,
24
Tiina N
~
oges,
24
Michelle Palmer,
35
Don C. Pierson,
12
David M. Post,
16
Matthew J. Pruett,
1
Milla Rautio,
36
Jordan S. Read,
37
Sarah L.
Roberts,
38
Jacqueline R
€
ucker,
34
Steven Sadro,
39
Eugene A. Silow,
40
Derek E. Smith,
41
Robert W.
Sterner,
3
George E. A. Swann,
38
Maxim A. Timofeyev,
40
Manuel Toro,
42
Michael R. Twiss,
43
Richard J. Vogt,
44
Susan B. Watson,
45
Erika J. Whiteford
46
and
Marguerite A. Xenopoulos
44
Abstract
Winter conditions are rapidly changing in temperate ecosystems, particularly for those that experi-
ence periods of snow and ice cover. Relatively little is known of winter ecology in these systems,
due to a historical research focus on summer ‘growing seasons’. We executed the first global quan-
titative synthesis on under-ice lake ecology, including 36 abiotic and biotic variables from 42
research groups and 101 lakes, examining seasonal differences and connections as well as how sea-
sonal differences vary with geophysical factors. Plankton were more abundant under ice than
expected; mean winter values were 43.2% of summer values for chlorophyll a, 15.8% of summer
phytoplankton biovolume and 25.3% of summer zooplankton density. Dissolved nitrogen concen-
trations were typically higher during winter, and these differences were exaggerated in smaller
lakes. Lake size also influenced winter-summer patterns for dissolved organic carbon (DOC), with
higher winter DOC in smaller lakes. At coarse levels of taxonomic aggregation, phytoplankton
and zooplankton community composition showed few systematic differences between seasons,
although literature suggests that seasonal differences are frequently lake-specific, species-specific,
or occur at the level of functional group. Within the subset of lakes that had longer time series,
winter influenced the subsequent summer for some nutrient variables and zooplankton biomass.
Keywords
Aquatic ecosystem, data synthesis, freshwater, lake, limnology, long-term, plankton, seasonal,
time series, winter ecology.
Ecology Letters (2017) 20: 98–111
1
Center for Environmental Research, Education and Outreach, Washington
State University, Pullman, WA, USA
2
Oregon Institute of Marine Biology, University of Oregon, Charleston, OR,
USA
3
Department of Biology & Large Lakes Observatory, University of Minnesota
Duluth, Duluth, MN, USA
4
Department of Ecology, Evolution, and Natural Resources, Rutgers Univer-
sity, New Brunswick, NJ, USA
5
Department of Geography-Geology, Illinois State University, Normal, IL, USA
6
Department of Biology, York University, Toronto, ON, Canada
7
Center for Limnology, University of Wisconsin, Boulder Junction, WI, USA
8
Center for Limnology, University of Wisconsin, Madison, WI, USA
9
Global Institute for Water Security, University of Saskatchewan, Saskatoon,
SK, Canada
10
Rubenstein Ecosystem Science Laboratory, University of Vermont, Burlington,
VT, USA
11
Department of Ecosystem Research, Leibniz Institute of Freshwater Ecology
and Inland Fisheries, Berlin, Germany
12
Department of Ecology and Genetics, Uppsala University, Uppsala, Sweden
13
Lammi Biological Station, University of Helsinki, Lammi, Finland
14
School of Environment and Sustainability, University of Saskatchewan,
Saskatoon, SK, Canada
15
Water Center, Graham Sustainability Institute, University of Michigan, Ann
Arbor, MI, USA
© 2016 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use,
distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.
Ecology Letters, (2017) 20: 98–111 doi: 10.1111/ele.12699
INTRODUCTION
Reduced ice cover on lakes and rivers worldwide (Magnuson
et al. 2000; Benson et al. 2012) highlights an urgent need for
research focused on under-ice ecosystem dynamics and their
contributions to whole-ecosystem processes. Recently a global
synthesis of summer lake temperature trends in lakes (O’Reilly
et al. 2015) revealed that winter ice cover is a major force in
determining the characteristics of summer warming trends,
demonstrating the cascading effects between seasons. Cross-
seasonal cascades can involve both abiotic and biotic vari-
ables, such as when winter ice characteristics influence spring
and summer algal growth (e.g. Gerten & Adrian 2000; Straile
2002; Adrian et al. 2006; Blenckner et al. 2007). Conse-
quently, in water bodies that freeze, the timing and physical
characteristics of ice cover are likely to drive some of the most
important biological changes for lakes overall (Moore et al.
2009; Salonen et al. 2009; Benson et al. 2012).
Marine research is ahead of freshwater research in studies of
under-ice ecology, providing compelling evidence that winter
conditions and changes in ice phenology play an important role
in sea-ice system dynamics (Arrigo & Thomas 2004; Arrigo
et al. 2008; Meier et al. 2014). The presence of ice in marine
systems drives primary productivity that is critical for food
webs (Lizotte 2001; Grebmeier 2012); for example ice-asso-
ciated algae in the Antarctic contribute 25–30% of total annual
productivity for the region (Arrigo & Thomas 2004). But for
lakes, there is very little information about the physics, geo-
chemistry and biology under ice, and this knowledge gap
severely limits our ability to predict how changes in winter con-
ditions will affect the ecology and productivity of inland waters.
A recent study reported that only 2% of peer-reviewed freshwa-
ter literature has included under-ice lake processes (Hampton
et al. 2015). The paucity of under-ice research in freshwater sys-
tems is especially surprising when one considers that half of the
world’s lakes periodically freeze, i.e. slightly more than 50 mil-
lion lakes (Verpoorter et al. 2014). Also, the majority of lakes
in the world are located between 60° and 66° N where annual
ice cover duration currently averages more than 150 days
(Weyhenmeyer et al. 2011).
The initial and highly influential model of the plankton ecol-
ogy group (the PEG model; Sommer et al. 1986) hypothesised
that winter in ice-covered lakes is a time of limited, if any, activ-
ity by primary or secondary producers. The widespread use of
the term ‘growing season’ to describe summer months in tem-
perate lakes reflects the prevailing viewpoint of winter as an
inactive period. In general, freshwater scientists have assumed
that overall biological activity under lake ice is inconsequential
or that under-ice primary producers resort to heterotrophy or
dormancy, as has been observed in some studies (e.g. McKnight
et al. 2000; Lepp
€
aranta 2015), particularly for high-latitude sys-
tems with heavy snow coverage. While the PEG model has
since been revised (Sommer et al. 2012) with a call for addi-
tional winter work, areas of uncertainty range from the identity
and activity of plankton to ecosystem-level processes such as
whole-lake metabolism and greenhouse gas emissions. The lake
studies that have included under-ice work strongly suggest that
winter food webs and physical processes are both active and
complex, but with few patterns that are readily generalisable
(reviewed in Salonen et al. 2009; Bertilsson et al. 2013; Bruese-
witz et al. 2015; Hampton et al. 2015).
Prior work indicates that winter under-ice conditions can be
very similar to, or very different from, the ice-free summer
conditions. Depending upon snow characteristics, ice can
allow for up to 95% of photosynthetically active radiation
transmission (Bolsenga & Vanderploeg 1992), fuelling winter
16
Department of Ecology and Evolutionary Biology, Yale University, New Haven,
CT, USA
17
Department of Biological Sciences, Virginia Tech, Blacksburg, VA, USA
18
CREAF, Consejo Superior de Investigaciones Cient
ıficas, Cerdanyola, Spain
19
Department of Biology, University of St. Thomas, St. Paul MN, USA
20
Department of Ecology, Universitat de Barcelona, Barcelona, Spain
21
Centre for Research, Monitoring and Evaluation, Sierra de Guadarrama
National Park, Rascafr
ıa, Spain
22
Department of Experimental Limnology, Leibniz Institute of Freshwater
Ecology and Inland Fisheries, Stechlin, Germany
23
Institute for Biochemistry and Biology, Potsdam University, Potsdam,
Germany
24
Centre for Limnology, Estonian University of Life Sciences, Tartu, Estonia
25
Department of Biology, University of New Brunswick, Fredericton, NB,
Canada
26
IISD Experimental Lakes Area, Winnipeg, MB, Canada
27
Columbia River Fisheries Program Office, U.S. Fish & Wildlife Service,
Vancouver, WA, USA
28
Department of Environmental Sciences, University of Helsinki, Helsinki,
Finland
29
Institute of Geology, Department of Isotope Paleoclimatology, Tallinn
University of Technology, Tallinn, Estonia
30
Department of Ecology, Evolution and Marine Biology, University of
California Santa Barbara, Santa Barbara, CA, USA
31
Department of Geography, University College London, London, UK
32
National Wildlife Research Centre, Science and Technology Division, Envi-
ronment and Climate Change Canada, Ottawa, ON, Canada
33
Department of Biological Sciences, Bowling Green State University, Bowling
Green, OH, USA
34
Department of Freshwater Conservation, Brandenburg University of Tech-
nology Cottbus - Senftenberg, Bad Saarow, Germany
35
Environmental Monitoring and Reporting Branch, Ontario Ministry of the
Environment and Climate Change, Toronto, ON, Canada
36
Department of Fundamental Sciences, Universit
eduQu
ebec
a Chicoutimi,
Chicoutimi, QC, Canada
37
Office of Water Information, U.S. Geological Survey, Middleton, WI, USA
38
School of Geography, University of Nottingham, Nottingham, UK
39
Department of Environmental Science and Policy, University of California
Davis, Davis, CA, USA
40
Institute of Biology, Irkutsk State University, Irkutsk, Russian Federation
41
Department of Biostatistics and Informatics, Colorado School of Public
Health, Aurora, CO, USA
42
Department of Aquatic Environment, Centre for Hydrographic Studies
CEDEX, Madrid, Spain
43
Department of Biology, Clarkson University, Potsdam, NY, USA
44
Department of Biology, Trent University, Peterborough, ON, Canada
45
Canada Centre for Inland Waters, Environment and Climate Change
Canada, Burlington, ON, Canada
46
Department of Geography, Loughborough Universit y, Loughborough, UK
*Correspondence: E-mail: s.hampton@wsu.edu
© 2016 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.
Review and Synthesis Ecology under lake ice 99
algal blooms that rival those of summer (e.g. Jewson et al.
2009). In Lake Erie, phytoplankton growth and loss rates dur-
ing winter can be similar to those of summer (Twiss et al.
2014). For certain lakes, the composition of phytoplankton
communities is different under ice, dominated by smaller spe-
cies (e.g. Wetzel 2001), or conversely dominated by large ice-
associated filamentous diatoms (e.g. Katz et al. 2015; Beall
et al. 2016), whereas other lakes do not appear to have dis-
tinct seasonal changes in phytoplankton community composi-
tion (Dokulil et al. 2014). Although zooplankton biomass
generally appears to be lower under ice, changes in commu-
nity composition can be highly variable across lakes (Dokulil
et al. 2014). Even more scarce is information about nutrient
and dissolved organic carbon concentrations under the ice
that may help to drive many of these plankton dynamics (but
see
€
Ozkundakci et al. 2016).
The pathways through which winter conditions may affect
lake ecology throughout the year are similarly diverse. Winter
ice conditions have been observed to alter phytoplankton bio-
mass and composition in the subsequent ice-free season (Wey-
henmeyer et al. 2008). For zooplankton, early emergence from
diapause, synchronised with the timing of warming at the end
of winter can be associated with higher summer density for
zooplankton grazers (Gerten & Adrian 2000; Adrian et al.
2006). Such carry-over between seasons is not restricted to
winter’s influence on summer, of course, and there is evidence
that under-ice zooplankton dynamics can depend in part on
late summer zooplankton biomass (Dokulil et al. 2014). The
diversity of responses found by under-ice studies suggests that
a synthesis of existing knowledge is greatly needed and would
help identify key next steps in winter limnology as well as pro-
mote productive collaborations (Hampton et al. 2015).
Research that builds a knowledge base about the processes
occurring over nearly half the annual cycle for approximately
half of the world’s lakes is a worthy challenge, with poten-
tially global repercussions. Here we explore differences
between winter and summer conditions both across and
within lakes, focusing on dynamics of phytoplankton, zoo-
plankton, nutrients and dissolved organic carbon. We address
two overarching questions on under-ice ecology: (1) What is
the magnitude and direction of ecological change from winter
to summer; and (2) For which variables and to what extent
are winter and summer seasons connected, i.e. what is the
influence of winter conditions on the following summer sea-
son, and the influence of summer conditions on the following
winter? We hypothesised that winter biomass and density of
phytoplankton and zooplankton are significantly lower than
that of summer, due to a low-light environment unfavourable
for emergence or growth (e.g. Vincent & Vincent 1982;
C
aceres & Schwalbach 2001; Jewson et al. 2009), low temper-
ature (e.g.
€
Ozkundakci et al. 2016) or nutrient limitation (e.g.
O’Brien et al. 1992;
€
Ozkundakci et al. 2016), and that these
differences would be modified by geophysical characteristics
of lakes. Furthermore, we hypothesise that lake conditions
can carry-over across seasons, as suggested in the revised
PEG model (Sommer et al. 2012; Domis et al. 2013), such
that an understanding of winter conditions will improve
understanding of summer conditions, and vice versa. The
presence of seasonal carry-over would indicate that winter is
not simply a ‘reset’ that leads back to similar spring ice-out
conditions year after year, and would suggest revisions to cur-
rent field and laboratory approaches currently focused on
‘growing season’ dynamics.
METHODS
Data acquisition
Data were acquired from both an initial literature review to
provide baseline expectations for ecological patterns and,
much more comprehensively, from a collation of primary data.
Literature review
As an initial step towards synthesising knowledge, we compiled
under-ice data for chlorophyll a (chl a) concentration from a
literature survey. We found 14 papers for which data would be
readily compared to those solicited from primary data contri-
butors (based on criteria in Supporting Information). From
these papers, we compiled data from 17 lakes (Fig. 1), extract-
ing data from text, tables or from figures. For the literature
review effort, we were unable to compare ice-on (winter) and
ice-off (summer) data, as only seven of the lakes in these papers
also included biological data during the summer season.
Primary data collation
The scientific community was solicited for data on physical,
chemical and biological variables of lakes and reservoirs (here-
after together called ‘lakes’) during ice cover. We used an
open call for participation through electronic mailing lists and
professional networks, and then interacted extensively with
data contributors. In total, we collated winter under-ice and
summer observations between 1940 and 2015 for 101 lakes at
135 unique sampling locations across wide gradients of lati-
tudes, production and trophic status (Fig. 1). For the Lauren-
tian Great Lakes, most sampling stations were located
nearshore or in bays.
Contributors of primary data used a structured template to
report values from winter periods when the lake had complete
ice cover (hereafter ‘winter’), and summer periods when the
lake was completely open and, in dimictic systems, stratified
(hereafter ‘summer’). For 10 lakes that were polymictic or
lack reliable summer stratification, summer data are from a
representative open water period chosen by the primary data
contributors, usually midsummer. We asked researchers to
provide data aggregated from the photic zone, for each lake
and season. Across all lakes, the median sample depth during
winter was 2.0 m, and the mean ratio of sample depths (win-
ter:summer) was 1.01. We did not include winter data from
those years that did not have ice cover (e.g. M
€
uggelsee some-
times does not freeze). Each seasonal value used in our analy-
sis was computed by the individual data providers (Box S1;
Fig. S1). The number of within season sampling events was
reported by researchers for 71% of our compiled seasonal
averages; of these, 64% of the winter averages and 79% of
the summer averages were based on 3 or more sampling
events. When a lake had multiple sampling stations, the sta-
tions were generally treated independently. Exceptions were
cases where researchers specified multiple stations that were
© 2016 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.
100 S. E. Hampton et al. Review and Synthesis
functionally similar and could be pooled in aggregate. After
pooling the functionally similar stations, the majority of lakes
(84 of 101 lakes) did not retain multiple distinct stations for
analyses (see Supporting Information).
Data availability differed among lakes and variables. For
several major variables, paired winter and summer observa-
tions were present in at least 30 stations, often over 10 years.
All stations had at least one variable with both winter and
summer data, and the variable-specific sample sizes and peri-
ods of record are in Table S1. The median period of record for
most variables was 2–3 years. Variables included water tem-
perature (107 unique stations with paired winter-summer
data), chlorophyll a (chl a as lgL
1
; 118 stations), total phos-
phorous (TP as lgL
1
; 106 stations), total dissolved phospho-
rus (TDP as lgL
1
; 72 stations), total nitrogen (TN as
lgL
1
; 75 stations), total dissolved nitrogen (TDN as lgL
1
;
73 stations), TN:TP (atomic ratio; 74 stations), TDN:TDP
(atomic ratio; 66 stations) and dissolved organic carbon (DOC
as mg L
1
; 81 stations). Our reported values for TDP and
TDN are conservative, because not all researchers performed
the digestion step. Nonetheless, because common nutrient
methods were usually used at a given lake, our approach still
captures the relative difference between seasons (winter-sum-
mer), except in lakes where the dissolved organic fraction var-
ies substantially between seasons. In addition, 36 stations had
data for total zooplankton density (individuals L
1
). Group-
specific zooplankton counts (proportion of total abundance)
for calanoid, cyclopoid, Daphnia, rotifer, other cladoceran and
unspecified other zooplankton were also available. Methodol-
ogy for zooplankton data collection differs across programs to
a degree that complicates comparisons across lakes for rotifers
and unspecified other zooplankton, such that those data were
not analysed here and total zooplankton densities were accord-
ingly adjusted as well. Subsequent references to zooplankton
density include Daphnia, other cladocerans, cyclopoid and
calanoid copepods for all 36 stations. For phytoplankton bio-
volume mm
3
L
1
, there were data for 17 stations. Group-spe-
cific phytoplankton counts (proportion of total abundance) for
chlorophyte, cryptophyte, cyanophyte, bacillariophyte,
dinoflagellate and other phytoplankter were available at 17
stations. Specific ultraviolet absorbance (L mg C
1
m
1
), and
colour (platinum units) were also available at some stations.
Although we solicited benthic data, only a few researchers pro-
vided data for any type of benthic variable, suggesting a wide-
spread lack of benthic winter sampling. The lake-specific
averages for winter and summer conditions, by variable, are
shown in Table S2. For chl a, TP, TDP, TN, TDN, DOC and
zooplankton density, more than 25% of stations had a period
of record ≥ 10 years. The complete data set is available in the
Knowledge Network for Biocomplexity (https://knb.ecoinfor
matics.org/, Hampton et al. 2016).
Data analysis
We approached data analysis in two ways. The first approach
was to quantify the average winter-summer differences across
all lakes in the data set, identifying major physical features of
lakes that affect the magnitude of observed winter-summer dif-
ferences. The second approach was to examine univariate sea-
sonal dynamics within lakes, including winter-summer
differences and winter-summer correlations, using the subset of
lakes where longer term (≥ 10 years) time series were available.
Winter-summer differences across lakes
We calculated the mean winter value and the mean summer
value for every station and variable, and examined mean win-
ter-summer differences across all lakes in the data set. Magni-
tude, direction and significance of differences between winter
Figure 1 Map of lakes/sampling stations included in the full synthesis under-ice data set (i.e. ‘primary data’) and the published literature review. See
Figure S2 for comparison of aggregated chl a between primary data and published literature samples.
© 2016 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.
Review and Synthesis Ecology under lake ice 101
and summer were determined using linear mixed effect (LME)
modelling with year as a random intercept (Bates et al. 2015).
For the multivariate plankton compositional data, we used
permutational analysis of variance (PERMANOVA; Ander-
son 2001) from the vegan package in R (‘adonis’ function,
Oksanen et al. 2016; R Core Team 2016) on sites that had
complete cases for both winter and summer communities. To
discern major physical variables correlated with the magnitude
and sign of winter-summer differences, we used a regression
tree approach (rpart package in R, Therneau et al. 2015; with
applications from Breiman et al. 1984). We used the variable-
specific average winter-summer difference as the response vari-
able; the candidate explanatory variables were lake area, lake
maximum depth, latitude (absolute) and elevation. Trees were
cross-validated and pruned using the complexity parameter
value which minimised the cross-validated error. Mean win-
ter-summer difference and standard error of the difference
were calculated for each branch of the regression trees. We
also used a regression tree approach to analyse average win-
ter-summer difference in plankton community composition as
a matrix response (mvpart package in R, Therneau et al.
2014), for both the crustacean zooplankton community and
the phytoplankton community data. Candidate explanatory
variables included the same four variables as previous trees,
as well as winter-summer difference in water temperature and,
for zooplankton, the summer chl a.
Due to differences in the available period of record, the
overall winter average can represent 30 + years for some lakes
and variables, whereas for others the overall average repre-
sents only 1 year of data. We expected that variation in sam-
ple size might create noise that could obscure differences
(Type 2 error), but not suggest differences that do not exist
(Type 1 error).
Winter-summer differences within lakes
For time series that were available, we examined within lake
differences between winter and summer. For this we used only
time series that had ≥ 10 winter values, meaning at least
10 years of data and 20 values overall. To allow a robust
examination of winter-summer correlations (below), we used
contiguous portions of each time series, allowing no more
than 1 data gap. Before examining differences, every time ser-
ies was detrended using a 7-point moving average filter
(3.5 years) to account for longer term trends, and we con-
firmed that no significant linear trends remained after filtering.
With each detrended time series, summer-winter differences
were examined using a simple seasonal model
y
t
¼ b
ice
D þ b
0
þ e ð1Þ
where y
t
represents the sequence of winter and summer values,
b
ice
is the coefficient describing the winter-summer difference,
D is a dummy variable (1 in winter, 0 in summer) that
employs the b
ice
coefficient, b
0
is the intercept (representing
the mean summer value) and e is the error term. We then
compared the seasonal model (2 parameters) to the simple
intercept model (1 parameter, b
0
, representing the overall
mean) using the Akaike Information Criterion corrected for
small sample sizes (AIC
c
) (Burnham & Anderson 2002). If the
seasonal model differed from the simple intercept model by
DAIC
c
≥2, we interpreted this result to mean that the time
series showed a seasonal difference. Detailed diagnostic plots
including raw and detrended time series are provided in
Figure S4 for one example lake (Big Muskellunge Lake, chl
a). For 194 of the 238 available time series (82%), residuals
from eqn 1 were not autocorrelated at lag 1 according to the
Box-Ljung test, and this is demonstrated by the partial auto-
correlation plot of the detrended+deseasoned data (Fig. S4).
For the other 44 time series, we added a first-order autocorre-
lated error structure to eqn 1. The percent of time series hav-
ing winter values greater than summer values, or vice versa,
was tabulated by variable.
Winter-summer correlations within lakes
Using the same univariate, contiguous, moving average
detrended time series as above (those with > 10 winter values),
we examined temporal correlations between winter and sum-
mer. These included: (1) correlations between winter and the
previous summer season (summer
t1
), or summer-into-winter
(SW) correlations; and (2) correlations between winter and
the subsequent summer (summer
t+1
), or winter-into-summer
(WS) correlations. We determined the sign of seasonal corre-
lations, if present, using a simple model of the detrended data
Y
winter; t
¼ b
sw
Y
summer;t1
þ b
0
þ e ð2Þ
where t is the index of the time series and b
SW
is the slope of
the relationship between winter and the previous summer. If
this SW correlation model did not show AIC
c
improvement
> 2 AIC
c
units compared to the intercept model (1 parameter,
b
0
, representing the overall mean), the time series was
interpreted as not seasonally correlated. We then sepa-
rately evaluated the corresponding WS correlation model,
Y
summer,t+1
= b
WS
*Y
winter,t
+ b
0
+ e, also using AIC
c
.A
minority of these SW and WS correlation models produced
autocorrelated residuals, and to these we added a first-order
autocorrelated error structure, although this modification did
not change the model selection nor the sign of b
SW
or b
WS
for
any time series. Here a positive WS correlation indicates that
high summer values follow high winter values, or low summer
values follow low winter values. Alternatively, a negative WS
correlation indicates anti-persistence, such that low summer
values follow high winter values, or high summer values fol-
low low winter values. As examples, we illustrate the pres-
ence/absence of winter-summer correlations for every chl a
time series, including SW correlations (Fig. S5) and WS corre-
lations (Fig. S6). The percent of time series having positive/
negative SW correlations or positive/negative WS correlations
was tabulated by variable (Table S5).
RESULTS
Seasonal differences across lakes
Indicators of plankton biomass were lower in the winter than
during the summer. Across lakes and latitude, average winter
chlorophyll a ( SE) (5.87 0.88 lgL
1
, Fig. 2) in the pri-
mary data ranged much more widely than in those from our
literature survey (Fig. S2), although still significantly lower
than that of summer (13.6 2.84 lgL
1
, P < 0.0001,
© 2016 The Authors. Ecology Letters published by CNRS and John Wiley & Sons Ltd.
102 S. E. Hampton et al. Review and Synthesis