Water clarity and temperature effects on walleye safe harvest: an empirical test of the safe operating space concept

Abstract

Successful management of natural resources requires local action that adapts to larger‐scale environmental changes in order to maintain populations within the safe operating space (SOS) of acceptable conditions. Here, we identify the boundaries of the SOS for a managed freshwater fishery in the first empirical test of the SOS concept applied to management of harvested resources. Walleye (Sander vitreus) are popular sport fish with declining populations in many North American lakes, and understanding the causes of and responding to these changes is a high priority for fisheries management. We evaluated the role of changing water clarity and temperature in the decline of a high‐profile walleye population in Mille Lacs, Minnesota, USA, and estimated safe harvest under changing conditions from 1987 to 2017. Thermal–optical habitat area (TOHA)—the proportion of lake area in which the optimal thermal and optical conditions for walleye overlap—was estimated using a thermodynamic simulation model of daily water temperatures and light conditions. We then used a SOS model to analyze how walleye carrying capacity and safe harvest relate to walleye thermal–optical habitat. Thermal–optical habitat area varied annually and declined over time due to increased water clarity, and maximum safe harvest estimated by the SOS model varied by nearly an order of magnitude. Maximum safe harvest levels of walleye declined with declining TOHA. Walleye harvest exceeded safe harvest estimated by the SOS model in 16 out of the 30 yr of our dataset, and walleye abundance declined following 14 of those years, suggesting that walleye harvest should be managed to accommodate changing habitat conditions. By quantifying harvest trade‐offs associated with loss of walleye habitat, this study provides a framework for managing walleye in the context of ecosystem change.

Full text

Water clarity and temperature effects on walleye safe harvest: an
empirical test of the safe operating space concept
GRETCHEN J. A. HANSEN,
1,6

LUKE A. WINSLOW,
2
JORDAN S. READ,
3
MELISSA TREML,
1
PATRICK J. SCHMALZ,
4
AND STEPHEN R. CARPENTER
5
1
Division of Fish and Wildlife, Minnesota Department of Natural Resources, St. Paul, Minnesota, USA
2
Department of Biological Sciences, Rensselaer Polytechnic Institute, Troy, New York, USA
3
U.S. Geological Survey Water Resources Mission Area, Middleton, Wisconsin, USA
4
Division of Fish and Wildlife, Minnesota Department of Natural Resources, Duluth, Minnesota, USA
5
Center for Limnology, University of Wisconsin-Madison, Madison, Wisconsin, USA
Citation: Hansen, G. J. A., L. A. Winslow, J. S. Read, M. Treml, P. J. Schmalz, and S. R. Carpenter. 2019. Water clarity and
temperature effects on walleye safe harvest: an empirical test of the safe operating space concept. Ecosphere 10(5):
e02737. 10.1002/ecs2.2737
Abstract. Successful management of natural resources requires local action that adapts to larger-scale
environmental changes in order to maintain populations within the safe operating space (SOS) of acceptable
conditions. Here, we identify the boundaries of the SOS for a managed freshwater fishery in the first empiri-
cal test of the SOS concept applied to management of harvested resources. Walleye (Sander vitreus) are popu-
lar sport fish with declining populations in many North American lakes, and understanding the causes of
and responding to these changes is a high priority for fisheries management. We evaluated the role of chang-
ing water clarity and temperature in the decline of a high-profile walleye population in Mille Lacs, Min-
nesota, USA, and estimated safe harvest under changing conditions from 1987 to 2017. Thermal–optical
habitat area (TOHA)—the proportion of lake area in which the optimal thermal and optical conditions for
walleye overlap—was estimated using a thermodynamic simulation model of daily water temperatures and
light conditions. We then used a SOS model to analyze how walleye carrying capacity and safe harvest relate
to walleye thermal–optical habitat. Thermal–optical habitat area varied annually and declined over time due
to increased water clarity, and maximum safe harvest estimated by the SOS model varied by nearly an order
of magnitude. Maximum safe harvest levels of walleye declined with declining TOHA. Walleye harvest
exceeded safe harvest estimated by the SOS model in 16 out of the 30 yr of our dataset, and walleye abun-
dance declined following 14 of those years, suggesting that walleye harvest should be managed to accommo-
date changing habitat conditions. By quantifying harvest trade-offs associated with loss of walleye habitat,
this study provides a framework for managing walleye in the context of ecosystem change.
Key words: adaptation; climate change; ecosystem change; fisheries; harvest; lake; Mille Lacs; oligotrophication; safe
operating space; thermal–optical habitat; walleye; water clarity.
Received 3 July 2018; revised 19 March 2019; accepted 22 March 2019. Corresponding Editor: Tobias van Kooten.
Copyright: ©2019 The Authors. This is an open access article under the terms of the Creative Commons Attribution
License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
6
Present address: Department of Fisheries, Wildlife, and Conservation Biology, University of Minnesota, St. Paul,
Minnesota, USA.
E-mail: ghansen@umn.edu
INTRODUCTION
Freshwater resources are threatened by environ-
mental change, including climate change, land-use
change, invasive species, and harvest (Carpenter
et al. 2011). Ecosystem responses to these drivers
of global change may be non-linear, responding
gradually until a tipping point or threshold is
reached from which recovery can be difficult or
impossible (Scheffer et al. 2015, Carpenter et al.
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2017).Thesafeoperatingspace(SOS)conceptfor
managing ecosystems identifies the boundaries of
acceptable conditions that are defined by interac-
tions between continental or global scale drivers
and local management (Scheffer et al. 2015). The-
ory suggests that by following the boundaries of
the SOS, local management actions can be
adjusted in response to environmental change to
maintain ecosystem services and increase resili-
ence. However, empirical tests of this important
resilience concept on scales relevant to natural
resource decision-making are lacking (Carpenter
et al. 2017). Here, we present an empirical test of
the SOS concept based on walleye (Sander vitreus),
an economically and ecologically important fresh-
water fish species. We estimate the effect of chang-
ing habitat on sustainable harvest of walleye,
identify the boundaries of the SOS for walleye har-
vest as a function of habitat, and show that safe
harvest levels based on the SOS differ from those
based solely on traditional fisheries models.
Walleye prefer low water clarity (Ryder 1977)
and cool temperatures (Christie and Regier
1988). Walleye are low-light specialists due to a
specialized retinal structure known as the tape-
tum lucidum that develops during the first year of
life and allows them to successfully forage in
dim conditions (Ali and Anctil 1977, Vandenbyl-
laardt et al. 1991). For most lakes, Secchi depths
of 2–3 m are optimal for walleye (Lester et al.
2004), and increasing clarity above this range
reduces optical habitat area. Thermal habitat area
can be positively affected by water temperature
due to increased growing season duration
(Fig. 1), or negatively affected if temperatures
exceed upper thermal limits. A lake’s clarity, tem-
perature, and bathymetry determine its thermal–
optical habitat area (TOHA), that is, the area of a
lake in which optical and thermal conditions for
walleye overlap. A lake’s TOHA is positively
related to walleye production and catch rates at
broad spatial scales (Lester et al. 2004, Tunney
et al. 2018). Increasing water clarity and warm-
ing temperatures are associated with declining
walleye and increasing Centrarchid (sunfishes
and black bass) populations in lakes throughout
North America (Robillard and Fox 2006, Hansen
et al. 2015, Irwin et al. 2016). It is assumed that
temporal trends in TOHA will influence walleye
carrying capacity and yield (Lester et al. 2004),
but to date, empirical tests of the effects of
changing thermal–optical habitat on walleye
populations are lacking (but see Chu et al. 2004).
Most fisheries models and stock assessments
assume that relationships between stock size and
population rates are stationary, and set harvest
policies accordingly (Walters 1987). However, cli-
mate change, invasive species, harvest, and other
stressors can alter productivity, with important
implications for sustainable harvest policies (Wal-
ters et al. 2008). Sustainable fisheries management
in the 21st century must account for the effects of
global change (Paukert et al. 2016), although few
concrete examples exist of recreational fisheries
management systems that explicitly incorporate
environmental change. The SOS of a recreational
fishery is defined by environmental conditions
and local management, and harvest reductions
may compensate for habitat loss and prevent pop-
ulation collapse as conditions change (Fig. 1; Car-
penter et al. 2017). Under this framework, long-
term harvest is increased by adapting annual har-
vest in response to changing environmental con-
ditions (Fig. 1).
In this study, we quantify relationships between
water clarity and temperature, walleye habitat,
and safe harvest. Our study focuses on Mille Lacs,
Minnesota, USA, where walleye populations have
dramatically declined since the 1990s. Due to the
lake’s popularity and economic importance,
strong social and political pressures exist to
restore walleye in Mille Lacs to support previous
levels of harvest. However, if ecological changes
have altered the productive capacity of the lake,
harvest may need to remain low to maintain a
sustainable fishery. The objectives of this study
were to (1) quantify changes in walleye habitat
area due to changing water clarity and tempera-
ture, and (2) quantify the effects of habitat area
and predators on sustainable walleye harvest
levels in an empirical test of the SOS concept.
METHODS
Study area
Mille Lacs is a large (519 km
2
), shallow (mean
depth =8.7 m), mesotrophic, polymictic lake
located in central Minnesota, USA (46.233,
93.6502). Mille Lacs was historically one of Min-
nesota’s most popular and productive walleye
fisheries, but the walleye population and thus har-
vest has declined since the 1990s (Fig. 2;
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HANSEN ET AL.

Venturelli et al. 2014). The timing of this decline
coincides with many changes, including warming
temperatures (Fig. 2), changes in the fish commu-
nity such as increasing smallmouth bass (Micro-
pterus dolomieu)andfluctuating northern pike
(Esox lucius) abundance (as measured by gillnet
catches in standardized surveys; Fig. 2), the estab-
lishment of an Ojibwe tribal fishery in 1997 when
treaty rights were reaffirmed (Minnesota v. Mille
Lacs Band of Chippewa Indians 1999), and the
invasion of zebra mussels in 2005 and spiny water
flea in 2009 (MN DNR 2018). Notably, a marked
increase in water clarity co-occurred with the
onset of walleye declines, with Secchi depth
changing from an average of 2.5 m from 1977 to
1996 to 3.5 m from 1997 to 2016 (Fig. 2). Other
water quality data are sparse, but suggest that
total phosphorus concentrations were higher in
the 1970s through early 1990s than during the
2000s (Fig. 2; Heiskary and Egge 2016).
Walleye data
Walleye population size in Mille Lacs is esti-
mated annually using a statistical catch at age
(SCAA) model (Schmalz and Treml 2014). The
SCAA model projects population numbers by
sex, age, and length using fishery-dependent and
fishery-independent data. Fishery-independent
data include sex- and age-specific gillnet catch
rates, catch rates of age-0 and age-1 walleye from
fall electrofishing, and six independent mark–
recapture population estimates. Outputs from
the SCAA model were used as observations in
the SOS model (described below). Relevant out-
puts used here include annual population esti-
mates of age-3 and older walleye and total
walleye kill from 1987 to 2017 (Fig. 2). Total kill
includes walleye harvested by tribal fisheries,
walleye harvested by recreational anglers
(estimated from non-uniform probability access-
based creel surveys; Pollock et al. 1994), and
walleye killed via hooking mortality in the recre-
ational fishery (estimated from creel surveys and
a temperature-dependent statistical model;
Reeves and Bruesewitz 2007). For brevity, these
three sources of walleye mortality are collectively
referred to as harvest throughout. The SCAA safe
harvest limit was set at 24% of the biomass of
walleye ≥35.6 cm (14 in) in total length from 1997
to 2014 (Minnesota v. Mille Lacs Band of Chip-
pewa Indians 1999). Actual harvest quotas were
negotiated based on these SCAA limits as well as
additional information, and total walleye kill was
always lower than SCAA safe harvest limits dur-
ing this period (M. Treml, unpublished data).
Declining populations have led to increasingly
strict walleye harvest regulations in the late 2000s
(Schmalz et al. 2011), and recreational harvest has
been closed at various times from 2015 to 2017.
Optical, thermal, and thermal–optical habitat
area
To estimate changes in walleye habitat area, we
quantified optical, thermal, and TOHA for Mille
Lacs for each day of 1980–2016. We used a combi-
nation of observed data, hydrodynamic modeling,
and statistical modeling to reconstruct thermal–
optical parameters. Water clarity was measured
by Secchi depth (Appendix S1: Table S1) and con-
verted to daily light extinction coefficients using a
non-linear hierarchical model (Appendix S1).
Daily water temperature profiles were estimated
using an open-source hydrodynamic model
(General Lake Model v2.2; Hipsey et al. 2019),
modified to incorporate daily estimates of light
attenuation. The temperature model was cali-
brated to in situ temperature data using a Nelder-
Mead gradient descent algorithm, whereby the
overall root-mean-squared error (RMSE) was
minimized by altering model parameters (Appen-
dix S1: Table S2; final RMSE of 1.26°C).
Daily water temperature and clarity estimates
were combined to calculate daily TOHA following
Lester et al. (2004), with minor modifications as
described in Appendix S1 (for R code, see Winslow
et al. 2017). Thermal habitat area was defined by
temperatures for which simulated walleye growth
rateswerewithin50%ofthemaximumfrom
bioenergetics model simulations (11–25°C; Lester
et al. 2004). We calculated thermal habitat area as
lake benthic area for which water temperature fell
within this range. Mille Lacs does not stratify, so
habitat area calculations included the entire lake
bottom. Optical habitat area was defined as lake
benthic area for which estimated light levels fell
between 8 and 68 lux (Ryder 1977, Lester et al.
2004). Thermal habitat area, optical habitat area,
and the combination (TOHA) were expressed as
the total benthic area satisfying the aforementioned
criteria for each day. Daily estimates were summed
to calculate annual habitat area estimates. This total
annual area estimate was divided by the total
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HANSEN ET AL.

Day of year
Day of year Day of year
Safe
operating
space
Thermal-optical habitat
Walleye harvest
Walleye harvest
Time
Gradual response to
environmental change
Constant
harvest
Collapse
Partial
recovery
Collapsed fishery - outside
safe operating space
Environmental change
Collapse
Partial
recovery
Alternative
adaptation
pathway
Thermal habitat
A. Calculating thermal-optical habitat
B. The safe operating space
Thermal-
optical
habitat
Optical
habitat
Proportion of
lake bottom
Longer growing
season increases
Lack of suitable
light conditions
decreases TOHA
Proportion of
lake bottom
Proportion of
lake bottom
TOHA
Warming
temperatures
Increasing
water clarity
Fig. 1. (A) Thermal–optical habitat was calculated for each day as the proportion of lake bottom area with both
optimal thermal and optical conditions and summed across all days of each year. In an unstratified lake that does
not usually exceed upper thermal limits for walleye such as Mille Lacs, the entire lake bottom is thermally opti-
mal for each day that temperatures fall within the optimal range, and warming temperatures increase this dura-
tion (but can also cause water temperatures to exceed thermal limits for optimal growth on some days). Optical
habitat changes daily and seasonally as a result of diurnal and seasonal sun angle and seasonality of water clar-
ity. In Mille Lacs, increasing water clarity reduces optical habitat as conditions become too bright throughout the
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HANSEN ET AL.

benthic area times the number of days in the year.
Thus, habitat area is expressed as the proportion of
the maximum potential habitat area averaged
across the entire year (Fig. 1A). Three-year moving
averages of annual TOHA were used as inputs to
the walleye population model.
Walleye population model and the safe operating
space
We assessed the effects of habitat area on wal-
leye abundance and harvest using a previously
studied model of fish population dynamics (Car-
penter 2002). This model allows for a SOS (Car-
penter et al. 2017) that is influenced by harvest
and lake conditions. The general form of the pop-
ulation models we considered was
xtþ1¼xtexp fx
t;Ht;Pt;bi
ðÞ½exp et
ðÞFt(1)
here f(...) is a particular model form (Eqs. 2a, b), x
t
is the number of age-3 and older walleye in year t,
H
t
is the TOHA (averaged across years t2,
t1, and t), P
t
isthecatchpernetnightofnorth-
ern pike and smallmouth bass from gillnet surveys,
b
i
are fitted parameters, F
t
is the number of walleye
killed by harvest (including hooking mortality),
and e
t
is the model residual error assumed to be
normally distributed, mean 0, variance r
2
esti-
mated from the data, and uncorrelated over time
.
Both x
t
and F
t
were estimated by the SCAA model
using observations from Mille Lacs (Schmalz and
Treml 2014). Models were fit by maximum likeli-
hood and compared using AIC (Akaike 1973).
Two model forms fit the data relatively well:
fxðÞ¼b1xtb2
x2
t
Ht
b3Ptxtð2aÞ
fxðÞ¼b1xtb2
x2
t
Ht
ð2bÞ
Both models include a linear autoregressive
term (b
1
) and a quadratic habitat term (b
2
)
analogous to a logistic equation. Model (2a)
includes a predator term (b
3
) with a linear (i.e.,
Lotka-Volterra) functional response. We consid-
ered more complicated functional responses
(Walters and Martell 2004) and none fitas
well as a linear response. In (2a) and (2b), we
write f(x) instead of f(x
t
,H
t
,P
t
,b
t
) to simplify
notation.
The SOS boundary is the highest possible fish-
ing mortality that still has a positive equilibrium
growth rate for given and fixed values of Hand
P(Carpenter et al. 2017). Solutions to Eq. 3 with
e
t
=0 provide deterministic equilibrium walleye
population sizes.
0¼xexp fxðÞðÞ1

F(3)
The edge of the SOS occurs where the flat line
Fis tangent to the hump-shaped relationship
between population size and population growth
rate as described by Eq. 3. F
s
is the maximum
walleye mortality, and x
s
is the corresponding
walleye population for specificfixed levels of
habitat area and predator biomass. If particular
values x
s
and F
s
are at the edge of the SOS, then
(3) is satisfied and the first derivative of (3) is
zero. Thus, x
s
can be found by solving the first
derivative of (3) with respect to x, which is
0¼d
dxxexp fx
ðÞðÞ
1

F

0¼xd
dxfxðÞ

exp fxðÞðÞþexp fxðÞðÞ1

(4)
Given estimates of the parameters b
i
, (4) is
solved numerically for x
s
using the uniroot()
package in R (R Core Team 2017). Then, F
s
can be
found by solving (3) using x
s
:
Fs¼xsexp fx
s
ðÞðÞ1

(5)
water column for most hours of most days. (B) The safe operating space (SOS) is defined by both habitat and har-
vest. Environmental change such as increasing water clarity and reducing habitat can push the system out of the
SOS (yellow dot), meaning that previously sustainable harvest levels now exceed safe harvest limits and the pop-
ulation collapses (red dot). Harvest reductions can move the system back to the SOS, and harvest will gradually
increase to a new equilibrium (dark blue dot). If harvest is gradually decreased as conditions change (dashed orange
line), total harvest over the time interval (area under the dashed orange curve) will be much larger than if the popula-
tion is allowed to collapse (area under the black line). Even though the final rate of annual harvest is the same in the
final year, the total harvest across all years is greater in the case where harvest adapts to changing habitat.
(Fig. 1. Continued)
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HANSEN ET AL.

Fig. 2. Annual time series of Mille Lacs fishery and ecosystem characteristics. (A) Population size of age-3 and
older walleye, estimated from statistical catch at age (SCAA) model. (B) Total walleye kill (recreational harvest,
hooking mortality, and tribal harvest), estimated from the SCAA model. (C) Catch per net night from assessment
gill nets of northern pike and smallmouth bass, two potential predators and/or competitors of walleye. (D) Med-
ian Secchi depth with 95% quartiles (data collected May–September by Minnesota Department of Natural
Resources and Pollution Control Agency). (E) Median total phosphorus levels with 95% quantiles (data collected
May–September by the Mille Lacs Band of Chippewa and the Minnesota Pollution Control Agency, and down-
loaded from the Water Quality Portal: https://www.waterqualitydata.us/portal/). (F) Mean summer (July–
August–September) air temperatures based on interpolated topoclimatic daily air temperatures: https://
catalog.data.gov/dataset/topowx-topoclimatic-daily-air-temperature-dataset-for-the-conterminous-united-states.
Note that zebra mussels were discovered in 2005.
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HANSEN ET AL.

Starting from observed time series of the wal-
leye population, TOHA, and predators, we esti-
mated the parameters b
i
of (2a) and (2b), as well
as the standard deviation of model errors, by
maximum likelihood. We examined residuals
from the model fits to assess that model errors
were approximately normally distributed and
uncorrelated in time. We then estimated errors of
the b
i
by bootstrapping, using 10,000 random
permutations of residuals with replacement
(Efron and Tibshirani 1993). We then computed a
population of bootstrap estimates of the SOS for
specified values of TOHA or predators.
An estimate of the SOS consists of a pair of
numbers, F
s
and x
s
, representing the maximum
fishing mortality with positive population
growth and the corresponding population size,
respectively. We estimated the boundaries of the
SOS by fitting the model to observed time series,
solving the model for the upper bound of the
SOS, and estimating errors of model parameters
and the SOS by nonparametric bootstrapping.
90% confidence intervals (CIs) for F
s
and x
s
were
approximated by estimating the 95% and 5%
quantiles from values estimated from the 10,000
bootstrapped parameter sets. In a small number
of cases, bootstrapped parameter sets yielded
negative values for the SOS. In these cases, we
set the SOS to zero. Maximum safe harvest at the
SOS (F
s
) and its CI were compared to total wal-
leye kill in Mille Lacs to assess whether the fish-
ery was overharvested based on the SOS
estimates. These differences in harvest were also
compared to change in estimated population size
in the following year to examine whether years
in which walleye were overharvested were fol-
lowed by population declines.
RESULTS
Thermal–optical habitat area for walleye in
Mille Lacs declined over time (Fig. 3). Optical
habitat area was most widespread in 1988 and
1999, when 15% of potential habitat area fell
within preferred optical conditions. By contrast,
optical habitat area was most restricted in 1997,
when only 3% of habitat area was optically suit-
able. Thermal habitat area remained relatively
constant over the same time period (Fig. 3). Ther-
mal–optical habitat area declined over time,
driven by changes in optical habitat area.
Thermal–optical habitat area was most restricted
in 1997, and most available in 1988, 1993, and
1999 when over 7% of potential habitat area fell
within preferred light and temperature ranges.
The walleye model without predators fitthe
data slightly better than a model containing
predator abundance (AIC [predators] =97.49;
AIC [no predators] =95.69). Here, we present
results for the model without predators; see
Appendix S2 for results of the model including
predators. The walleye population model was
able to recreate population trends (Appendix S2:
Fig. S1). The autoregressive parameter and the
effect of TOHA on carrying capacity were both
positive (Appendix S2: Table S1). Maximum safe
harvest at the SOS boundary (F
s
) was positively
and non-linearly related to TOHA (Fig. 4). Popu-
lation size at the SOS boundary (x
s
) was also posi-
tively related to TOHA (Appendix S2: Fig. S2).
Small changes in habitat led to relatively large
changes in safe harvest level—for example, when
TOHA was 6.5% of lake area, maximum safe
harvest was approximately 430,000 walleye. If
Fig. 3. Three-year moving average of walleye habi-
tat, in terms of (A) optical (6-68 lux), (B) thermal
(11–25°C), and (C) thermal–optical (both 6-68 lux and
11–25°C) habitat in Mille Lacs. Habitat metrics are
shown as proportion of total available lake benthic
area over time.
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HANSEN ET AL.

habitat area declined by half (TOHA =3.2%),
maximum safe harvest dropped to less than a
quarter of peak values to under 100,000 wall-
eye. Actual harvest exceeded the maximum likeli-
hood predicted safe harvest in 16 of 30 yr, and
exceeded upper bootstrapped 90% CIs in 3 yr
(1992, 1996, and 1998). In recent years (2013–2016),
harvest has been well below estimated safe har-
vest levels. Walleye abundance declined follow-
ing 14 of the 16 yr in which actual harvest
exceeded the maximum safe harvest estimated
by the SOS model (Fig. 5). Population increases
were observed in 10 yr out of the time series,
and in 8 of these years, the previous years’
harvest fell below estimated safe levels.
DISCUSSION
The SOS for fisheries defines the range of con-
ditions that maintains fish biomass and harvest
at acceptable levels even as the environment
changes (Carpenter et al. 2017). We identified the
SOS for walleye populations in Mille Lacs as a
function of habitat (TOHA) and walleye harvest
in the first empirical test of the SOS concept
applied to the management of harvested
resources of which we are aware. Walleye habitat
area in Mille Lacs declined over the past several
decades, with important implications for fish-
eries management. The historical range of TOHA
resulted in estimated safe walleye harvest levels
that varied by nearly an order of magnitude.
Walleye mortality in Mille Lacs exceeded mean
safe levels based on TOHA in about half of the
Fig. 4. Walleye harvest (in 100,000s of walleye) as a
function of thermal–optical habitat area. Maximum
safe harvest at the safe operating space across a theo-
retical gradient of habitat values estimated from maxi-
mum likelihood parameter estimates (black line) and
90% confidence intervals (CIs) estimated from 10,000
bootstrapped parameter sets (gray band) based on the
SOS model. Walleye kill from 1987 to 2016 is also
shown as a function of estimated thermal–optical habi-
tat in each year (three-year moving averages). Colored
points represent walleye harvest relative to the maxi-
mum safe harvest generated from the SOS model (red,
harvest exceeded safe harvest; green, harvest was less
than safe harvest). Filled circles represent years in
which actual harvest fell outside the 90% CIs of safe
harvest estimated by the SOS model.
Fig. 5. Walleye harvest relative to estimated maxi-
mum safe harvest (x-axis) versus change in walleye
abundance the following year (y-axis). Quadrants indi-
cate years where the population was overharvested
and declined (red), overharvested and increased (yel-
low), harvested within safe limits and increased
(green), and harvested within safe limits and
decreased (blue). Years are harvest years. Lines are
90% confidence intervals (CIs) of the x-axis values, rep-
resenting uncertainty in safe harvest levels. Filled cir-
cles represent years in which actual harvest fell
outside (either above or below) the 90% CIs of safe
harvest estimated by the SOS model.
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HANSEN ET AL.

past 30 yr, though uncertainty surrounding these
safe harvest estimates is high. In the majority of
cases where harvest exceeded estimated safe
levels, the walleye population declined in the fol-
lowing year. Similarly, population increases were
more likely to occur following years in which
harvest fell within estimated safe levels. The
major exception to these patterns occurred fol-
lowing harvest year 1990, when the walleye pop-
ulation increased in 1991 due to much higher
than average recruitment to the fishery in spite of
overharvest. The walleye population also
declined in five years for which harvest fell
within safe levels (blue quadrant in Fig. 5),
although the magnitude of these decreases was
small, indicating other sources of mortality not
accounted for in our analysis. While TOHA and
harvest cannot explain all variation in walleye
populations, accounting for TOHA in harvest
decisions makes harvest less risky and more
likely to stay within the SOS.
In response to observed walleye population
declines, walleye mortality has been well below
estimated safe harvest levels in recent years
(2013–2016). Based on our population model
incorporating TOHA, such precautionary man-
agement should allow the walleye population to
increase, depending on future habitat availabil-
ity. Note that maximum safe harvest levels and
population size at SOS are equilibrium values for
afixed TOHA value (x-axis in Fig. 4) and do not
account for annual dynamics of TOHA. Further-
more, our model does not account for all poten-
tial drivers of walleye population abundance,
such as population, food web, or ecosystem pro-
ductivity changes associated with invasive zebra
mussels (Irwin et al. 2016) or spiny water flea
(Strecker et al. 2011) beyond what is captured by
changing water clarity, and therefore may over-
estimate the walleye production that could cur-
rently be supported. Continued precautionary
management and monitoring will help elucidate
whether changes in TOHA are the main driver of
walleye declines.
Increasing water clarity was the main driver of
changing TOHA. Several mechanisms could
account for this increase. Total phosphorus
declined from 1992 to 2005–2013, and improve-
ments to septic systems and land use around the
lake may have played a role (Heiskary and Egge
2016). Zebra mussels increase water clarity
(Higgins and Vander Zanden 2010) and hence
optical habitat area (Geisler et al. 2016), but
zebra mussels were discovered in Mille Lacs in
2005 and cannot explain the observed increase in
water clarity in the 1990s. Water clarity peaked
in 2013, suggesting that zebra mussels may have
further increased water clarity once they estab-
lished. Thermal habitat area was relatively unaf-
fected by increasing temperatures; Mille Lacs
water temperatures exceeded 25°C in only
12 days of the 30 yr modeled here. However,
changes in thermal habitat as defined by optimal
growth conditions may not correlate with
changes in fish populations. For example,
increasing temperatures are associated with wal-
leye declines in inland lakes (Robillard and Fox
2006, Hansen et al. 2017), despite increased wal-
leye thermal habitat area in most lakes as climate
warms (Fang et al. 2004). As the climate contin-
ues to warm, the number of days per year
exceeding walleye thermal tolerance will increase
and may negatively influence survival and
growth of walleye in the future.
The response of TOHA to changing conditions
depends on lake characteristics including mor-
phometry, historical baseline, and stratification,
although on average across all lakes TOHA is
optimized at Secchi depths of 2 m (Lester et al.
2004). Mille Lacs is shallow and well-mixed lake,
and historic Secchi depths were around the opti-
mum value of 2 m. These factors increase sensi-
tivity to increased water clarity and likelihood of
impacts to walleye (Geisler et al. 2016). The tra-
jectory of Mille Lacs in terms of ecosystem and
fish community changes appears to be similar to
what has been documented in Lake Oneida
(New York, USA), another high-profile walleye
fishery which has undergone dramatic changes
in recent decades (Irwin et al. 2016), suggesting
that these dynamics may not be unique. Still,
other lakes with more complex bathymetries and
different trophic status may respond differently
to changing conditions.
Lakes with more TOHA support higher wal-
leye biomass and harvest (Christie and Regier
1988, Lester et al. 2004, Tunney et al. 2018),
although changes in TOHA over time have rarely
been quantified or linked directly to walleye
abundance (but see Chu et al. 2004, Jones et al.
2006). Water clarity and TOHA affect walleye
populations through a number of pathways.
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HANSEN ET AL.

Walleye are more active in low-light conditions
(Ryder 1977), and increased water clarity is asso-
ciated with a shift from feeding during the day
in turbid water to crepuscular or nocturnal feed-
ing in clear water (Ali et al. 1977). Recent
research has also demonstrated that walleye pop-
ulations in lakes with low water clarity can
access multiple prey sources and achieve higher
biomass compared to lakes with high water clar-
ity (Tunney et al. 2018). As water clarity
increases and TOHA decreases, walleye may be
restricted to offshore and deepwater habitats
throughout most daylight hours. If energy
resources in these habitats are limiting (as is
likely to be the case in a system invaded by zebra
mussels, Higgins and Vander Zanden 2010),
populations are likely to be negatively affected
by increasing water clarity. Understanding the
mechanisms through which changes in water
clarity affects walleye behavior, growth, and
population dynamics and how such responses
differ among lakes is a fruitful area of future
research.
Successful fisheries management requires
accounting for climate change and other global
and regional stressors (Paukert et al. 2016). Sus-
tainable harvest policies can differ substantially
as ecosystem productivity changes (Walters et al.
2008). Changes in habitat area can alter popula-
tion growth rates such that harvest levels that
were once sustainable are no longer so (Carpen-
ter et al. 2017). Our results suggest that altering
harvest in response to changing conditions may
allow Mille Lacs to retain its function as a wal-
leye fishery. Our model estimates safe harvest
levels as a function of walleye stock size and
TOHA averaged over the previous three years,
and could be run annually to estimate safe har-
vest. Continued monitoring of water clarity and
temperature is relatively inexpensive and is
already a part of standard monitoring of Mille
Lacs and many other lakes; these data can be
used to adjust harvest in response to environ-
mental changes. Of course, a management
regime that adjusts harvest based on environ-
mental changes will require flexible structures
and institutions that can adapt to change (Green
et al. 2017), as well as a commitment to sustain-
ing walleye populations over the long term.
Accepting harvest reductions is socially and
politically difficult, and will require coordination,
communication, and collaboration among stake-
holders, policy makers, and scientists (i.e., adap-
tive governance; sensu Folke et al. 2005).
However, under rapidly changing conditions, the
potential for exploitation is constrained and
reductions in harvest can facilitate adaptation
(Roberts et al. 2017). Our results, like all models
fit to empirical data, are bounded by the range of
variability in our dataset and the assumptions in
our model. Parameter estimates and manage-
ment implications may change if critical variables
move outside the range we have previously
observed. Therefore, sustained monitoring is
essential for managing walleye and adapting to
rapid and uncertain ecosystem change.
Theories of global change suggest the need for
approaches based on a SOS for living resources,
whereby harvest or other local variables are
adjusted to compensate for large-scale changes in
climate or other drivers (Scheffer et al. 2015, Car-
penter et al. 2017). This study uses field observa-
tions to estimate the SOS, explain changes in
walleye stocks in relation to the SOS, and suggest
local changes in harvest that could sustain a
valuable walleye stock in its SOS for the long
term. We thereby demonstrate empirically a gen-
eral approach that could be used to sustain
diverse living resources in a time of extensive
long-term environmental change (USGCRP 2018).
ACKNOWLEDGMENTS
Thanks to the numerous MN DNR, GLIFWC, Mille
Lacs Band of Ojibwe, and Fond du Lac Band of Lake
Superior Chippewa staff who collected Mille Lacs data
over the past three decades. Thanks especially to Tom
Jones, Eric Jensen, and Rick Bruesewitz for their
engagement with this work. We appreciate the com-
ments provided by Brian Weidel, two anonymous
reviewers, and the associate editor which greatly
improved this manuscript. Steven Carpenter acknowl-
edges support by awards from NSF DEB-1440297 and
USGS G11AC20456 and G16AC00222. Luke Winslow
acknowledges support from NSF MSB-1638704. Jordan
Read, Gretchen Hansen, and Luke Winslow acknowl-
edge support from the Department of the Interior
Northeast Climate Adaptation Science Center. This
work was supported in part by Sport Fish Restoration
Funds to the MN DNR. Any use of trade, firm, or pro-
duct names is for descriptive purposes only and does
not imply endorsement by the US Government. The
authors declare no conflict of interest.
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HANSEN ET AL.

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Additional Supporting Information may be found online at: http://onlinelibrary.wiley.com/doi/10.1002/ecs2.
2737/full
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