Ecological Monographs, 85(3), 2015, pp. 413–436
Ó 2015 by the Ecological Society of America
Establishing the link between habitat selection and animal
population dynamics
JASON MATTHIOPOULOS,
1,7
JOHN FIEBERG,
2
GEERT AARTS,
3,4
HAWTHORNE L. BEYER,
5
JUAN M. MORALES,
6
AND DANIEL T. HAYDON
1
1
Institute of Biodiversity, Animal Health and Comparative Medicine, College of Medical, Veterinary, and Life Sciences,
Graham Kerr Building, University of Glasgow, Glasgow G12 8QQ United Kingdom
2
Department of Fisheries, Wildlife and Conservation Biology, University of Minnesota, St. Paul, Minnesota 55108 USA
3
IMARES Wageningen UR, Institute for Marine Resources and Ecosystem Studies,
P.O. Box 167, 1790 AD Den Burg, The Netherlands
4
Department of Aquatic Ecology and Water Quality Management, Wageningen UR, P.O. Box 47,
6700AA Wageningen, The Netherlands
5
ARC Centre of Excellence for Environmental Decisions, Centre for Biodiversity & Conservation Science,
University of Queensland, Brisbane, Queensland 4072 Australia
6
Laboratorio ECOTONO, INIBIOMA-CONICET, Universidad Nacional del Comahue, Quintral 1250, (8400) Bariloche, Argentina
Abstract. Although classical ecological theory (e.g., on ideal free consumers) recognizes the
potential effect of population density on the spatial distribution of animals, empirical species
distribution models assume that species–habitat relationships remain unchanged across a range of
population sizes. Conversely, even though ecological models and experiments have demonstrated
the importance of spatial heterogeneity for the rate of population change, we still have no practical
method for making the connection between the makeup of real environments, the expected
distribution and fitness of their occupants, and the long-term implications of fitness for population
growth. Here, we synthesize several conceptual advances into a mathematical framework using a
measure of fitness to link habitat availability/selection to (density-dependent) population growth
in mobile animal species. A key feature of this approach is that it distinguishes between apparent
habitat suitability and the true, underlying contribution of a habitat to fitness, allowing the
statistical coefficients of both to be estimated from multiple observation instances of the species in
different environments and stages of numerical growth. Hence, it leverages data from both
historical population time series and snapshots of species distribution to predict population
performance under environmental change. We propose this framework as a foundation for
building more realistic connections between a population’s use of space and its subsequent
dynamics (and hence a contribution to the ongoing efforts to estimate a species’ critical habitat and
fundamental niche). We therefore detail its associated definitions and simplifying assumptions,
because they point to the framework’s future extensions. We show how the model can be fit to data
on species distributions and population dynamics, using standard statistical methods, and we
illustrate its application with an individual-based simulation. When contrasted with nonspatial
population models, our approach is better at fitting and predicting population growth rates and
carrying capacities. Our approach can be generalized to include a diverse range of biological
considerations. We discuss these possible extensions and applications to real data.
Key words: accessibility; climate change; conservation; density dependence; generalized functional
response; generalized linear model; habitat suitability; ideal free distribution; mathematical model; resource
selection function; simulation; species distribution models.
INTRODUCTION
Accelerating environmental change requires us to
understand not just how species distributions will adjust,
but also whether their population sizes will go up or
down. The mechanisms linking the environment of a
population to its spatial distribution and growth are
considered textbook material (e.g., Chapman and Reiss
1999, Begon et al. 2006, Levin 2009). Environmental
variables are distributed across space, their combina-
tions forming habitats that are differentially used by
different species. Populations track the heterogeneity in
their environment either actively (when individuals
navigate the landscape in search of suitable habitats)
or passively (when dispersers settle at habitats that
differentially affect their survival and reproduction).
These processes are tightly linked: increases in popula-
tion density will tend to l ower local fitness and,
additionally, cause some individuals to move to subop-
timal habitats, directly impacting the overall ability of a
population to grow (Fig. 1).
Manuscript received 24 Novembe r 2014; accepted 18
December 2014; final version received 12 January 2015.
Corresponding Editor: B. E. Kendall.
7
E-mail: Jason.Mat thiopoul os@glasgow. ac.uk
413
Much of the ecological theory developed over past
decades has focused on different stages of this causal
chain: reaction–diffusion models (Sole
´
and Bascompte
2006, Okubo and Levin 2010) have explored the
emergence of complex spatial patterns, optimal foraging
(MacArthur and Pianka 1966, Emlen 1968) has deter-
mined the behavioral strategies that maximize energy
intake (indirectly highlighting the limits of environmen-
tal profitability for the individual), ideal free distribution
theory (Fretwell and Lucas 1970) has opened the debate
about the implications of competition for the distribu-
tion of conspecifics, movement ecology (Turchin 1998,
Codling et al. 2008, Schick et al. 2008) has created useful
abstractions to describe how organisms navigate their
environment, behavioral ecology (Krebs and Davies
1997) has increasingly considered energetic and risk-
related trade-offs in trying to explain the decisions of
individuals from a fitness perspective, and population
ecology persistently aims to incorporate the implications
of individual fitness for demographic rates and net
population growth (Clutton-Brock et al. 1991, Silver-
town et al. 1993, Gaillard et al. 2000, Clutton-Brock and
Coulson 2002, Coulson et al. 2005, Matthiopoulos et al.
2014).
Yet, despite our ability to enumerate the links in the
chain that ties a population to its environment, and
despite the multitude of theoretical insights obtained
since the 1960s, we still lack practicable models with
estimable parameters that can capture species–environ-
ment relationships in an integrated spatial and temporal
fashion (Keith et al. 2008).
Statistical species distribution models (SDMs) have
thrived in the last 25 years because of the emergence of
new data-collection technologies (Millspaugh and Mar-
zluff 2001, Cagnacci et al. 2010) and data analysis
techniques (Buckland and Elston 1993, Boyce and
McDonald 1999, Guisan and Zimmermann 2000,
Guisan et al. 2002, Manly et al. 2002, Scott et al.
2002, Aarts et al. 2008). Despite their bewildering
variety (Guisan and Zimmermann 2000, Elith and
Leathwick 2009), fundamentally different assumptions,
and regularly conflicting outputs (Elith and Graham
2009), the basic thrust of these models is the same:
organisms have a reason for being where we find them.
They are observed at (or near) places that, in some way,
help them survive and reproduce. By using one of
several possible quantitative methods that can correlate
the distribution of species observations (i.e., counts or
occurrences) to different environmental gradients,
SDMs hope to empirically capture enough of the spatial
signal to further our ecological understanding of the
species. The predictions from these models are used for
interpolating patchy spatial data, expanding the spatial
range of available species maps, or anticipating redistri-
bution under environmental change.
Habitat selection functions ( HSFs, more widely
referred to in the lite rature a s resource selection
functions; Boyce and McDonald 1999, Manly et al.
2002) are arguably the best-established and best-
understood type of SDM. A HSF is often defined as
any model that yields values proportional to usage.
More precisely, a HSF models the expected density (i.e.,
the intensity) of observations as a function of covariates
(Aarts et al. 2012). A t their si mples t, they are
implemented as generalize d linear mod els (GLMs;
McCullagh and Nelder 1989), with more recent exten-
sions such as generalized additive (GAMs; Wood 2006),
or mixed-effects models (GLMMs or GAMMs; Pinheiro
and Bates 2000, Wood 2006) aimed at capturi ng
nonlinear responses to the environment that are affected
by multiple sources of variability. HSFs are supported
by extensive statistical theory, widely available software,
and graphical diagnostics, and they frequently outper-
form more opaque machine-learning methods such as
neural nets (Wenger and Olden 2012). Furthermore,
they are more general than (although conceptually
related to) more recent, popular methods such as
maximum entropy (Phillips et al. 2006, Elith et al.
2011, Aarts et al. 2012, Renner and Warton 2013).
Therefore, HSFs are a solid foundation upon which to
start developing the empirical link between habitat use
and population dynamics (McLoughlin et al. 2010).
However, both the deductive and predictive abilities
of SDMs have come under s evere criticism. The
phenomenological origin of their mathematical structure
has encouraged the proliferation of ad hoc methodo-
logical variants, impeding the biological interpretation
of model structure and results (Elith and Leathwick
2009). Their misleading use as descriptors of a species’
realized/fundamental niche (Stockwell 2007, Hirzel and
Le Lay 2008) has received negative and r ecurrent
FIG. 1. Conceptu al links between the makeup of the
environment and the dynamics of a population that lives in it.
Habitat availability (1) describes the amounts of all habitats
that are accessible to an organism. The suitability of different
habitats (2) gives rise to an organism’s spatial distribution (3).
Across different locations, organisms may experience different
conditions, access different amounts of resources, and be
subjected to different degrees of risk. These experiences of
individuals determine their fitness (4). The collective measure of
fitness for the entire population determines annual rates of
population growth and subsequent population dynamics (5).
Population density (6) then feeds back into population
dynamics, but it may also affect habitat availability (through
resource depletion or niche engineering), spatial distribution
(through behavioral responses to crowding), a nd fitness
(through demographic responses to crowding). Note that the
suitability of different habitats is a characteristic of a species
and therefore cannot be changed by population density.
JASON MATTHIOPOULOS ET AL.414
Ecological Monographs
Vol. 85, No. 3
attention (Elith and Leathwick 2009, Sobero
´
n and
Nakamura 2009, Peterson et al. 2011, Warren 2012,
2013, McDonald et al. 2013, McInerny and Etienne
2013). Their sensitivity on arbitrary scale decisions made
by the analyst (Austin 1999, Beyer et al. 2010) and
instability in changing environments (Randin et al. 2006,
Zurell et al. 2009, McLoughlin et al. 2010, Sinclair et al.
2010, Matthiopoulos et al. 2011, Wenger and Olden
2012) has alerted practitioners to the dangers of their
widespread and unvalidated application. Additionally, a
crucial fact that seems to have escaped the attention of
the SDM literature is that estimates of habitat suitability
are not likely to be invariant to population density.
Given that these models evaluate habitat suitability on
the basis of relative usage, which is certain to be affected
by density-dependent processes, SDMs run the risk of
returning different parameter estimates depending on
how close an observed population is to its carrying
capacity.
Despite the development of more mechanistic spatial
approaches (Chase and Leibold 2003, Kearney and
Porter 2004, Moorcroft and Lewis 2006, Patterson et al.
2008, Schick et al. 2008, Higgins et al. 2012), empirical
SDMs are unparalleled in their taxonomic generality,
ease of use, and computational expediency for popula-
tion-level inferences. For this reason, there is a concerted
remedial effort to try and improve their shortcomings
(Arthur et al. 1996, Mauritzen et al. 2003, Gillies et al.
2006, Hebblewhite and Merrill 2008, Godvik et al. 2009,
McLoughlin et al. 2010, Matthiopoulos et al. 2011) and
help them fulfill their original deductive and predictive
promise (Warren 2013). In this study, we propose a
pragmatic synthesis between models of habitat selection
and models of population change. Our overarching
objective is to mathematically link empirical estimates of
habitat availability and apparent habitat preference with
the observed rates of growth of populations living in
these environments. We believe that such a synthesis can
ultimately lead to both a deeper mechanistic under-
standing and stronger statistical inference. Therefore, to
illustrate the utility of our paradigm, we take the first
steps along both of these routes. On the mechanistic
side, we explore how apparent habitat suitability,
gleaned through observations of space use, may be
connected to the unobserved fitness that animals gain
from each habita t. On the statistical side, using
simulated data, we show how inference on spatial usage
and population time series can improve our predictions
of population change.
Since we aim for a convergence between the relatively
independent areas of species distribution modeling and
population dynamics, we begin by explaining our
terminology, which borrows vocabulary from both
areas. We limit our attention to a specific, but still quite
broad set of circumstances that we believe can serve
both as proof of concept and as a suitable basis for
expansion. Hence, in Ecological scope and simplifying
assumptions, we set out the basic premises of our study.
In Environmental determinants of fitness, we outline a
general link between fitness and the environment of an
organism and in Linking fitness, habitat suitability, and
habitat use, we introduce the connection between fitness,
habitat suitability, and space use. In Pa ra met r ic
formulations of habitat availability, we import, from
the statistical literature, methodology that can abstract
the composition of environmental space, reducing the
detailed availability profile for all habitats to a simple
parametric approximation. This approximation allows
us to obtain computationally efficient expressions for
the fitness of organisms living in different environments
under exponential (Connecting habitat use to exponential
population growth) and density-dependent (Connecting
habitat use to density-dependent population growth)
population growth. In A note on the relationship between
partial fitness and habitat suitability, we discuss the link
between measures of habitat suitability (derived from
observations of habitat usage) and the underlying fitness
offered by different habitats. In Parameter estimation
from space-use and population time-series data,we
describe how the analytical expressions from Connecting
habitat use to exponential population growth and
Connecting habitat use to density-dependent population
growth can be used with r eal data on po pulation
distribution and growth to estimate the parameters
linking the environment to the average fitness of a
population. We apply these methods to data from a
simulation of animal redistribution and demography
(described in Simulation) in three simulation experi-
ments (outlined in Simulation experiments) that examine
the goodness of fit of the method, its predictive ability,
and its sensitivity to the amount and type of available
data. Finally, we discuss how the work presented here
can be extended, hence outlining a research program
that aspires to the development of practitioner-friendly
joint inference from spatial and temporal data.
T
ERMINOLOGY
We retain the basic distinction between geographical
space (G-space) and environmental space (E-space),
historically known as Hutchinson’s duality (Hirzel and
LeLay 2008, Colwell and Rangel 2009, Elith and
Leathwick 2009). G-space comprises the three dimen-
sions of latitude, longitude, and altitude/depth, often
projected onto a Cartesian system of coordinates. In
contrast, each dimension in E-space represents a biotic
or abiotic environmental variable, i.e., a continuous,
discrete, or qualitative random variable representing a
condition (e.g., pH, temperature, sea depth), resource
(e.g., soil nutrients, prey, breeding sites), or perceptible
threat (e.g., predators, pollution). Environmental vari-
ables may or may not correlate with the geographic
distribution of the study species. Those that do are
called its covariates.
Here and elsewhere (Aarts et al. 2008, Matthiopoulos
et al. 2011), we define a habitat x as a point in E-space,
the combination of specific values for K environmental
August 2015 415LINKING HABITAT TO POPULATION GROWTH
variables (e.g., geomorphology and climate variables
combining into the characteristic makeup of polar
habitat). Alternatively, habitat has been defined in a
species-dependent way as the region in geographical
space in which an organism lives (e.g., polar bear
habitat). The two definitions are not interchangeable
(see Hall et al. 1997). We opt for the first definition
because it allows objective comparisons between species
and quantitative gradations of suitability.
Space use (u
s
) is the expected usage of the neighbor-
hood (e.g., a grid cell) centered at a point s in G-space,
i.e., the proportion of an individual’s or a population’s
time that is likely to be spent there on average. Use can
be equally well defined infinitesimally on single points in
space as the spatially varying intensity function of an
inhomogeneous Poisson process (Warton and Shepherd
2010, Aarts et al. 2012). Habitat use (u
x
), the proportion
of time spent in regions of E-space, or equivalently, the
intensity of use of points in E-space, is not only
influenced by the suitability of these habitats to an
organism, but also by the abundance and accessibility
(Matthiopoulos 2003) of these habitats (collectively,
their availability). Assuming purely continuous environ-
mental vari abl es (wit h no lo ss of ge nera lity ), we
introduce the function f
x
representing habitat availabil-
ity as the probability density of habitat x in E-space (i.e.,
the unconditional likelihood with which this habitat
occurs at any given point of G-space).
If the behavior and demography of organisms were
unaffected by their environment and they were allowed
to move/disperse randomly for a long time within the
study area (resulting in an asymptotically homogeneous
distribution in G-space), habitats would be used in
proportion to their availability. Therefore, deviations
from proportional usage indicate the existence of a
response (apparent preference or avoidance). Conse-
quently, many analyses define preference w
x
as propor-
tional to the ratio of habitat use over availability
(Johnson 1980, Manly et al. 2002, Aarts et al. 2008,
2013). Different animals will vary in the behavioral
perceptiveness, speed, and precision with which they can
track good habitats in the environment. The presence of
an organism in a particular habitat may be as much the
result of active selection as of passive happenstance (an
individual may be encountered there because of differ-
ential survival rather than choice). Here, we will replace
the active term ‘‘habitat preference’’ by the more passive
‘‘apparent habitat suitability’’.
The average fitness F(f) that a population can acquire
from its environment (denoted f, the vector of individual
availabilities f
x
for all habitats x in E-space ) is defined
as the population’s log-rate of change (we will expand
on this definition of fitness in Environmental determi-
nants of fitness). A habitat that can satisfy all life-history
priorities of a species (e.g., nutrition, rest, mating, birth)
may be called sufficient. A habitat that can satisfy only
part (or none) of the life-history priorities is called
insufficient. We will call multifunctional those habitats
that can satisfy more than one life-history priority.
Sufficient habitats are multifunctional but the reverse
may not be true. We define partial fitness F
x
2 (‘,‘)as
the contribution of each unit of habitat x to the average
fitness of a population. Partial fitness can be interpreted
as the fitness of a population living in an environment
made up entirely of habitat type x.
E
COLOGICAL SCOPE AND SIMPLIFYING ASSUMPTIONS
We collect here 10 important assumptions that set out
the scope of this study. Relaxing these assumptions will
form the basis for future extensions of our work, so we
return to them in Discussion.
1. Accessibility of environment to the population.—An
assumption implicitly made by most analyses of species
distribution is that the populations are not systemati-
cally (or due to historical effects) prevented from
accessing good-quality habitats (Manly et al. 2002,
Matthiopoulos 2003). This assumption could, for
example, be violated by natural or manmade boundaries
(Beyer et al. 2014), or by the existence of transient
processes such as invasion fronts. In practice, this
requires the user to define an appropriate G-space in
which all areas are accessible by the population
(Northrup et al. 2013). For our simulations (Simulation),
we reduce the effects of accessibility by implementing
toroidal spatial boundaries and employing a settlement
phase at the start of each simulation.
2. Spatial pseudo-equilibrium.—Our assumption here
(as in most SDM approaches; Guisan and Thuiller 2005)
is that the spatial usage data do not capture a
population whose distribution is still undergoing chang-
es due to a delayed response to the environment. In the
context of a continually changing environment, we
assume that the spatial distribution of a population
adjusts readily, and thus, SDMs fitted to annual data are
not likely to be misguided by transient patterns. This
assumption builds on assumption 1 (on accessibility) by
requiring that all of space is accessible by the population
rapidly enough to allow the pseudo-equilibrium distri-
bution to be approximately achieved between sampled
snapshots of spatial distribution. Note that this does not
require the population size to have reached equilibrium.
3. Habitat use by individuals is representative of the
population’s habitat use.— Our methods, as they cur-
rently stand, apply to freely moving animals whose
survival and reproductive success depend on all of the
habitats they have experienced d uring a year. We
assume that any population member experiences and
uses approximately the same mix of available habitats as
all the others. This assumption need not require
accessibility of all the landsc ape by every single
individual, if the environmental composition at the scale
of movement of individuals is sufficiently representative
of the composition of the entire landscape.
4. Treatment of resource depletion.—Although our
model examine s the effect of limited resources on
generating density dependence, for this study, we have
JASON MATTHIOPOULOS ET AL.416
Ecological Monographs
Vol. 85, No. 3
not examined the impact of the focal species on the
resources it relies on. Our framework can, in principle,
be extended to model resource–consumer dynamics (by
running coupled dynamical models for more than one
species), but we have here focused on the single-species
case. We justify this assumption by distinguishing
between three possibilities. For some species (e.g.,
generalist consumers), resources may regenerate quickly,
or their abundance may be driven by processes other
than the focal species’ density. In such a scenario, any
process of depletion will not be strongly coupled with
the dynamics of the study species. If the species of
interest causes slow depletion (e.g., over multiple years),
then this effect can be represented by snapshot data on
the annual distribution of the resources that enter the
model as a covariate. If depletion exists and is fast, a
resource layer can be depleted within the interval of a
year, potentially removing any initial spatial heteroge-
neity in its distribution. An SDM trying to correlate
species distribution with such a depleted resource would
usually fail to find a signal. This is a recognized issue in
the SDM literature and one advantage of correlating
usage with non-depletable environmental proxies of
resource productivity, instead of data on resource
abundance (Torres et al. 2008, Aarts et al. 2014).
5. Linearity in density dependence.—We have as -
sumed that use of a particular spatial unit by each
additional member of the population lowers that unit’s
suitability for the other individuals in it. Thi s excludes
processes such as the Allee effect, which would signify
that, at low overall values of density, increases in
density can have a positive effect on fitness (e.g., by
alleviating the per capita effect of predation risk at
larger populations). Although such a feature is not
included here, it could be captured by higher-order
(e.g., quadratic) terms in our model of d ensity
dependence.
6. Linearity in the response of fitness to increasing
usage of habitats or to increases in individual resources.—
For mathematical simplic ity, we here exclude the
possibility of diminishing fitness benefits from the
superabundance of any given habitat, or specific
resource. This means that every additional unit of good
habitat or resource has an unsaturating contribution to
population growth. From an individual’s point of view,
the benefit obtained from increasing amounts of a
resource or increasing usage of a particular habitat
should plateau to an asymptotic maximum (Austin
2002), for example, due to satiation. However, from a
population perspective, the number of individuals that
can be sustained by an ever-increasing resource is
unlimited. Hence, any short-term effects (such as the
daily satiation of an individual) should be counterbal-
anced by high survival and increases in the production
of new individuals.
7. Additivity of covariates in determining partial
fitness (within a habitat).—Although it is certainly true
that different resources, conditions, or sources of risk
may interact nonlinearly ( in a complementary or
antagonistic way) in determining organism fitness (Til-
man 1982), this important extension is beyond the scope
of the present study. We will instead model these effects
as purely additive influences within the linear predictor
of our statistical model of fitness (see Eq. 4).
8. Additivity of partial fitness in determining average
fitness (across different habitats).—We will assume that
the use of different habitats has an additive effect on
fitness. For example, this implies that organisms cannot
construct sufficient habitats by complementary use of
insufficient ones.
9. No population structure.—The population models
examined in this study are simple. Beyond the focal
features of de nsi ty dependence and sp atia l/habi tat
effects, we have eschewed the possibility of reproductive
time delays, age structure, or any other form of
individual variation that is not driven by habitat.
10. No genetic change.—Assumption 9 also implies
that no evolutionary processes take place. Hence, we
require that the study questions are posed over short
time-horizons, population members are genetically
similar, and any environmental change is sufficiently
non-directional that the only adaptation takes the form
of spatial redistribution.
E
NVIRONMENTAL DETERMINANTS OF FITNESS
In our approach, the fundamental link between spatial
distribution and population dynamics is the average
fitness of a population. Fitness formalizes the intuitive
notion that different environments (i.e., collections of
habitats) should differentially affect a population’s short-
term rate of growth and long-term size (its carrying
capacity). In general, the fitness F(f,N
t
)thatapopulation
can acquire from a given environment f ¼ff
x
, for every
habitat x in Eg is defined as the population’s log-rate of
change, given its current size (N
t
)
N
tþ1
N
t
¼ expðFðf; N
t
ÞÞ: ð1Þ
We will further expand on issues of density depen-
dence in Connecting habitat use to density-dependent
population growth, and focus here on the dependence of
fitness on environmental makeup. Discrete-time models
are used because they offer a n easier entry point for
empirical investigations (population data are l ikely to
be discrete in time), but the same ideas could be
couched in continuous time. This ecological interpre-
tation of Eq. 1 has been extensively discussed in the
literature (Stenseth 1983, 1984, Nur 1984, 1987,
Murray 1985, Ollason 1991, Mills 2012) and the
equation has a long hi story of us e in evolutionary
models (Fisher 1930, Lande 1982, Roff 2008). Due to
the exclusion of genetic adaptation (assumption 10),
the interpretation of fitness in this study is purely
ecological, not evolutionary. Hence, our framework
currently builds no link between evolutionary fitness
(the viabil ity of a particular genotype living in a
August 2015 417LINKING HABITAT TO POPULATION GROWTH
