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Limnol. Oceanogr. 9999, 2018, 1–13
© 2018 The Authors. Limnology and Oceanography published by Wiley Periodicals, Inc.
on behalf of Association for the Sciences of Limnology and Oceanography.
doi: 10.1002/lno.11029
Long-term research reveals multiple relationships between
the abundance and impacts of a non-native species
David L. Strayer,
1,2
Christopher T. Solomon,
1
Stuart E. G. Findlay,
1
Emma J. Rosi
1
1
Cary Institute of Ecosystem Studies, Millbrook, New York
2
Graham Sustainability Institute, University of Michigan, Ann Arbor, Michigan
Abstract
Non-native species are among the most important drivers of the structure and function of modern ecosys-
tems. The ecological impacts of a non-native species ought to depend on the size and characteristics of its popu-
lation, but the exact nature of this population-impacts relationship is rarely defined. Both the mathematical
form of this relationship (e.g., linear, exponential, and threshold) and the attributes of the invading population
(e.g., density, biomass, and body size) that most efficiently describe its impacts could vary greatly across
invaders, ecosystems, and ecological variables. Knowing the shape of this relationship could improve manage-
ment and help to infer mechanisms of interaction between the invader and ecosystem. We used a long-term
data set on the invasion of the Hudson River ecosystem by two species of Dreissena (the zebra mussel, Dreissena
polymorpha, and the quagga mussel, Dreissena rostriformis) to explore the shape of the population-impacts rela-
tionship for selected ecological variables, including seston, phytoplankton, and several taxa of zooplankton.
Most population-impacts relationships appeared to follow a negative exponential form, but we also found
apparent thresholds and scatterplots for some variables. Including information on the traits of Dreissena (body
size and filtration rate) often substantially improved models of impacts. We found only slight evidence that the
resistance of the Hudson River ecosystem to the Dreissena invasion might be increasing over time. Our results
suggest important refinements to widely used conceptual models of invasive species impact, and indicate that
defining the population-effects relationship will be essential in understanding and managing the impacts of
non-native species.
Non-native species are one of the most important drivers of
the structure and function of modern ecosystems, affecting
everything from population genetics to biogeochemical cycles
(e.g., Strayer 2010; Lockwood et al. 2013). The most common
way to assess the impacts of a species invasion has been to
compare the ecosystem before and after invasion; that is, to
treat the invading population as a binary variable (either pre-
sent or absent). However, there may be substantial variability
in impacts after the invasion as a result in changes in the size
or traits of the invader’s population.
Parker (1999) proposed to incorporate this variation by
describing the impact of a non-native species as:
Impact I
ðÞ
¼abundance A
ðÞ
×range R
ðÞ
×per capita effect E
ðÞ
Although appealing, this equation has several possible short-
comings. For instance, impacts may not be a linear function of
abundance (Fig. 1). Although abundance is most obviously inter-
preted as population density, some other measure of the abun-
dance of the invader (e.g., biomass, % cover) may more
effectively describe its impacts. If the per capita effect term is to
be understood as something other than a catch-all to be inter-
preted post hoc after observing impacts, then we must consider
the possibility of changing per capita effects as a result of
changes in traits of the invader or resistance of the ecosystem.
Parker et al. did recognize some of these complications in their
original paper, but subsequent authors have not always consid-
ered these nuances, and the Parker et al. equation often is
quoted uncritically.
Why does the form of the relationship between the
invader’s population and the impacts on the ecosystem mat-
ter? In addition to any interest this relationship may have for
*Correspondence: strayerd@caryinstitute.org
Special Issue: Long-term Perspectives in Aquatic Research.
Edited by: Stephanie Hampton, Matthew Church, John Melack and Mark
Scheuerell.
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.
Additional Supporting Information may be found in the online version of
this article.
1
academic invasion ecologists, the details of this relationship
are of the highest importance to management (e.g., Yokomizo
et al. 2009). Consider the simple question of whether it would
be worthwhile to spend a certain amount of money to cut the
invader’s population by 50%. As Fig. 1 shows, a 50% reduc-
tion in an invader’s population could reasonably be expected
to have an effect of anywhere between 0% and 100%, or be
completely unpredictable, depending on the form of this rela-
tionship. Without knowing something about the form of the
relationship between the invader’s population and ecosystem
structure and function, it is difficult to evaluate proposed
management actions (Yokomizo et al. 2009). Additionally,
knowing the shape of the population-impacts relationship
may reveal fundamental information about the mechanisms
by which the invader influences other species or processes in
the ecosystem.
There are many ways by which invasion ecologists might
test and refine alternative models of invasion impacts,
including direct experimentation, modeling, cross-system
comparisons, and long-term studies (cf. Carpenter 1998;
Vander Zanden et al. 2017). Here, we use long-term data
from the Hudson River ecosystem to compare alternative
models of how the invasion of Dreissena spp. (the zebra mus-
sel, Dreissena polymorpha, and the quagga mussel, Dreissena
rostriformis) affected the Hudson River ecosystem.
Specifically, we compare the effectiveness of several kinds
of models to describe the impact of Dreissena. First, we com-
pare models based solely on the presence or absence of the
invader with models that include some measure of its abun-
dance. Although it seems obvious that models including some
measure of abundance would outperform presence–absence
models, presence–absence ( = before/after invasion designs)
are very common in invasion ecology, either because abun-
dance data are lacking or because such simple models are con-
venient and effective (e.g., Strayer et al. 2008). If the
abundance of the invader varies over a sufficiently wide range,
either over time or across sites, such presence–absence models
will be inadequate to describe these impacts.
Fig. 1. Hypothetical examples of several kinds of possible relationships between population density of an invader and ecosystem characteristics. The
points could represent either conditions at different times in a single place or conditions in different places.
Strayer et al. Population size and impacts of Dreissena
2
Second, we compared models using a linear function of
abundance (as suggested by the Parker et al. formulation) with
a specific nonlinear model (a negative exponential function).
Although linear models are simple and widely used, they are
likely to be inappropriate for many kinds of interactions
between invaders and the ecosystems they invade (Yokomizo
et al. 2009; Thiele et al. 2010; Vander Zanden et al. 2017). For
instance, the impacts of suspension feeders like Dreissena are
more likely to follow a negative exponential form than be lin-
ear with Dreissena density (e.g., Caraco et al. 2006; Higgins
and Vander Zanden 2010).
Third, we compared models that included some informa-
tion on the traits of the invader with models based solely on
abundance. Individuals within an invading species often
vary in traits such as body size, gape width, chemical con-
tent, and so on, in ways that affect their roles within an eco-
system. Body size of Hudson River Dreissena has varied
considerably from year to year (Strayer and Malcom 2014),
which could have two important consequences. To begin
with, filtration rate is a nonlinear function of body size
(Kryger and Riisgard 1988), so a population of large animals
filters more water than a population of small animals of the
same population density. In addition, there is some evidence
that large Dreissena can capture a different mix of particles
than small Dreissena,andspecificallyaremoreeffectiveat
capturing zooplankton (MacIsaac et al. 1995). Therefore, we
compared models based on population density with those
that were based on filtration rates, and those that included
only filtration rates of the largest animals.
Fourth, we searched for evidence that the Hudson ecosys-
tem has developed resistance to the Dreissena invasion over
time, so that per capita Dreissena impacts have declined. There
is a persistent idea in invasion ecology that ecosystems might
become more resistant to an invader over time as species
already in the ecosystem develop morphological or behavioral
defenses against the invader, incorporate the invader into
their diets, and so on (e.g., Carlsson et al. 2009; Strayer 2012;
Iacarella et al. 2015; Langkilde et al. 2017), or as new enemies
of the invader arrive in the ecosystem.
Finally, we close by using the results of these comparisons
to extend Parker et al.’s framework for describing the impacts
of non-native species.
The study area
The study area is the freshwater tidal section of the Hudson
River in eastern New York, extending from RKM 99–247
(i.e., river kilometers from the mouth of the river at The Bat-
tery in New York City). This part of the Hudson averages
900 m wide and 8 m deep, and is well mixed by strong tidal
currents, which prevent stratification. Mean annual discharge
is ~ 500 m
3
/s, depending on location along the river, but tidal
flows usually are much larger than net freshwater flows down-
river. Mean water residence time during the growing season in
the years of our study was 3–17 weeks. The river bottom is
predominately sand or mud, although ~ 7% of the area is
rocky; these rocky areas support most of the Dreissena popula-
tion. The water is turbid (Secchi transparency ~ 1 to 2 m,
chiefly a result of suspended silt), moderately hard (pH ~ 8,
Ca ~ 20 to 25 mg/L) and rich in nutrients (TP ~ 80 μg/L, NO
3
-
N ~ 400 μg/L). Allochthonous inputs dominate the organic
carbon budget, although autochthonous production by phyto-
plankton and rooted plants can be important locally or to
parts of the food web (Caraco et al. 2010; Cole and Solomon
2012). Bacterial production greatly exceeds phytoplankton
production (Findlay 2006). Dominant species include diatoms
and cyanobacteria in the phytoplankton; rotifers, cyclopoids,
and Bosmina in the zooplankton; bivalves and oligochaetes in
the zoobenthos; and young-of-the-year of Alosa and Morone in
the fish. Further information about the freshwater tidal Hud-
son is available in Levinton and Waldman (2006).
The zebra mussel, D. polymorpha,appearedintheHudsonin
1991 and quickly developed a large population; by the end of
1992, the biomass of zebra mussels exceeded the biomass of all
other heterotrophs in the ecosystem (Strayer et al. 1996). We
observed large and pervasive effects of zebra mussels throughout
the Hudson River ecosystem, including on water chemistry and
clarity (Caraco et al. 1997, 2000), bacterioplankton (Findlay
et al. 1998), phytoplankton (Caraco et al. 1997, 2006), zoo-
plankton (Pace et al. 2010), zoobenthos (Strayer et al. 2011;
Strayer and Malcom 2014), and fish (Strayer et al. 2014b). Zebra
mussels have caused similarly large and wide-ranging impacts in
many other freshwater ecosystems (reviewed by Higgins and
Vander Zanden 2010). A second species of Dreissena, the quagga
mussel (D. rostriformis,formerlycalledDreissena bugensis)
appeared in the Hudson in 2008, although it still constitutes
< 10% of the combined Dreissena population in the river
(Strayer and Malcom 2014, and unpubl.). In this article, we
combine the two species as Dreissena spp.
Methods
We analyzed the responses of suspended particulate inor-
ganic matter (PIM), phytoplankton biomass, tintinnid ciliates
(henceforth, “ciliates”), rotifers, nauplii, cladocerans, and
copepods to different densities of Dreissena, as expressed by
the presence, population density, aggregate filtration rate, and
filtration rate of the largest animals (shell length > 20 mm) of
Dreissena. We chose particulate inorganic matter as a variable
that we expected to be unaffected by Dreissena. These mussels
do take up particulate inorganic matter, but it is egested in
feces and pseudofeces and rapidly resuspended into the water
column by strong tidal mixing in the Hudson (Roditi
et al. 1997). Thus, we expected to see no effect of Dreissena on
this variable. In contrast, we expected that Dreissena would
cause the other, biotic, variables to decline, either because of
direct ingestion by Dreissena (phytoplankton, ciliates, rotifers,
and nauplii) or because of indirect effects transmitted through
Strayer et al. Population size and impacts of Dreissena
3
the food web (cladocerans and copepods). Furthermore, we
expected that the body size of Dreissena would matter more to
larger, more motile particles than smaller, less motile particles,
in the sequence copepods ~ cladocerans > nauplii ~ rotifers >
ciliates > phytoplankton.
Field and laboratory methods were described in detail by
Findlay et al. (1991), Strayer et al. (1996), Caraco et al. (1997),
and Pace et al. (1998). Briefly, water chemistry and plankton
were sampled during 1987–2016 every 2 weeks during the ice-
free season near Kingston (RKM 151). Water samples for anal-
ysis of seston and chlorophyll were taken from 0.5 m below
the water’s surface using a peristaltic pump. Triplicate samples
for seston were filtered onto precombusted Whatman 934-AH
filters which were dried at 70C for at least 12 h before being
weighed, then combusted at 450C for 4 h and reweighed to
estimate both organic and inorganic particulate matter. Tripli-
cate samples for chlorophyll analysis were filtered onto What-
man GFF filters which were frozen until a basic methanol
extraction was performed and analyzed using a Turner Designs
fluorometer. Microzooplankton were sampled by filtering
water collected using the peristaltic pump through a 35 μm
mesh in the field, and macrozooplankton were sampled by fil-
tering water collected using a calibrated open-diaphragm bilge
pump through a 73 μm mesh in the field. Animals in these
samples were narcotized using carbonated water and preserved
in a buffered 4% formaldehyde solution (60 g/L of sucrose
plus 8.4 g/L of NaHCO
3
) to yield a final formaldehyde concen-
tration of 2%, then counted in the laboratory under an
inverted microscope (microzooplankton) or a dissecting
microscope (macrozooplankton). Data used here are growing
season means (1 May–30 September).
The density, body size distribution, and filtration rate of the
Dreissena population were estimated from samples deployed in
a stratified random design throughout the freshwater tidal
Hudson. Seven hard-bottom sites were sampled by divers in
June (no June samples were taken in 1993, 1994, 1995, or
2000) and August and 44 soft-bottom sites were sampled by
standard (23 by 23 cm) PONAR grab in June–July, then sieved
in the field. Rocks collected by divers and sieve residues from
PONAR samples were sorted in the laboratory, and representa-
tive subsamples of animals were measured (shell length using
calipers and shell-free dry mass after animals were dried for at
least 24 h at 60C). We estimated filtration rates using the
regression of Kryger and Riisgard (1988), which is based on the
body mass of individual mussels, and combined the data from
the different sampling times into a single growing-season
mean. The range of Dreissena in the Hudson has not changed
substantially since 1992 (Strayer et al. 1996, and unpubl.), so
we do not include range in our models (including it would
simply introduce a scaling constant to the models and not
affect any of our conclusions). More than 75% of the Dreissena
population lives in RKM 151–213 (Strayer and Malcom 2006),
immediately upriver from the Kingston station where plankton
samples were taken.
We fit generalized linear models to describe the relation-
ships between the response variables and several measures of
the abundance or potential impact of the Dreissena popula-
tion. We considered both linear models (using an identity link
function) and exponential models (using a log link function)
of Dreissena effects on the response variables. (We did not
attempt to fit any other mathematical functions because our
understanding of suspension-feeding suggested to us that a
negative exponential was the most promising nonlinear func-
tional form.) For both types of models we assumed that obser-
vations were Gamma distributed, given that the response
variables were all bounded by zero with relatively high vari-
ances. We included the freshwater flow of the Hudson as a
covariate in all models, and also fit null models including only
this covariate, because previous work suggests that freshwater
flow is an important predictor of plankton and seston in the
Hudson (e.g., Strayer et al. 2008). We considered using mean
water temperature as an additional covariate, but it was corre-
lated with flow (r=−0.40, p= 0.03, log–log), and including it
often created convergence problems in the fitting algorithm.
The models were fit using the glm() function in R (R Core
Team 2017). We used likelihood profiles to determine 95%
confidence intervals for the parameters of each model using
the confint() function, calculated Nagelkerke’s pseudo-R
2
for
each model using the pR2() function in the pscl package
(Jackman 2017), and compared models using the small-sample
Akaike Information Criterion (AIC
c
).
To test whether the resistance of the Hudson ecosystem to
Dreissena might be changing over time, we plotted the resid-
uals of our best model against year, and tested whether the
linear regression slope was significantly greater than 0 (i.e., a
one-tailed test). If the ecosystem has been getting more resis-
tant to Dreissena, these residuals should rise through time.
Results
The population size of Dreissena, as well as all of the
response variables, varied greatly from year to year over the
course of our study (Fig. 2). The results of the statistical
models are summarized in Fig. 3, with full details in Support-
ing Information Table S1. As expected, the null model (fresh-
water flow only), which did not include any Dreissena-related
variable, was a satisfactory model (i.e., lowest AIC
c
and high
R
2
) only for particulate inorganic matter. Concentrations of
suspended inorganic matter were positively correlated with
freshwater flow and not much affected by Dreissena; adding
Dreissena-related variables to models for suspended inorganic
matter slightly increased AIC
c
over the null model (ΔAIC
c
=
0.6 to 2.7). In contrast, effects of freshwater flow on biotic
variables almost always were negative, though rarely signifi-
cantly different from zero at p= 0.05. Our further description
of the modeling results for the biotic variables, which were
affected by Dreissena, is organized around the five questions
presented in the Introduction.
Strayer et al. Population size and impacts of Dreissena
4
Presence–absence vs. abundance models
Models based on the presence or absence of Dreissena
usually were outperformed by models that included some
measure of the size or traits of the Dreissena population.
The striking exception was for phytoplankton, for which
the presence–absence model had substantially the lowest
AIC
c
. Plots of phytoplankton biomass vs. Dreissena density
or filtration rates (Fig. 4) showed a steep, consistent
decline between pre-invasion years with growing season
meansof17–29 μg chlorophyll a(Chl a)/L and postinva-
sion years with growing season means of 4–11 Chl a/L,
but relatively little interpretable variation in the postinva-
sion years.
Presence–absence models for particulate inorganic matter
and cladocerans were also slightly better than models based
on measures of Dreissena population size or traits. However,
none of these was very good: as just noted, PIM was best pre-
dicted by freshwater flow alone, and cladoceran densities were
not well predicted by either freshwater flow or any of the
Dreissena-related variables that we used (Fig. 3, Supporting
Information Table S1).
Linear vs. nonlinear models
Attempting to fit linear models to the bounded positive
and clearly nonlinear data (Fig. 4) led to convergence prob-
lems in fitting models. Furthermore, linear models assume
a
Fig. 2. Population density of Dreissena and growing season means for response variables at the long-term monitoring station on the Hudson River at
Kingston, 1987–2016. See Methods section for details.
Strayer et al. Population size and impacts of Dreissena
5
constant variance and allow for negative values of the
response variable, but the response variables often had non-
constant variance and of course must always be positive. Fit-
ting linear models to the data led to negative and nonsensical
predicted values of response variable at high Dreissena densi-
ties. Therefore, we abandoned further attempts to fit linear
models to the data, and rejected linear functions of Dreissena
abundance as an appropriate description of impacts.
Population density of Dreissena vs. trait-based approaches
Models using the estimated total filtration rate of the Dreis-
sena population outperformed models using population
density, except in the case of macrozooplankton (copepods
and cladocerans), for which no model performed very well.
The gap between density-based models and filtration-based
models was especially large for rotifers (ΔAIC
c
~ 9). Models
using filtration rate of only the largest Dreissena were better
than models using total population filtration rate for rotifers,
nauplii, and copepods, but substantially worse than models
using total population filtration rate for phytoplankton and
ciliates. There was little difference (ΔAIC
c
< 0.5) among
models based on density, total filtration rate, or filtration rates
of large Dreissena for cladocerans, for which no models
performed well.
Fig. 3. Akaike weights of competing models based on different measures of the Dreissena population for each response variable. Akaike weights indicate
the relative likelihood of each model, given the data, and sum to 1 across the set of candidate models. FR(large) = river-wide filtration rate of large (shell
length > 20 mm) Dreissena, FR(total) = river-wide filtration rate of all Dreissena, and PIM = particulate inorganic matter.
Strayer et al. Population size and impacts of Dreissena
6
a
Fig. 4. Plots of each response variable against Dreissena density, total filtration rate of the Dreissena population, and filtration rate of only the largest
Dreissena. Each point represents the mean value for a year.
Strayer et al. Population size and impacts of Dreissena
7
Development of ecosystem resistance to Dreissena
There is just a hint in the pattern of residuals that ecosys-
tem resistance to the effects of Dreissena may be increasing
over time (Fig. 5). Residuals from the best models for phyto-
plankton, nauplii, and copepods all had positive slopes against
time, although these slopes were only marginally significant
(one-tailed p-values are 0.04, 0.09, and 0.02, respectively). No
variables showed a pattern of declining residuals (suggesting
declining ecosystem resistance) over time.
Discussion
Model agreement with predictions
The results of the model comparisons were mostly consis-
tent with our predictions. As predicted, concentrations of sus-
pended inorganic particles were not strongly related to the
Dreissena population, regardless of the variable that we used to
describe it. For the biotic variables that we expected to be
affected by Dreissena, population density of Dreissena was usu-
ally better than presence as a predictor of impacts. Including
Fig. 5. Residuals from the best model for each dependent variable (i.e., the model having the lowest AIC
c
) plotted against time after the Dreissena inva-
sion. If the ecosystem is developing resistance to the effects of this invader, the residuals should rise through time.
Strayer et al. Population size and impacts of Dreissena
8
some trait information (total filtration rate) usually further
improved the models, and focusing only on the filtration by
large Dreissena improved models for large particles (zooplank-
ton) but not for smaller particles (phytoplankton and ciliates).
This is consistent with the idea that only large-bodied Dreis-
sena can ingest small zooplankton such as rotifers (MacIsaac
et al. 1995), whereas Dreissena of all sizes can ingest small par-
ticles such as phytoplankton and ciliates.
We found only a slight indication that ecosystem resistance
to the Dreissena invasion may be rising in the Hudson, in the
form of rising residuals through time (Fig. 5). Although the
idea of increasing ecosystem resistance to invaders is pervasive
in invasion ecology, it has not yet well tested empirically
(Strayer 2012; Iacarella et al. 2015). More evidence like Fig. 5 is
needed to resolve this question.
Model failures
However, we also found two important deviations from our
expectations. First, impacts on phytoplankton were not
related to any measure of Dreissena population size, but were
well predicted by simply considering the presence of Dreissena.
Phytoplankton biomass declined steeply when Dreissena
appeared in the Hudson, but interannual variation in postin-
vasion years was small and unrelated to any measure of the
Dreissena population that we considered. It is possible that the
Hudson’s phytoplankton are extremely sensitive to grazing
because their growth rates are so slow as a result of severe light
limitation (Cole et al. 1992; Caraco et al. 1997). Because Dreis-
sena did not reduce concentrations of suspended inorganic
matter (Supporting Information Table S1), water clarity rose
only modestly after the Dreissena invasion (Caraco et al. 1997;
Strayer et al. 1999, Strayer et al. 2014a), so phytoplankton
would have been severely light limited even after Dreissena
arrived. If this explanation is correct, the presence–absence
effect that we detected could actually be an extremely steep
negative exponential function that reaches its asymptote at a
very low level of grazing. The fact that the asymptote is not
zero suggests that a fraction of the phytoplankton is either
not captured by Dreissena, or is returned to the water column
undigested as pseudofeces and feces disintegrate. This expla-
nation is consistent with previous work on the Hudson show-
ing that Dreissena biodeposits (feces and pseudofeces) contain
substantial amounts of live algae (Roditi et al. 1997; Bastviken
et al. 1998) that could be resuspended in the turbulent Hud-
son. Alternatively, the relationship between grazing and phy-
toplankton biomass could be a threshold function with the
threshold at low grazing rates. The data (Fig. 4) are consistent
with all three of these interpretations and currently insuffi-
cient to distinguish among them.
The second failure of our modeling is our inability to
describe cladoceran densities; all of our models had low R
2
,
and none contained significant terms for either freshwater
flow or Dreissena (Supporting Information Table S1). We can
suggest two causes for this poor model performance. First,
cladoceran populations in the Hudson, consisting almost
entirely of Bosmina freyi, are extraordinarily dynamic, typically
blooming in June for just a few weeks at densities ~ 100- to
1000-fold above background (Pace and Lonsdale 2006). This
high variability makes our estimates of growing season means
(based on samples taken every 2 weeks) imprecise. Imprecision
in estimating both Bosmina and Dreissena populations may
degrade model performance. Second, it appears that Bosmina
is too large for even large Dreissena to capture effectively
(MacIsaac et al. 1991, 1995), so impacts of Dreissena are indi-
rect, transmitted through the food web. Unsurprisingly,
models of parts of the ecosystem that were affected directly by
Dreissena grazing (phytoplankton, ciliates, and rotifers) tended
to have higher R
2
than models for particles too large for Dreis-
sena to graze, and therefore affected only by indirect pathways
(copepods and cladocerans). Populations of these latter organ-
isms presumably are affected by factors such as predation from
young-of-year fish (Limburg et al. 1997; Pace and Lonsdale
2006) as well as changes in their food supply arising from
Dreissena grazing.
Functional relationships between invaders and ecosystems
The different functional forms shown in Fig. 1 have strik-
ingly different implications for management (cf. Yokomizo
et al. 2009). As we have noted, a control program that reduces
the population of the invader by 50% could nearly eliminate
the impacts of the invader, have no effect on those impacts,
be more than is needed to produce the desired relief from
impacts (“overkill”), or have completely unpredictable effects.
Such programs often require substantial time and money, and
often have harmful side-effects on other species and the envi-
ronment (e.g., Davis 2009, pp. 154–156; Rinella et al. 2009;
Zarnetske et al. 2010). Management undertaken without con-
sidering the functional relationship between the invader’s
population and the ecosystem thus may waste money and
produce unnecessary harm to ecosystems (Yokomizo
et al. 2009).
Is it practical to predict the functional relationships
between invaders and ecosystems without making detailed
measurements on every invader and every ecosystem that is
invaded? This is an open question, but given the diversity and
complexity of the relationships between invaders and ecosys-
tems, it seems unlikely that we will be able to predict such
relationships with precision. Nevertheless, it may be possible
to develop useful predictions by considering the traits of the
invader, the ecosystem, and the response variable being con-
sidered. The easiest cases probably will be those in which a
single direct process links the invader to the ecosystem
(e.g., an invading predator eating a native prey). In such cases,
it may be possible to use laboratory experiments and simple
models to define the functional and numerical response
curves of the actors (e.g., Dick 2017; Laverty 2017) and predict
the shape (linear, exponential, and threshold) and perhaps
even the parameters of the relationship between invader and
Strayer et al. Population size and impacts of Dreissena
9
ecosystem. Suspension feeding by Dreissena and other bivalves
might seem to be a promising example, but even here interac-
tions between grazing, nutrients, and the development of
toxic algae (e.g., Vanderploeg et al. 2001; White et al. 2011;
Horst et al. 2014) complicate matters. Conversely, if the effects
of an invader on one part of an ecosystem are strongly
affected by other parts of the ecosystem, as will be the case for
indirect effects, the relationship between invader and ecosys-
tem may be noisy and even unpredictable. The poor relation-
ships we observed between Dreissena and crustacean
zooplankton in the Hudson may be an example of this, where
factors such as fish predation (Limburg et al. 1997), advection
(Pace et al. 1992), the availability of alternative food resources
(Maguire and Grey 2006), or indirect effects propagated
through the food web may have obscured the effects of Dreis-
sena on the food resources of the crustaceans. Time lags may
also introduce unpredictability and hysteresis into the
invader-ecosystem relationship, whether they arise from dif-
ferent dynamic speeds of the invading population and the
response variable, or from the processes that indirectly link
the invader and the response variable. Thus, predicting the
shape and parameters of the relationships linking invaders
and ecosystem variables may be tractable, but it is not likely
to be easy.
Improving the Parker et al. equation
The simple Parker et al. model failed in two ways as an ade-
quate description of Dreissena impacts in the Hudson. First,
impacts are clearly not a linear function of Dreissena abun-
dance, whether that abundance is expressed as population
density, total population filtration rate, or filtration rate of the
largest animals (Fig. 4). Considering the mechanisms that link
invading species to their ecosystems (see above), we suggest
that nonlinearity is more likely than linearity to be the rule in
invasions (see also Yokomizo et al. 2009; Thiele et al. 2010;
Vander Zanden et al. 2017).
Second, the “per capita impact”term in the Parker
et al. equation is vague, and could benefit from closer exami-
nation. Rather than estimating this term by measuring range,
abundance, and impact and solving the equation for per
capita impact (E=I/[A×R]), it could be fruitful to explicitly
consider what contributes to the per capita impact of a non-
native species, and consider how those factors might vary
across time and space. In general, we might recognize that per
capita impact depends on the traits of the invader and the
resistance of the ecosystem (i.e., its response to a given popu-
lation of an invader, with a particular density and traits).
Many traits could vary over space and time and affect the
impacts of an invader. In the case of Dreissena in the Hudson,
temporal changes in body size were important in modulating
impacts, probably both by affecting filtration rates and by
determining what kinds of particles could be captured (Kryger
and Riisgard 1988; MacIsaac et al. 1995). These changes in
body size allowed partial recovery of some (e.g., rotifers) but
not all (e.g., phytoplankton) parts of the ecosystem towards
pre-invasion conditions. Body size or growth in Dreissena is
affected by predation (Hamilton et al. 1994; Naddafi
et al. 2010), disturbance regimes (MacIsaac 1996; Chase and
Bailey 1999), and food availability (Sprung 1995; Baldwin
2002), and might diminish over time as predators become
more adept at eating the introduced prey, as they have in the
Hudson (Carlsson et al. 2011). Thus, differences in body size
of Dreissena are likely to underlie differences in per capita
impacts across sites and over time. The body size of many
other invaders is likely to change over the course of the inva-
sion and affect their impacts.
Traits other than body size likewise will affect per capita
effects of invaders. The per capita effects of another invader in
the Hudson, the aquatic plant Trapa natans, are determined not
by individual plant size, but by the size of the plant bed: large
beds have much more pronounced effects on dissolved oxygen
and denitrification (Hummel and Findlay 2006). Other invader
traits that might affect per capita impact include nutrient stoi-
chiometry, chemical or morphological defenses against preda-
tion, phenology, virulence, and so on. Incorporating trait
information into models of impacts of invading species will
require careful attention to (and testing of ) the specificmecha-
nisms of interaction between the invader and the ecosystem.
Ultimately, the Parker et al. equation might be improved
either by making it more specific or more general. We have
suggested that it could be made more specific by replacing the
linear form with nonlinear functions where appropriate, and
by being more explicit about what “per capita effects”means,
perhaps even expanding this term into two separate terms to
recognize the distinct roles of invader traits and ecosystem
resistance. In addition, because it is clear that all of the terms
in the equation can vary over time (as they have in the Hud-
son), it would be useful to time index all of the terms in the
equation. Furthermore, because of the likelihood of irrevers-
ible, lagged, or hysteretic effects of invaders, this time index-
ing would have to consider not only the state of the system at
time t, but at all previous times back to t−k, where kis the
depth of the time memory in the system. The resulting equa-
tion would thus be tailored to each invader and ecosystem
being analyzed and would become temporally dynamic.
Conversely, it may be better to write the Parker et al. equa-
tion in a more general form, and to use it simply as an orga-
nizing framework rather than as a formal equation to be
evaluated and solved. In such a case, we might replace
Impact IðÞ¼abundance AðÞ×range RðÞ×per capita effect EðÞ
with
Impact It
ðÞ
¼f abundance At
ðÞ
,range Rt
ðÞ
,per capita effect Et
ðÞ½
and time index all of the variables, as described above. Such a
general formulation would allow for great flexibility and
Strayer et al. Population size and impacts of Dreissena
10
would remind invasion ecologists, ecosystem scientists, and
managers of the factors that need to be considered when ana-
lyzing the effects of an invasion.
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Acknowledgments
The authors are grateful for financial support from the National Sci-
ence Foundation, including the Long-Term Research in Environmental
Biology program (most recently DEB-1556246) and the Hudson River
Foundation, and are deeply indebted to Nina Caraco, Jon Cole, David
Fischer, Heather Malcom, and Mike Pace, who helped design this research
program and contributed many ideas and data over the years. Mark
Scheuerell and two anonymous reviewers provided useful suggestions for
improving the article. The authors also appreciate the contributions of the
many people who collected and analyzed samples since 1987.
Conflict of Interest
None declared.
Submitted 29 January 2018
Revised 27 June 2018
Accepted 26 July 2018
Associate editor: Mark Scheuerell
Strayer et al. Population size and impacts of Dreissena
13