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Cohort Dynamics Give Rise to Alternative Stable Community States.
Author(s): Magnus Huss, André M. de Roos, Anieke Van Leeuwen, Michele Casini, and Anna
Gårdmark
Source: The American Naturalist, Vol. 182, No. 3 (September 2013), pp. 374-392
Published by: The University of Chicago Press for The American Society of Naturalists
Stable URL: http://www.jstor.org/stable/10.1086/671327 .
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vol. 182, no. 3
the american naturalist
september 2013
Cohort Dynamics Give Rise to Alternative
Stable Community States
Magnus Huss,1,* André M. de Roos,2 Anieke Van Leeuwen,2 Michele Casini,3 and Anna Gårdmark1
1. Swedish University of Agricultural Sciences, Department of Aquatic Resources, Institute of Coastal Research, Skolgatan 6, SE-742 42
Öregrund, Sweden; 2. Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, P.O. Box 94248, 1090 GE
Amsterdam, The Netherlands; 3. Swedish University of Agricultural Sciences, Department of Aquatic Resources, Institute of Marine
Research, Turistgatan 5, SE-453 21 Lysekil, Sweden
Submitted July 17, 2012; Accepted March 19, 2013; Electronically published July 18, 2013
abstract: Many ecological systems can exhibit alternative stable
states (ASS), which implies that ecological communities may diverge
depending on their initial state, despite identical environmental conditions. Here we present a new mechanism that can cause ASS in
competition systems. Using a physiologically structured model of
competing populations, representing Baltic Sea sprat and herring and
their resources, we show how cohort-driven population cycles may
result in priority effects leading to ASS. Similar mechanisms could,
depending on mortality level, also result in a “resident strikes back”
phenomenon. We argue that the prerequisites for the occurrence of
ASS in our model system, that is, communities with competing populations exhibiting cohort cycles and variation in size at maturation,
may be common in ecological systems.
Keywords: alternative stable states, competition, herring, mortality,
size structure, sprat.
Introduction
Alternative stable states (ASS), implying that ecological
systems can exist in contrasting states despite identical
environmental conditions, have become a major research
topic in ecology over the past decades (May 1977; Scheffer
et al. 2001). It is currently recognized that many ecosystems are characterized by ASS, whose occurrence has important management implications (Folke et al. 2004; Levin
and Lubchenko 2008). Small changes in external drivers
such as harvesting or nutrient loading may lead to sudden
shifts in ecosystem state, from which recovery may be
difficult despite restored environmental conditions (Scheffer et al. 2001). Sudden regime shifts (which suggest but
do not necessarily imply the existence of ASS) have been
documented in a variety of ecosystems, including fresh* Corresponding author. Present address: Department of Ecology and Evolutionary Biology, Yale University, New Haven, Connecticut 06520; e-mail:
[email protected].
Am. Nat. 2013. Vol. 182, pp. 374–392. 䉷 2013 by The University of Chicago.
0003-0147/2013/18203-53986$15.00. All rights reserved.
DOI: 10.1086/671327
water, marine, and terrestrial environments (Folke et al.
2004). For example, overfishing in marine ecosystems has
in several cases led to sudden shifts in ecosystem state that
may hamper the reestablishment of large predatory fish,
such as collapsed cod populations in the northwest Atlantic and Baltic Sea (Myers and Worm 2003; Casini et al.
2009). Understanding the mechanisms leading to ASS in
ecosystems is therefore crucial for the management of exploited systems such as the world oceans.
The occurrence of ASS implies that ecological communities in identical environments may differ as a function of the initial community state (May 1977). Consequently, the timing of species invasions can in some cases
lead to different community compositions, referred to as
priority effects (Schulman et al. 1983). That is, species
identity may not be the only determinant of competitive
dominance, but also the order of species arrival may matter, as shown both theoretically (Gilpin and Case 1976;
Tilman 1982) and empirically for many different taxa in
competition systems, one example being reef fish, for
which the order of arrival may determine competitive outcome (Warren et al. 2003; Geange and Stier 2009). This
may occur because species that establish early alter the
environment such that species arriving later cannot successfully establish, although they would have done so if
they themselves had been the first to establish.
Although seldom noted, assembly history may influence
not only community composition but also population dynamics (Jiang et al. 2011), rendering ASS that represent
different types of alternative dynamical states (Henson et
al. 2002; Ives et al. 2008). One example of such alternative
dynamical states, established in both theory and experiments, is the existence of small- and large-amplitude cycles
in Daphnia-algal systems under common environmental
conditions (McCauley et al. 2008). In such cases, the characteristic dynamics of ecological systems may change
abruptly after small changes in external drivers. The dynamic behavior of populations, in turn, may affect com-
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Cohort Dynamics and Alternative States 375
munity composition (and hence potentially the occurrence
of ASS). For example, it has been theoretically shown for
competition systems that species that cannot coexist under
constant conditions may do so when populations fluctuate
(Chesson 1994; Huisman and Weissing 1999; Abrams and
Holt 2002). Interestingly, this is valid not only when there
are external drivers causing the variability but also when
variability is caused endogenously (Armstrong and
McGehee 1980; Adler 1990). While implications of size
structure for the occurrence of ASS have been previously
acknowledged (Miller and Rudolf 2011 and references
therein), endogenously generated variability, that is, population cycles, caused by size-dependent interactions has
not been addressed in studies trying to resolve mechanisms
governing community composition and alternative stable
community states.
Another example of how the dynamics of populations
may affect community composition is when mutual invasibility is possible (i.e., all populations experience positive population growth rates when they are rare) but longterm coexistence is not (Chesson 2000). This relates to the
possibility that species may experience alternative attractors. If an invading species, after an initial population expansion, becomes rare again, the ecological system in
which it resides does not always return to the same state
it had before the species invasion. Given multiple population dynamical attractors of the resident species, an invasion can lead to altered resident population dynamics
under which the invading species is an inferior competitor
and hence again excluded from the system despite successfully invading, a phenomenon known as the “resident
strikes back” (Doebeli 1998; Mylius and Diekmann 2001;
Edmunds 2007).
A major factor governing population dynamics, and
hence potentially the presence of multiple dynamical attractors, is size-dependent mortality. The potential of sizedependent mortality to influence population dynamics has
long been recognized (Murdoch and Oaten 1975), but the
effects of size-dependent mortality in systems explicitly
characterized by trait (e.g., size) variation among individuals in populations have rarely been focus of study (but
see van Kooten et al. 2007). Still, many consumer species
are expected to exhibit cycles driven by mortality induced
by intraspecific size-dependent competition (e.g., Persson
et al. 1998). Accordingly, it has been repeatedly shown that
the population dynamics of, for example, many fish populations are driven by interactions among size cohorts,
leading to alternating strong- and weak-year classes (Persson 1988; Sanderson et al. 1999).
Here we investigate the significance of cyclic population
dynamics driven by cohort interactions for different levels
of size-dependent mortality as a mechanism causing ASS
based on priority effects. To this end, we use a size-struc-
tured model of competing populations previously developed to represent two competing species, Baltic Sea sprat
(Sprattus sprattus) and herring (Clupea harengus), and
their resources (Huss et al. 2012). As our findings are
especially relevant in the context of cycles driven by cohort
interactions, we review literature supporting cohort-type
dynamics in natural populations and also illustrate population dynamics of sprat and herring stocks in the Baltic
Sea during contrasting mortality regimes using monitoring
data ranging over 2 decades. Finally, given the strong productivity gradient in the Baltic Sea (Dahlgren et al. 2010)
and that the likelihood for ASS often varies with system
productivity (de Roos and Persson 2002; Chase et al. 2003),
the occurrence of ASS in the model was studied over a
range of productivity values. We provide compelling examples of ASS and the “resident strikes back” phenomenon in a community of competitors and their resources
ultimately caused by variation in size at maturation and
asymmetric competitive interactions between size cohorts.
Model Formulation
We have used the framework of physiologically structured
population models (PSPMs), specifically developed to handle the dynamics of populations involved in size-dependent interactions (Metz and Diekmann 1986). PSPMs distinguish individual (i), population (p), and environmental
(e) states. The i state represents the state of the individuals
in terms of a collection of physiological traits (e.g., body
size), the p state is a frequency distribution over all the i
states, and the e state describes, in our case, the current
density of the different food resources. The PSPM analyzed
here was recently developed and parameterized by Huss
et al. (2012), following the approach outlined in Persson
et al. (1998) and Claessen et al. (2000). It describes the
interaction between sprat and herring and their respective
resources, including two zooplankton and one benthic
prey. We assume that in the absence of consumers, resources grow following semichemostat growth, implying
constant resource productivity independent of resource
density. Resource densities decrease following consumption, which, in turn, decreases the amount of food available
for other consumers. Consequently, we explicitly considered the feedback between individuals and their environment, leading to food-dependent individual growth as well
as competition for resources. See appendix A for model
parameters (table A1), the individual-level model formulation (table A2), and equations describing the state
variables (tables A3, A4). Our model represents a mixed
continuous-discrete time system of two size-structured
competitor species and their three resources, where
growth, survival, consumption, and resource production
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376 The American Naturalist
are continuous processes but reproduction occurs as a
discrete process.
We use the model to study the occurrence of, and analyze the mechanisms behind, alternative stable dynamics
(note that here and below we will refer to these alternative
stable patterns of dynamics as ASS, even though they do
not represent stable equilibria), with particular focus on
the impact of interspecific variation in cohort cycle periodicity on species priority effects. We use different levels
of size-dependent mortality to obtain settings in which
interspecific variation in cycle length is present. Depending
on the level of size-dependent mortality, sprat and herring
may experience cycles of either the same or different
lengths (fig. 1). In addition, a species may exhibit cycle
periods of different lengths for an identical mortality level;
that is, they may exhibit alternative dynamical states (fig.
1). For our analyses of the occurrence of alternative community states caused by the order of species invasion, we
therefore chose two different values of the size-dependent
mortality constant (ms p 0.05 and 0.1 day⫺1, scaling constants determining the level of size-dependent mortality;
see table A2, eq. [A22]) for which sprat and herring exhibit
a cycle period of 1–3 years, depending on species identity
and basin of attractor (fig. 1). Below we give only a brief
general introduction to model formulations (for equations
and parameter values, see apps. A–C), while details on
individual-level formulations are found in Huss et al.
(2012).
Figure 1: Changes in sprat (a) and herring (b) density as a function of the size-dependent mortality constant (ms) in cases without the
other species present. The figure shows the number of sprat and herring at the end of each of the last 50 years of each integration period
for each ms. Hence, populations exhibiting a 2-year regular cycle (as for sprat at ms p 0.05 day⫺1) show up as two points at the same
mortality value (for corresponding time series, see inset, top) whereas populations with fixed-point dynamics, where the population state
is identical every year (as for sprat at ms p 0.1 day⫺1), show up as only one point (for corresponding time series, see inset, bottom). Gray
symbols indicate alternative dynamical states. Kz p 0.5 ; Kb p 10 . Vertical dashed lines indicate parameter values used for invasion and
extinction analyses (see figs. 3, 5).
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Cohort Dynamics and Alternative States 377
The model formulation consists of a mathematical description of how individual growth, survival, and reproduction depend on individual physiology and food densities (table A2). Both sprat and herring can feed on
zooplankton throughout ontogeny. In addition, herring
start to feed on benthos when they reach a body length
of 15 cm (Casini et al. 2004). They thereafter gradually
increase their time spent foraging on benthos according
to a sigmoidal function and decrease their time spent foraging on zooplankton correspondingly (table A2, eqq.
[A3], [A4]). Two zooplankton resources are accounted for.
The parameter R represents the degree to which sprat and
herring overlap in their use of these zooplankton resources,
and at R p 0.5 (i.e., full resource overlap) both species
spend half of their time on each zooplankton resource.
The physiological state of individuals is determined by
irreversible mass, which consists of bones and organs that
cannot be starved away, and reversible mass, including
tissues such as fat, muscle, and gonads that can be starved
away when maintenance costs exceed energy intake. All
functions describing foraging intake and energy expenditure depend on body mass. The attack rate of sprat and
herring on zooplankton is modeled as a hump-shaped
function (for rationales for using a hump-shaped function
over body size for fish, see Persson et al. 1998), and the
attack rate of herring on benthos is modeled as a power
function (for its derivation see Persson et al. 2004), both
a function of consumer irreversible mass (table A2, eqq.
[A5], [A6]). The feeding rate is a function of prey mass
encounter and the capacity to digest prey and follows a
Holling type II functional response (table A2, eqq. [A12],
[A13]). Digestion capacity is assumed to increase with
irreversible mass (table A2, eq. [A14]; for underlying biological reasons for such a positive relationship for fish,
see also Persson et al. 1998; Claessen et al. 2000), and prey
mass encounter is the product of the consumer’s attack
rate, prey density, and prey individual mass (table A2, eqq.
[A7]–[A11]). Consumed prey is converted to energy assuming a constant conversion factor. Assimilated energy
is first used to cover maintenance costs and is thereafter
used for growth only in irreversible and reversible mass.
Maintenance rate is modeled as a power function of total
weight (table A2, eq. [A17]). Given our parameterization
of attack rate, digestion capacity, and maintenance, small
individuals can sustain themselves on lower resource densities than large individuals can and are therefore competitively superior to large individuals (which is in accordance with experimental results for several planktivorous
fish species; e.g., Hjelm and Persson 2001; Byström and
Andersson 2005). Our parameterization also results in herring sustaining themselves on lower zooplankton densities
than sprat throughout ontogeny (for details on critical
resource densities, see Huss et al. 2012).
The growing season is set to be 250 days, assuming that
the remainder of the year is a period of stasis. For both
species, reproduction takes place during a discrete time
period in the beginning of the growing season (e.g., Rajasilta et al. 1993), assuming that spawning intensity is a
hump-shaped function with a maximum in the middle of
the spawning period (table A2, eq. [A21]). All energy for
spawning is assumed to be irreversibly allocated to egg
production at the start of the growing season.
Several sources of mortality are implemented. All fish
experience size-independent background mortality.
Young-of-the-year individuals additionally experience a
size-dependent mortality, which decreases with body size,
reflecting that small fish commonly suffer higher mortality
rates than large individuals as they are more exposed to
predation, disease, and lethal abiotic conditions (Wootton
1998). Finally, if the reversible mass decreases below a
threshold value (qstarv; table A1), individuals will start to
die from starvation. Hence, total mortality includes background, starvation, and size-dependent mortality (table
A2; eqq. [A22]–[A24]). For model analyses we focus on
variation in size-dependent mortality.
Model Analyses
Populations are divided into groups of identical individuals born within the same 3 days of the spawning period
(i.e., cohorts; see tables A3, A4). The dynamics of these
cohorts are described by sets of ordinary differential equations and were analyzed using the escalator boxcar train
method (a numerical method for integration of PSPMs
developed by de Roos et al. [1992]). To study the population dynamic consequences of size-dependent mortality,
we identified the long-term population dynamics using
bifurcation analysis by integrating the model equations
over a very long time while systematically increasing or
decreasing the value of the size-dependent mortality constant (ms) in small steps at regular intervals. To determine
the persistence of sprat and herring over different values
of zooplankton productivity and to study the possibility
for alternative stable states, we identified extinction and
invasion boundaries. Integrations were run with benthos
productivity kept constant at K b p 10 or, to control for
a possible benthos effect, assuming no benthos feeding at
all. Analyses were carried out for R ranging from 0 to 0.5,
but only results for R p 0.5 (i.e., 100% resource overlap)
are presented in detail. Extinction boundaries were determined using bifurcation analyses with both populations
initially present. After every change in the bifurcation parameter, system dynamics were integrated over a period
of 400 years, of which only the last 50 years were assessed
for long-term dynamics to discard possible transient dynamics resulting from the small parameter change. When
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378 The American Naturalist
the number of individuals in a population dropped below
1e⫺9/m3, the population was considered extinct. To determine the parameter space for which an invading species
could establish in an environment set by the resident species, we used a similar approach but now for a situation
in which the invading population was not initially present.
For the last 40 years of each bifurcation period, a fixed
number of eggs was introduced, and the number of offspring produced by these invaders was calculated. An invasion was considered successful when the invading population experienced positive population growth (based on
the average lifetime reproductive output of individuals introduced in each of the different phases of the population
cycle; for methodological details see de Roos et al. 2006).
As default we assumed that the number of invading individuals is small and therefore does not influence the
resource. However, for scenarios in which the invading
population showed positive population growth, we confirmed whether the invading population could also establish if its feedback on resource densities was taken into
account (i.e., when the resource environment was determined by both the invading population and the resident
population). Note that results are presented only for scenarios assuming one invading egg per cubic meter (simulations using fewer or more invaders were also carried
out but gave qualitatively similar results and are therefore
not reported). For detailed investigations of population
dynamics, time series of different consumer life-history
stages were studied in the contrasting community states
constituting ASS. By presenting length-at-age curves for
sprat, we also exemplify differences in growth dynamics
under single-species, coexistence, and invasion dynamics
(app. B).
abundance shifted forward in time. Here juveniles refer
to 1-year-olds and adults to ages 2–4 (which constitute
the majority of the abundance and biomass of the spawning individuals in the central Baltic Sea). The aim of this
analysis was to identify whether strong cohorts of recruiting individuals lead to abundant adult cohorts (i.e., a positive lag). If the abundances of young and old individuals
instead covary, factors other than cohort interactions
clearly rule dynamics (e.g., external forcing, predation).
We performed these cross correlation analyses on abundance estimates obtained from the Baltic International
Acoustic Survey (ICES 2011b; Swedish University of Agriculture Sciences 2012) covering 1985–2010, to use only
abundance estimates that are independent of the estimates
of predation mortality, which confound estimates based
on catch data. Estimates of annual predation mortality on
1-year-old herring and sprat during 1974–2010 and their
abundance during the same period were taken from ICES
(2011a; Baltic International Fish Survey Working Group
2011). Also, we examined changes in age at maturity length
for sprat and herring to see whether (1) we can expect
interspecific differences in age at maturation and (2) age
at maturation changed due to slower growth rates following the collapse of the cod population. The latter analysis
was assessed from the mean weight at age for each cohort
obtained from Swedish sampling within the Baltic International Acoustic Survey (as these covered a longer time
period, cohorts 1977–2009; ICES 2011b; Swedish University of Agriculture Sciences 2012) in relation to the weight
corresponding to the assumed length at maturation in the
model (18 and 4 g for herring and sprat, respectively; tables
A1, A2).
Results
Data Analysis
To illustrate how shifts in size-dependent mortality may
influence dynamics of natural sprat and herring populations, we contrasted cycle demography during periods of
high (time period 1974–1992) and low (1994–2010) cod
biomasses (representing periods with high and low sizedependent mortality) in the central Baltic Sea (Baltic International Fish Survey Working Group 2011; ICES
2011a). Magnitudes of cross correlation coefficients between juvenile and adult abundances were estimated with
one of the series of these abundances shifted in time (app.
C). If juvenile abundance and adult abundance covary, the
maximum positive correlation is expected to occur at zero
lag (without any shift in the time series). In the case that
dynamics is driven by alternating weak- and strong-year
classes (as in cohort cycles; Persson et al. 1998), the maximum cross correlation coefficient between juvenile abundance and adult abundance is expected to occur with adult
Sprat and herring population cycles were characterized by
cohorts of juvenile individuals dominating the population
until reaching maturity, that is, cohort cycles. Varying sizedependent mortality (ms) strongly influenced the length of
these cycles (fig. 1). Increased mortality reduced cycle
length of both species, and at high values of ms only fixedpoint dynamics with yearly reproduction occurred, meaning that the population state was identical at the start of
every year. Note, however, that for some parameter values,
yearly reproduction does not lead to fixed-point dynamics
(i.e., fig. 1, herring dynamics; for 0.107 ! ms ! 0.122 there
is yearly reproduction, but the population exhibits a 2year cycle because the first individuals to hatch in a given
season mature within their first year of life, while individuals that hatch later do so only in their second year).
Finally, at high enough ms (10.17 day⫺1), populations became extinct. There is a negative relationship between cycle
length and mortality because higher mortality reduces
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Cohort Dynamics and Alternative States 379
Figure 2: Sprat (top; gray symbols) and herring (bottom; black symbols) density at the start of the growing season (averaged over the last
60% of the integration period at every productivity value) as a function of zooplankton productivity (Kz) for size-dependent mortality (ms)
equal to 0.05 day⫺1. Solid and dashed lines indicate different alternative stable states. Roman numerals refer to regions with different possible
community states (see “Results”). For corresponding population dynamics, see figure 3. Total zooplankton resource overlap between herring
and sprat is assumed (i.e., 100%, R p 0.5).
abundances of juvenile fish more quickly, leading to faster
resource recovery following reproduction, which allows for
earlier maturation and hence faster population turnover
rate. When alone, for ms p 0.05 day⫺1, sprat exhibited 2year cycles, whereas herring exhibited 3-year cycles. For
ms p 0.1 day⫺1 sprat exhibited fixed-point dynamics in
the absence of herring and herring either 2-year cycles or
fixed-point dynamics; that is, herring exhibited alternative
dynamics when alone (fig. 1). Hence, two alternative dynamical states are possible for the same mortality value
within the same population (fig. 1, black and gray sym-
bols). Note that cycle length may change when accounting
for interspecific competition (see below). Figure 1 presents
results for the case that all individuals mature exactly when
they reach a fixed maturation size threshold. However, the
bifurcation pattern remains the same if it is assumed that
maturation occurs more gradually over a range of individual body sizes (results not shown).
Over a gradient in resource productivity (Kz) several
community states were identified, including a large productivity range where ASS occurred (fig. 2, regions III,
IV). For ms p 0.05 day⫺1 there was first a shift from a
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380 The American Naturalist
resource-only (region I) to a sprat-only (region II) community state. The lowest value of Kz for which sprat could
first persist/invade relates to a resource level high enough
for sprat to reach its maturation size (i.e., the resource
level at which sprat maintenance requirements at maturation size were met). At productivity levels just above
that, a sprat-only system prevailed. As productivity increased, several ASS were identified. For intermediate
productivities there was either a sprat-only (fig. 2, region
III, solid lines) or a herring-only (fig. 2, region III, dashed
lines) state, which resulted because neither species could
invade the system when the other species was already present. As productivity increased further, sprat and herring
could coexist. Still, sprat could not invade a herring-only
system. Consequently, there were again two possible ASS:
a sprat-herring state (fig. 2, region IV, solid lines) and a
herring-only state (fig. 2, region IV, dashed lines).
The occurrence of ASS relates to differences in population cycles, resource environment, and consumer growth
rates between established sprat-only, herring-only, and
sprat-herring communities (fig. 3; app. B). In coexistence,
the dynamic behavior of sprat and herring always converged at high resource overlap (i.e., both species exhibited
cycles of identical lengths; for parameter combinations
leading to different cycle lengths in absence of interspecific
competition, see fig. 3d). Therefore, cycle length during
an invasion attempt, where initially (by definition) only
the resident species sets the resource environment, may
differ from the cycle length in a scenario with both species
initially present and competing. For example, for ms p
0.05 day⫺1 the herring-only state was characterized by a
3-year cycle irrespective of the value of Kz (fig. 3a, 3c),
but the sprat-herring state that occurred for K z p 0.5 exhibited 2-year cycles (fig. 3d). This implies that when sprat
invaded a herring-only state, it had to do so facing a resource environment set by the herring population undergoing a 3-year cycle. In contrast, in coexistence when exhibiting 2-year cycles, the resource environment was set
by both species (fig. 3d, cf. resource dynamics before invasions and in coexistence). This explains why sprat could
persist in a system with herring (fig. 3d) but not invade
a herring-only system (fig. 3c); when coexisting with herring, sprat influenced the dynamics such that herring alone
could not control resource dynamics (i.e., resource biomass fluctuated with a period of 2 years, contrasting the
3-year period observed in the herring-only scenario) and
therefore did not exclude sprat. The observation that both
species could persist when alone at low Kz but not invade
relates to the same mechanism; that is, the invading population faced a resource environment set by the resident
population, forcing the invader to shift dynamics (fig. 3a,
3b; no shifts in resource dynamics are observed following
invasions). While herring could invade a sprat-only system
characterized by 2-year cycles at high productivity (fig.
3d), they suffered from their larger size at maturation when
productivity was low (fig. 3b) because they could not reach
maturation size within the same growing season as sprat
(old herring cohorts were outcompeted by newborn sprat).
ASS (at ms p 0.05 day⫺1) were not restricted to scenarios
with total resource overlap but occurred for overlap of
80%–100% (R p 0.4–0.5; results not shown). Also, ASS
with either coexistence or herring alone (i.e., fig. 2, region
IV) was not exclusive for ms p 0.05. For example, at zooplankton productivity Kz p 0.5, it occurred for 0.032 !
ms ! 0.054. At higher mortality (ms p 0.1 day⫺1), when
sprat exhibited fixed-point dynamics, no ASS were identified involving both sprat and herring. Instead, a herringonly state prevailed throughout productivity space (fig. 4,
regions V, VI) because at this mortality level herring could
always mature within the same season as sprat irrespective
of productivity level. Still, for a substantial range of productivities sprat could invade herring-only systems exhibiting a 2-year cycle (fig. 4, region VI; fig. 5a). However,
they could not successfully establish. The temporarily successful invasion of sprat relates to the fact that the introduced sprat individuals induced a switch in dynamic attractor of the resident herring population, from a 2-year
cycle to fixed-point dynamics (fig. 5a; see also fig. 1b) and
a concurrent shift in resource environment (fig. 4, dashed
lines; fig. 5a). In this new state, with fixed-point herring
dynamics, resource densities were on average lower and
the invading sprat population was again kicked out of the
system, that is, a “resident strikes back” situation. Hence,
in this case, two distinct phases could be distinguished
during a sprat invasion: an initial phase characterized by
herring exhibiting 2-year cycles and sprat positive population growth (fig. 5a, early years) and a second phase with
an attractor switch leading to both populations exhibiting
yearly reproduction and sprat negative population growth
(fig. 5a, late years). The competitive dominance of herring
under fixed-point dynamics was evident as herring could
successfully invade and establish in a sprat-only system
(fig. 5b). Irrespective of zooplankton productivity, sprat
could never invade a herring-only state when herring exhibited fixed-point dynamics. The “resident strikes back”
phenomenon (at ms p 0.1 day⫺1) occurred for a resource
overlap of 88%–100% (R p 0.44–0.5). None of the results
obtained were qualitatively dependent on the assumption
that herring can feed on benthos (results are not shown
for scenarios without benthos feeding). Furthermore, as a
test of robustness we repeated part of our analyses using
identical parameterization for herring and sprat (i.e., using
only sprat parameters for both species) except for digestion
capacity (a difference in digestion capacity is needed to
allow for coexistence; see Huss et al. 2012) and size at
maturation, which were still herring specific. Also in this
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Figure 3: Sprat (gray) invading a herring-only system (a, c) and herring (black) invading a sprat-only system (b, d) for low (a, b; Kz p 0.012 ) and high (c, d, Kz p 0.5) zooplankton
productivity. Bottom graphs show corresponding resource biomasses. Invasions from time p 10 years. Note different scales on left Y-axes. In d herring and sprat coexist in the time
period 70–80 years. Other parameters as in figure 2.
382 The American Naturalist
Figure 4: a, Sprat (gray) and herring (black) density (averaged over the last 60% of the integration period at every productivity value) as
a function of zooplankton productivity (Kz) for size-dependent mortality (ms) equal to 0.1 day⫺1. Note that sprat densities always equal 0.
In b herring density in region VI is shown for two alternative dynamical states (present but difficult to see in a). The dashed line indicates
fixed-point dynamics and the solid line a 2-year cohort cycle. In c zooplankton biomass is shown for these two alternative states. Roman
numerals refer to regions with different possible community states (see “Results”). For corresponding population dynamics, see figure 5.
Total zooplankton resource overlap between herring and sprat is assumed (i.e., 100%, R p 0.5).
analysis, ASS were observed (albeit for somewhat higher
productivities than in the original setting; results not
shown).
Data Analysis
During the period 1974–1992, when sprat and herring
experienced high predation mortality (fig. 6a), the abundance of juveniles and adults fluctuated in synchrony (i.e.,
with zero lag) for both species (r p 0.93 and 0.69 for sprat
and herring, respectively; cross correlation time series analysis; see table C1 for details), and no regular cyclic dynamics in population abundance was observed (fig. 6b).
In contrast, during the period 1994–2010, with low predation mortality (fig. 6a), peaks in adult abundance lagged
behind peaks in juvenile abundance for both sprat and
herring (sprat: 1-year lag, r p 0.56; herring: 3-year lag,
r p 0.62; cross correlation time series analysis; see table
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Cohort Dynamics and Alternative States 383
Figure 5: Sprat (gray) invading a herring-only system (a) and herring (black) invading a sprat-only system (b). Bottom graphs show
corresponding resource biomasses. Invasions from time p 10 years. Sprat is approaching extinction in a. Kz p 0.5 . Other parameters as
in figure 4.
C1 for details), and visual inspection of variation in population abundances suggests that both species exhibited
regular cyclic dynamics (fig. 6b), although there was no
evidence for a significant cycle period (autocorrelation
analyses; results not shown). In the low-predation period
sprat exhibited mainly 2-year cycles but occasionally 3year cycles. Similarly for herring, there was an alternation
between 2- and 3-year cycles (fig. 6b). The average age at
which individuals reached length at maturation during the
period with high predation mortality was 1 and 1.1 years
for sprat and herring, respectively (fig. 6c). During the
low-predation period, sprat still reached maturation length
at age 1 (despite smaller size at age), whereas herring on
average reached length at maturation at age 1.9 years (note
that reproduction takes place in the year following maturation). This analysis suggests that herring might be exhibiting a shift from 2 to 3 years at first reproduction (first
period vs. second period; one-way ANOVA, P p .002),
whereas sprat reproduction age might not have changed.
Discussion
Alternative stable ecosystem states may prevent recovery
of populations and ecosystem services despite restored environmental conditions (Scheffer et al. 2001). Identifying
the conditions under which ASS can occur is therefore
crucial, not only for our ability to understand ecosystem
function but also for ecosystem-based management. We
have shown how endogenously driven population cycles
resulting from interactions among size cohorts may lead
to ASS in competition systems through priority effects.
Several ASS were identified in our model system (representing Baltic Sea sprat and herring populations) across a
productivity gradient, including coexistence and one-species states. This suggests that reestablishment following
extinction of one of the species could be difficult. We also
observed how successful invasion could be followed by
extinction of the invaders as a result of an attractor switch
of the resident population. Both phenomena were critically
dependent on size- and food-dependent development
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384 The American Naturalist
Figure 6: Estimated predation mortality from cod on 1-year-old
herring (black) and sprat (gray; a) and abundance of 1-year-old
herring and sprat (b) and age when they reach the threshold size for
maturation (c).
(leading to cohort dynamics) and a difference in size at
maturation (leading to differences in cycle lengths).
Our results support previous analyses that suggest an
increased likelihood of revealing ASS in modeled ecological
systems when size-dependent development and interactions are taken into account (de Roos and Persson 2002;
Miller and Rudolf 2011). The results we present here relate
to the occurrence of two types of ASS. The first type of
bistability occurs between two single-species attractors
characterized by different cycle lengths (i.e., fig. 1, black
and gray lines), while the second type of bistability represents alternative community states with either coexis-
tence or one-species state (fig. 2). Cohort-driven dynamics,
an essential component leading to the occurrence of alternative stable community states as described here, have
been thoroughly discussed before but so far only in a
single-species context (Persson et al. 1998; van Kooten et
al. 2007). Previous studies have found similar types of
alternative dynamical states within species (e.g., small- and
large-amplitude cycles; McCauley et al. 2008), but their
occurrence was critically dependent on the resource being
modeled according to the logistic growth model. In contrast, cyclic dynamics in our model (which assumes constant resource productivity independent of resource density) are endogenously driven, resulting from a difference
in competitive ability between consumer life stages. The
effects of within-population size structure on the dynamics
of competing populations have also been previously studied but only in models assuming a more discrete subdivision of life stages, not allowing for cohort-type dynamics
(i.e., stage-structured biomass models; see Schellekens et
al. 2010). Here we synthesize the aspect of competition
between populations with the occurrence of cohort cycle
dynamics in these populations. Accordingly, we present
the occurrence of alternative community states in a setting
that reconciles previously disjointed aspects in community
ecology. The concept of ASS in size-structured communities has been studied mainly in systems focusing on predator-prey dynamics (e.g., De Roos and Persson 2002; van
de Wolfshaar et al. 2006). In the context of pure competition systems accounting for within-population size
structure, alternative stable states have been discussed only
in a stage-structured setting (assuming continuous reproduction; Schellekens et al. 2010). The alternative community states in these previous studies are hence of a
completely different nature and caused by fundamentally
different mechanisms than those described here, which are
based on differences in cycle properties among competing
species exhibiting oscillations.
The first main outcome of our model analysis is the
occurrence of ASS based on priority effects. When coexisting, both species influence shared food resources and
population dynamics, to the extent that both species can
avoid competitive exclusion and hence coexistence is a
stable attractor for the system. Nevertheless, invasion of a
single-species state by a competitor can be prevented by
the shared resource dynamics being determined solely by
the resident species. When these resource dynamics differ
from the dynamics in the coexistence state, invasion by
the competitor may be impossible. This implies that a
competitor population driven to extinction may not be
able to reinvade despite environmental conditions that
would allow for its persistence, both when alone and in
coexistence, because the resident population dynamics
have changed since it coexisted with the invader. The sec-
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Cohort Dynamics and Alternative States 385
ond main outcome of our analysis is that even when a
population experiences positive population growth at low
numbers, long-term recovery will not necessarily ensue,
because of a “resident strikes back” phenomenon (Doebeli
1998; Mylius and Diekmann 2001; Edmunds 2007). That
is, the invading species may induce a shift in dominant
cycle period of its competitor, shifting the competitive
balance such that the invader is again excluded from the
system. Hence, a sudden shift in community state may
constitute the end point of a long-term transient state.
This highlights the importance of considering long-term
transient dynamics in community ecology (see also Fukami and Nakajima 2011).
In summary, the prerequisites for the type of ASS (and
“resident strikes back” phenomenon) identified in our
size-structured model were (1) populations exhibiting cohort-driven dynamics, (2) different maturation sizes for
the two species (leading to variation in age at maturation
and hence in cycle length), and (3) strong interspecific
competition. We argue that all of these factors may be
present in natural food webs. In a literature review of cyclic
consumer populations, Murdoch et al. (2002) highlighted
the importance of cohort-type dynamics and showed that
the majority of species examined, including fish, aquatic
crustaceans, insects, mammals, and birds, exhibited cycles
driven by individual development (growth), which scales
to the generation time of the consumer (i.e., cohort cycles
rather than predator-prey cycles, which have much longer
cycle periods). The occurrence of cohort cycles in natural
populations is also supported by more detailed analyses
of the population cycles of different fish populations such
as roach (Townsend et al. 1990), yellow perch (Sanderson
et al. 1999), and vendace (Hamrin and Persson 1986), as
well as zooplankton populations (e.g., McCauley and Murdoch 1987). Based on all these analyses, including a diverse
variety of taxa, we conclude that the type of cycles emerging in our model system are not a special case but occur
across taxa in many natural systems.
Mortality risk is generally found to be size dependent
and has repeatedly been shown to have profound influences on populations and communities (Paine 1976; de
Roos and Persson 2002; van Kooten et al. 2007). In populations with food-dependent growth and intraspecific
competition, mortality (especially if targeting competitively dominant juvenile individuals) relaxes food competition, leading to increased growth rates and reduced
cycle length (fig. 1; van Kooten et al. 2007). Our analyses
show that small changes in juvenile mortality may dramatically alter not only population dynamics but also
community structure (figs. 2, 4). Due to differences in size
at maturation, sprat and herring, for most mortality values,
experienced cycles of different lengths in absence of interspecific competition and exhibited shifts between pop-
ulation states characterized by cycles of different lengths
at different thresholds of mortality.
Casini et al. (2009) identified two periods characterized
by different ecosystem states in the Baltic Sea: a coddominated period (pre-1993) when zooplankton dynamics was largely controlled by hydrological condition and
a sprat-dominated period (post-1993) when predation
by cod was low and sprat abundance rather than hydrology became the major driver of zooplankton dynamics (however, it is still possible that the physical environment may influence variability in sprat recruitment;
e.g., Baumann et al. 2006). During the first period, where
sprat and herring experienced high predation mortality,
the abundance of juveniles and adults fluctuated in synchrony (table C1). In contrast, in the latter period, when
predation mortality was low, peaks in juvenile abundance
were followed with time delay by peaks in adult abundance (suggesting adult abundance to be controlled by
juvenile abundance rather than factors such as hydrological condition). Time series of sprat and herring abundances also suggest that both populations exhibited more
regular cyclic dynamics when predation mortality was
low (fig. 6). These results illustrate potential differences
in population dynamics following shifts in mortality
pressure (for a mortality effect on herring population
dynamics in the North Sea, see Fässler et al. 2011). Furthermore, recent studies have revealed intense interspecific competition between herring and sprat following the
cod collapse, as well as a positive correlation between
predation mortality and individual growth rates (Casini
et al. 2006, 2010). Our analysis shows that the slower
growth rate has resulted in a shift in age at which length
at maturation is reached for herring and thereby a difference in age at maturation between sprat and herring
(note that maturation is set by body size rather than by
age; Vainikka et al. 2009). Consequently, although observations on the present community state of the central
Baltic Sea with sprat dominance and a low herring abundance can never be sufficient to determine the occurrence
of ASS, our illustration suggests that the prerequisites for
ASS induced by variation in cycle length may be present:
strong interspecific competition, cycles driven by strong
cohorts, and variation in age at maturation. Likewise,
these prerequisites may be encountered in many other
ecological systems, given that oscillating populations
characterized by food-dependent growth and sizedependent interactions are general characteristics of
many consumer species (Murdoch et al. 2002; de Roos
et al. 2003). For example, several planktivorous fish and
zooplankton species have been shown to exhibit oscillations driven by interactions among size cohorts (e.g.,
McCauley and Murdoch 1987; Persson et al. 2004). In
conclusion, we show how cohort-driven population cy-
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386 The American Naturalist
cles may result in priority effects leading to ASS in competition systems. Especially in the face of recent predator
collapses in the world’s oceans (e.g., Myers and Worm
2003), leading to communities characterized by guilds of
forage fish competing for zooplankton and zoobenthos,
the type of ASS identified in our model system should
not be overlooked.
Acknowledgments
We thank three anonymous reviewers for their helpful
comments. This study is part of the PLAN FISH project,
financially supported by the Swedish Environmental Protection Agency and the Swedish Agency for Marine and
Water Management (formerly the Swedish Board of
Fisheries).
APPENDIX A
Model Parameters, Equations, and State Variables
Table A1: Model parameters for herring (Clupea harengus) and sprat (Sprattus sprattus) foraging on zooplankton and benthos
Value
Symbol
Herring
Sprat
Spatial dimensions:
VB
50
50
V
1
1
B
...
...
Season and spawning:
Y
250
250
S
0
200
Sm
38
45
Sd
76
90
Sg
3
3
Ontogeny:
wb
.0007
.0005
qj
.7
.9
Unit
Interpretation
...
m3
m2
Volume-to-bottom ratio
Volume
Bottom
day
day
day
day
day
Duration of growing season
Date of spawning decision
M. Casini, personal communication
Date of maximum spawning Rajasilta et al. 2001, 2006; Krasovskaya 2002
Duration of spawning period Rajasilta et al. 2001, 2006; Krasovskaya 2002
Spawn group
g
...
qa
1.13
1.4
...
qr
.7
.9
...
kr
.5
.5
...
Total weight at hatching
Juvenile maximum
condition
Adult maximum condition
Ed
17
6
day
Threshold condition for
spawning
Gonad to offspring conversion efficiency
Duration of egg period
Af
25
14
day
Age at first feeding
Lm
14
9
cm
Maturation length
cm g⫺l2
Allometric scalar
Length-weight
relationship:
l1
l2
Planktivory:
a
Amax
Mopt
R
5.65
.32
.5
150
50
0–.5
5.4
.33
.5
150
50
0–.5
Source
...
...
m3 day⫺1
g
...
Allometric exponent
Allometric exponent
Maximum attack rate
Optimum consumer size
Degree of resource overlap
(herring/sprat)
Arrhenius and Hansson 1993
McGurk 1984; Mathers et al. 1994; Folkvord et al. 2000
McGurk 1984; Mathers et al. 1994; Folkvord et al. 2000; Rajasilta et al. 2001
Persson et al. 1998
Blaxter and Hempel 1963; Arrhenius and
Hansson 1993
Arrhenius and Hansson 1996; Daewel et al.
2008
Grygiel and Wyszynski 2003; Vainikka et al.
2009
ICES 2010; Baltic International Acoustic
Survey, unpublished data
ICES 2010; Baltic International Acoustic
Survey, unpublished data
Hjelm and Persson 2001
Hjelm and Persson 2001
Hjelm and Persson 2001
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Cohort Dynamics and Alternative States 387
Table A1 (Continued)
Value
Symbol
Herring
Benthivory:
Lb
L50
Bmax
b1
b2
Digestion:
d1
d2
Metabolism:
m1
m2
ke
Mortality:
m0
ms
mc
me
my
qstarv
s
Resources:
rz
rb
Kz
Kb
a
Sprat
Unit
Interpretation
15
...
cm
20
...
cm
.4
...
...
.2
.4
...
...
m2 day⫺1 gb2
...
Length at first benthos
feeding
Length at 50% of maximum
benthos foraging
Maximum time foraging on
benthos
Allometric scalar
Allometric exponent
4.8
⫺.74
6.7
⫺.63
.03
.8
.5
.03
.8
.5
.005
Variable
.005
Variable
day⫺1
day⫺1
.5
.5
g
Casini et al. 2004; Möllman et al. 2004
Casini et al. 2004; Möllman et al. 2004
Casini et al. 2004; Möllman et al. 2004
Persson et al. 2004
Persson et al. 2004
day g⫺(1⫹d2) Allometric scalar
...
Allometric exponent
De Silva and Balbontin 1974
De Silva and Balbontin 1974
g(1⫺r2) day⫺1 Allometric scalar
...
Allometric exponent
...
Food energy conversion
efficiency
Opalanski et al. 2004
Opalanski et al. 2004
Persson et al. 1998
Variablea Variablea
Variablea Variablea
.2
.2
day⫺1
day⫺1
...
.2
.2
day⫺1
.1
.1
Variable
.1
.1
Variable
day⫺1
day⫺1
g m⫺3
...
g m⫺2
10
Source
Background mortality rate
Size-dependent mortality
constant
Size-dependent mortality
characteristic size
Egg mortality
Mortality of yolk sac larvae
Starvation mortality
threshold
Starvation rate coefficient
Renewal rate of zooplankton
Renewal rate of benthos
Maximum zooplankton population density
Maximum benthos population density
Mortality for egg and yolk sac larvae is set to the same value as the size-dependent mortality imposed on newborn individuals (table A2, eq. [A22]).
Table A2: Individual-level model equations
Subject
Equation
Equation no.
Standardized mass (g)
Body length (cm)
H
Proportion benthos foraging time
Proportion zooplankton foraging time (NB: Bt p 0 for sprat)
Zooplankton attack rate (m3 day⫺1)
m(x) p (1 ⫹ qj )x
L(x) p l 1 m(x)l2
Bt(L) p Bmax Si(L, L b , L 50 )
Z t(L) p 1 ⫺ Bt
Benthos attack rate (m2 day⫺1)
Zooplankton encounter (g day⫺1)
S
Zooplankton encounter (g day⫺1)
H
Benthos encounter rate (g day⫺1)
S
Total encounter rate (g day⫺1)
H
Total encounter rate (g day⫺1)
A b(x) p b1x b 2
hz(x) p (1 ⫺ R)(A z(x)R zh) ⫹ R(A z(x)R zs )
hz(x) p (1 ⫺ R)(A z(x)R zs ) ⫹ R(A z(x)R zh)
h b(x) p A b(x)R b
h(x) p hz(x)
h(x) p hz(x) ⫹ h b(x)
H
H
A z(x) p A max
[
m(x)
exp
M opt
(1 ⫺ )]
m(x)
M opt
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a
(A1)
(A2)
(A3)
(A4)
(A5)
(A6)
(A7)
(A8)
(A9)
(A10)
(A11)
388 The American Naturalist
Table A2 (Continued)
Subject
Equation
⫺1
Zooplankton intake (g day )
Benthos intake (g day⫺1)
I z(x) p
hz(x)
Z
1⫹H(x)hz(x) t
(A12)
I b(x) p
h b(x)
B
1⫹H(x)h b(x) t
(A13)
H
Digestion time (day g⫺1)
Energy balance (g day⫺1)
Acquired energy (g day⫺1)
Energy requirements for maintenance (g day⫺1)
Energy allocation to x when L ! Lm
H(x) p d 1m(x)d 2
E g(x, y) p E a(x) ⫺ E m(x, y)
E a(x) p k e(I z(x) ⫹ I b(x))
E m(x, y) p r1(x ⫹ y) r 2
f(x, y) p
Energy allocation to x when L 1 Lm
f(x, y) p
Fecundity (no.)
F(x, y) p
2
{
{
()
1
y
(1 ⫹ qj )q j2 x
1
1 ⫹ qj
if
y
! qj
x
2
()
y
! qa
x
if
(A21)
(A22)
⫺m
msize(x) p ms exp m
c
{(
s
mstarv(x, y) p
)
qstarv x
⫺ 1 if y ! q starv x
y
0
(A23)
otherwise
m(x, y) p m 0 ⫹ mstarv(x, y) ⫹ msize(x)
Total mortality (day⫺1)
(A20)
otherwise
N(x, y) p FS i(Sg , Sm)
Starvation mortality (day⫺1)
(A19)
otherwise
kr(y ⫺ q j x)
if L 1 L m, y 1 q j x
wb
{
(A14)
(A15)
(A16)
(A17)
(A18)
otherwise
1
y
2
(1 ⫹ qa )q a x
1
1 ⫹ qa
0
Newborns produced (no. day⫺1)
Size-dependent mortality (day⫺1)
Equation no.
(A24)
Note: Parameter information is given in table A1. x and y indicate irreversible and reversible mass, respectively. Superscripts indicate that the equation
is valid for that species only (H for herring, S for sprat). Si indicates a sigmoidal function (see Huss et al. 2012).
Table A3: Definition of state variables
Individual level:
Irreversible mass
Reversible mass
Population level:
No. individuals in cohort
Environment:
Density of herring zooplankton
Density of sprat zooplankton
Density of benthos
Symbol
Unit
xi, n, xj, n
yi, n, yj, n
g
g
Ni, n, Nj, n
no. m⫺3
Rzh
Rzs
Rb
g m⫺3
g m⫺3
g m⫺2
Note: The indexes i and j refer to sprat and herring, respectively, and n refers to
cohort number. As all equations for cohort dynamics apply to both sprat and herring,
no species indexes are given. Parameter values and their references are given in table
A1.
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Cohort Dynamics and Alternative States 389
Table A4: Definition of state dynamics
Equation
Cohort dynamics:
Cohort mortality
dNn
dt
p ⫺m(xn , yn)Nn
Cohort per capita growth in x
dxn
f(xn , yn)Eg(xn , yn) if Eg 1 0
p
0
otherwise
dt
Cohort per capita growth in y
dyn
(1 ⫺ f(x n , yn))E g(x n , yn) if E g 1 0
p
Eg(x n , yn)
otherwise
dt
Resource dynamics:
Sprat zooplankton
Herring zooplankton
Benthos
{
{
(x )N
RA (x )N
冘 (1⫺R)A
Z ⫺ R 冘 1⫹H(x )h (x
1⫹H(x )h (x )
k
dR zs
dt
p rz(K z ⫺ R zs ) ⫺ R zs
dR zh
dt
p rz(K z ⫺ R zh) ⫺ R zh
dR b
dt
p rb(K b ⫺ R b ) ⫺ R b
k
np1
z
i, n
i, n
z
i, n
RA (x )N
冘 1⫹H(x
)h (x
k
z
np1
i, n
i, n
i, n
z
A (x )N
冘 1⫹H(x
)h (x
z
t
i, n
)
i, n
zs
np1
Z t ⫺ R zh
j, n
j, n
j, n
z
)
j, n
Zt
(x )N
冘 (1⫺R)A
Z
1⫹H(x )h (x )
k
np1
z
j, n
j, n
z
j, n
j, n
t
k
b
np1
j, n
j, n
j, n
b
)
j, n
BVB
t
Note: The indexes i and j refer to sprat and herring, respectively, and n refers to cohort number. As all equations for cohort
dynamics apply to both sprat and herring, no species indexes are given. The functions for mortality (m), energy balance (Eg), energy
allocation (f), attack rates (Az, Ab), handling time (H), encounter rate (h), degree of resource overlap (R), and time feeding on
zooplankton (Zt) and benthos (Bt) are given in table A2. Parameter values and their references are given in table A1.
APPENDIX B
Length-at-Age Curves
Figure B1: Length-at-age curves for sprat when alone (a), coexisting with herring (b), and invading (at time 0) a herring-only community
(c). Total zooplankton resource overlap between herring and sprat is assumed (R p 100%). K z p 0.5, K b p 10, ms p 0.05.
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390 The American Naturalist
APPENDIX C
Cross Correlation Statistics
Table C1: Cross correlation coefficients obtained for different lags between juvenile (1-year-old)
and adult (adults lagged after juveniles) biomass of herring and sprat before and after the change
from a cod-dominated food web to a sprat-dominated food web (i.e., from high to low predation
mortality on herring and sprat) in 1993
Sprat
Lag
Herring
Before 1993
After 1993
Before 1993
After 1993
.93
.68
.07
.19
.07
.56
.33
.16
.69
.06
.24
.16
.32
.22
.096
.62
0
1
2
3
Note: Significant results (P ! .05) are shown in bold.
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“Codfish visit the shallow water of Massachusetts Bay to spawn about the first of November, and towards the last of this month deposit
their eggs on the sandy banks and rocky ledges. About eight or nine millions of ova are annually deposited by each female. The codfish
remain in the vicinity of their eggs till June, when they again retire to deeper water, the shallow water having become too warm for them.”
From “The Habits and Migrations of Some of the Marine Fishes of Massachusetts” by James H. Blake (American Naturalist, 1870, 4:513–
521).
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