Abstract
Fish spawning phenology is a major concern for conservation and
fisheries management. New intensive data sources such as GPS-based
tracking data or high resolution catch declaration data are
progressively becoming available in the field of marine ecology. These
benefit from high spatio-temporal resolution and open new research
avenues to investigate inter-annual and seasonal variability of
phenology.
In this paper, we illustrate
how catch declarations modeling coupled with spatio-temporal dimension
reduction methods known as Empirical Orthogonal Functions (EOF) can be
used to synthetize spatio-temporal signals in fish distribution;
Specifically, we address the following questions; (1) can we identify
spatio-seasonal patterns that can be interpreted in terms of seasonal
migration between essential habitats? (2) can we identify changes in the
phenology? (3) are those changes related to environmental drivers?
The analysis is illustrated through the analysis of the reproduction
phenology on three key commercial species in the Bay of Biscay (Hake,
Sole and Sea Bass). The EOF analysis on these species emphasizes strong
seasonal spatio-temporal patterns that correspond to migration patterns
between feeding areas and reproduction areas. Based on this methodology,
we identify seasonal variations in the timing of the reproduction and we
relate them to Sea Surface Temperature, a key driver of fish
reproduction.
Keywords: species distribution, spatio-temporal modeling,
reproduction timing, spawning season.
Introduction
To complete their life cycle, fish require different habitats specific
to different life stages (Harden, 1969). Those habitats, also known as
Essential Fish habitats (Magnuson-Stevens Fishery Act, 2007) are
associated with key demographic processes in the fish life cycle such as
spawning, feeding and migrations and are characterized by a strong
concentration of individuals within a spatially restricted area.
However, rapid environmental changes may force fish to adapt, by
tracking their essential habitat in space and time, and by changing the
seasonal timing of their demographic processes (termed “phenology”).
Understanding changes in phenology of demographic processes is critical
for the management of fish population. Seasonal habitat utilization,
timing of migrations and location of spawning areas are key knowledge to
preserve fish essential habitats and ensure the renewal of marine
resources (Delage and Le Pape, 2016; Lieth, 2013). For instance, areas
where fish aggregate for spawning may require specific attention in
terms of fisheries management (Biggs et al., 2021; Grüss et al., 2019).
Also,marine Spatial Planning requires a good knowledge of fish essential
habitats to implement offshore wind farms or limit the impact of marine
aggregate extraction (Bastardie et al., 2015, 2014; Campbell et al.,
2014).
Still the available data to investigate fish spatio-temporal demographic
processes generally have sparse spatio-temporal coverage (e.g.scientific survey data, mark-recapture tagging data). Typically,
scientific surveys usually occur once a year and provide samples only on
the time span of the survey (Bastardie et al., 2015). Onboard observer
data provide additional data on the whole year by recording fishing
catches on a small portion of the commercial fleets (Rufener et al.,
2021). With these data, it is possible to infer fish distribution at a
seasonal or at a quarterly level at best (Kai et al., 2017; Olmos et
al., 2023). However, this temporal resolution is generally not enough to
investigate precisely the phenology of demographic processes that occur
at a shorter temporal scale e.g. month, week (Biggs et al.,
2021).
In the last decade, methods to combine fishermen declarations (logbook)
with Vessel Monitoring System (VMS) data (‘VMS x logbook’ hereafter)
have been developed to provide a fine scale information on fishing
activity and fishing landings (Bastardie et al., 2010; Hintzen et al.,
2012). In the last decade, ‘VMS x logbook’ data sources have been used
to infer fish spatio-temporal distribution at a fine scale (Alglave et
al., 2022; Azevedo and Silva, 2020; Dambrine et al., 2021; Murray et
al., 2013). These data benefit from a high spatio-temporal resolution
and consequently they open huge research avenues to investigate inter-
and intra-annual variability of fish spatial distributions.
Recently, a modeling framework has been built (1) to integrate ‘VMS x
logbook’ data from distinct fishing fleets to infer fish spatial
distributions and (2) to handle preferential sampling of fisheries data
(Alglave et al., 2022). The framework has been extended in time at a
monthly time step. It has been applied to map fish aggregation areas to
identify spawning grounds for a few key species of the Bay of Biscay
(Alglave et al., 2023). Still, these approaches only investigate a small
part of the time series: single year of data in Azevedo and Silva (2020)
or a specific period over several years in Alglave et al. (2023).
Consequently, they left apart the huge amount of information that can be
extracted from the analysis of a long-term time series. One reason for
this is the difficulty of simultaneously interpreting inter-,
intra-annual and spatial variations in fish distribution.
Dimension-reductions techniques such as Empirical Orthogonal Functions
(EOF - Hannachi et al., 2007; Lorenz, 1956) can provide insights into
the spatio-temporal variability of fish population processes. EOF have
been mostly used to characterize physical oceanography conditions. Some
recent studies have investigated fish processes using EOF (Grüss et al.,
2021; Petitgas et al., 2014; Thorson et al., 2020b, 2020a). However, to
the best of our knowledge, previous studies on EOFs for biological
processes have only aimed to synthesize the inter-annual variability of
these processes and have never studied the intra-annual variability
(i.e. phenology).
In this paper we aimed at demonstrating the potential of integrated
spatio-temporal hierarchical models (ISTHM - Alglave et al., 2023, 2022)
combined with EOF to:
- (i) identify spatio-seasonal patterns that can be interpreted in terms
of essential habitats and migration between these habitats;
- (ii) infer temporal changes in phenology over long term time series;
- (iii) to explore the role of environmental drivers in controlling the
phenology.
Taking sole, sea bass and hake in the Bay of Biscay as case studies,
inferences derived from EOF analyses are compared to the literature.
This allows to highlight the added value of our results with regards to
the available knowledge of the location of spawning grounds, the
intra-annual variability of spawning, and the environmental drivers of
reproduction. Finally, we also expect that the EOF analysis will help to
identify lesser-known or unknown essential habitats, such as feeding
grounds.
Material and methods
Outline of the approach
Our approach includes different steps that are detailed hereafter:
- Case studies and synthesis of the available knowledge on their
phenology. Sole, hake and sea bass are important fisheries of the Bay
of Biscay. Based on a literature review, we provide expectations on
the demographic processes, the essential habitat and the associated
seasons to be compared with our results.
- Inferring species distribution based on the ISTHM introduced
by Alglave et al.
(2022, 2023). We
rely on the framework developed by Alglave et al. (2023, 2022) to map
the biomass of the mature fraction of the population for each species
(hake, sole and sea bass) at a monthly time step over 2008 – 2018.
The statistical approach integrates data from distinct trawler fleets
that cover the whole Bay of Biscay.
- EOF and clustering analysis of the model outputs. To identify
and visualize essential habitats and related seasons, we synthetize
the temporal variation of the maps of abundance of mature fish through
an EOF analysis (realized independently for each species) followed by
a clustering analysis.
- Investigating intra-annual variability of the demographic
processes and relating phenological processes to environmental
drivers. Finally, we interpret the main modes of variability of the
EOF with regards to adult reproduction phenology. We investigate
intra-annual variability of reproduction and the drivers influencing
reproduction timing.
- Case studies description
We selected three case studies that are important species in the Bay of
Biscay and for which some knowledge on essential habitats is available
but incomplete: sole , hake and sea bass(ICES 2020, 2022).
Most of the literature on these species focus on spawning phenology
(summarized in Figure 1). For sole , Arbault et al.
(1986), Petitgas
(1997) and Alglave et al. (2022) identified spawning grounds along the
Bay of Biscay from January to March. For hake , Alvarez et al.
(2004) provided similar analysis based on surveys conducted in the 90’s
and Poulard (2001) have investigated rough scale spatio-temporal
distribution of hake based on logbook data. For seabass , recent
analyses have investigated the spawning area and timing based on ‘VMS x
logbooks’ data and provide information on phenology (Dambrine et al.,
2021). Additional information on the adults feeding grounds is available
for Sole (Figure 1).
Model structure and data to fit the model
Data and commercial fleets
We analyze catch per unit of effort (CPUE) of trawlers between 2008 –
2018, a relatively long period that allows to evidence intra- and
inter-annual changes in species distribution and phenology.
As we only want to interpret the spatio-temporal dynamics of adult
individuals, we filtered the mature fraction of the declarations by
crossing catch declarations with the size distribution in each
commercial category (see
Alglave et al. (2023)
for further details).
We selected the data of several trawler fleets as they benefit from a
relatively opportunistic behavior, and they usually cover a wide area
(Figure 2). Furthermore, their CPUE provides a good indicator of fish
relative biomass
(Hovgêrd et al.
2008). The selected fleets for each species are presented in Table 1.
Model structure and spatio-temporal resolution
To map the spatio-temporal distribution of the biomass of these
different species, we used the framework developed in Alglave et al.
(2023, 2022). The framework is a hierarchical integrated statistical
model that combines multiple data sources to infer spatial distribution
of fish density. The model is fitted to the data between 2008 and 2018
at a monthly time step on a 0.05° grid. It is structured in 3 layers:
(1) the latent field of relative biomass spatial distribution (the field
we want to infer);
(2) the observations layer; this layer can handle CPUE data from
different fleets including the distinct catchability of the fleets; CPUE
data are related to the same unique spatio-temporal field of relative
abundance
(3) unknown parameters, including the ones that control the shape of the
biomass latent field;
We simplified the framework developed by Alglave et al. (2022) by
ignoring the preferential sampling of fishermen. Indeed, previous
results by Alglave et al. (2022) have shown that preferential sampling
of trawlers is low. Considering it will therefore only slightly affect
spatial predictions while strongly increasing the computation burden
(Alglave et al., 2022).
EOF to identify essential habitats and to highlight
changes in phenology
EOF Basics: a gentle overview
EOF was initially developed by Lorenz (1956) for weather forecasting.
The broad idea is to generalize the classical dimension reduction
techniques like Principal Component Analysis to spatio-temporal
dimensions. EOF seeks to summarize the information brought by a set of
spatio-temporal maps into a smaller set of maps that best describe and
summarize the spatio-temporal patterns.
Let’s defined \(S(x,t)\ \)a biomass field defined at a time step\(t\ (t\ =\{1,\ldots,T)\) and spatial cell \(x\), and the centered
field of biomass\(S^{*}(x,t)=S(x,t)\ -\ \overset{\overline{}}{S(x,\cdot)}\) (with\(\overset{\overline{}}{S(x,\cdot)}\) the spatial average of\(S(x,t)\)). \(S^{*}(x,t)\) is expressed as a linear combination of
spatial patterns \(p_{m}\) (or maps, named EOF) related to temporal
indices (or loading factors) \(\alpha_{m}(t)\).
\begin{equation}
S^{*}(x,t)=\sum_{m=1}^{M}{\alpha_{m}(t)\cdot p_{m}(x)}\ ;\ \ \ x\in\{1,...,n\},\ t\in\{1,...,T\},\ M\ \leq\ T\nonumber \\
\end{equation}The loading factors \(\alpha_{m}(t)\) and the spatial patterns\(p_{m}(x)\) are defined to maximize the variation captured by the
spatial patterns \(p_{m}(x)\) and to ensure the spatial patterns and the
loading factors are orthogonal between each other. The first spatial map\(p_{1}(x)\) captures the biggest amount of spatial variation; the
second spatial pattern \(p_{2}(x)\) is orthogonal to the first one and
captures the second biggest amount of spatial variation. In matrix
terms, this falls back to a diagonalization problem and is equivalent to
make a PCA analysis on a data frame where individuals are time steps and
variables are locations (Lorenz, 1956). Classical PCA representation can
be used to represent EOF results. Typically, the first two loading
factors can be projected on the first two spatial patterns to get a
visual representation of the spatio-temporal decomposition of the signal
on the first plan of variability.
In practice, the diagonalization is performed through Singular Value
Decomposition (Banerjee and Roy (2014). It is available in R through the
function svd (R Core Team, 2023). Spatial patterns are normalized
to 1 and loading factors are standardized by the square root of their
eigenvalue.
Filtering EOF dimensions and locations of the spatial
pattern
For each species, we filter the number of dimensions based on the graph
of the variance explained by each dimension. As a commonly used
empirical rule of thumb, we cut the graph at the dimension where there
is a drop in the variance explained. When plotting the spatial patterns,
all the locations that contribute less to 1 / (number of grid cells over
the spatial domain) are shaded to highlight the locations that
contribute most to the variation. In standard PCA, this is equivalent to
keeping only the variables (i.e. locations in our case) that
explain or contribute more than a single variable (or location).
Identifying EOF results to phenological phases