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\begin{document}

\title{Sink populations decouple species occupancy and persistence across a
productivity gradient}



\author[1]{Emilie Craig}%
\author[2]{Megan Szojka}%
\author[3]{Rachel Germain}%
\author[2]{Lauren Shoemaker}%
\affil[1]{University of Colorado Boulder}%
\affil[2]{University of Wyoming}%
\affil[3]{University of British Columbia}%


\vspace{-1em}



  
  \date{May 25, 2024}


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\selectlanguage{english}
\begin{abstract}
For decades community ecology has examined empirical relationships
between ecosystem productivity and diversity. Despite this long history,
tests of hypothesized mechanisms, namely the interplay between
environmental filtering, biotic interactions, and dispersal, are
lacking, largely due to their intractability using traditional
approaches. Across a productivity gradient in a serpentine grassland in
California, USA, we coupled occupancy data for four annual plants with
persistence measures of paired transplants under natural conditions and
reduced biotic interactions with neighbors. We found a positive
relationship between productivity and biodiversity (i.e., the proportion
of our four focal species found in a location) despite strong
competition limiting species persistence in productive environments.
Additionally, across species and for the community, we found a strong
mismatch between occupancy and persistence, largely due to dispersal
excess. Our results suggest that biodiversity-productivity relationships
can be largely driven by dispersal and its interactive effects with
local biotic and abiotic conditions.%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

The relationship between ecosystem productivity and biodiversity has
been examined well over 1,000 times since it was proposed (Pianka 1966;
Odum 1969), with multiple conceptual frameworks and empirical tests. Yet
evidence of its direction is inconsistent among (e.g., (Mittelbach
\emph{et al.}2001) and even within (e.g., Adler \emph{et al.} 2011)
studies: sometimes it takes on the expected hump shape, other times a
positive relationship, while in some cases a negative or non-existent
relationship (Mittelbach\emph{et al.} 2001; Gillman \& Wright 2006;
P\selectlanguage{ngerman}ärtel\emph{et al.} 2007). These inconsistencies have led to criticism
and intense debate (e.g., Fridley \emph{et al.}2012; Tredennick \emph{et
al.} 2016) behind the mechanisms underpinning these relationships
(Abrams 1995) and methodological approaches (Whittaker 2010). Focusing
on pinpointing the mechanisms that underlie diversity-productivity
relationships could address how different biodiversity patterns emerge,
identify significance of the patterns, and allow for predictive models.
A parallel goal in population ecology is understanding mechanisms that
yield variability in the performance of individual species along
gradients of environmental stress (i.e. productivity): the
`stress-gradient hypothesis' (Malkinson \& Tielbörger 2010). Although
the stress-gradient hypothesis tends to be tested at geographic scales
and for individual species, such as across a species' range
(Ziffer-Berger \emph{et al.} 2014), similar processes likely occur
within landscapes. Despite the similar goals of these two subfields, to
our knowledge, methods from population ecology have not been applied to
the study of mechanisms underlying diversity-productivity relationships
in community ecology.

To understand how methods of testing the stress-gradient hypothesis
apply to diversity-productivity relationships, it is useful to see the
net biodiversity of communities as collections of populations across
environments. If a population can persist in an environment, it adds to
the richness of the community. `Persistence' is defined as a
population's ability to maintain itself via survival and reproduction,
i.e., per capita population growth rates (\selectlanguage{greek}\emph{λ} \selectlanguage{english}) [?] 1. In studies of
the stress-gradient hypothesis, fitness is commonly measured on
individuals that have been transplanted across the stress gradient. When
averaged across individuals, absolute fitness is equivalent to per
capita population growth (Brady \emph{et al.} 2019). By employing
methods that measure persistence, we can then identify (i) where along
the productivity gradient different species are expected to persist and
whether occupancy mirrors persistence, (ii) if different species exhibit
similar or dissimilar relationships with productivity, and consequently,
(iii) what biodiversity patterns emerge as we aggregate species together
in a given environment. For example, biodiversity-productivity
relationships might emerge if species differ in how sensitive they are
to conditions across the gradient, if the magnitude of species
interactions differs between environments, or if species are
increasingly lost in poor conditions due to an increased effect of
stochasticity within smaller population sizes (Lande 1993;
Shoemaker\emph{et al.} 2020). In order to make these inferences,
persistence of all species under consideration must be tested together
across the extent of the same productivity gradient. As we will
describe, adopting this approach can help answer two outstanding
questions about why populations and communities are affected by
environmental gradients and address the implicit assumption that
patterns in species occurrence and biodiversity across gradients mirror
persistence.

The first outstanding question is to what extent are species
interactions (e.g. competition, facilitation) versus environmental
filtering driving biodiversity-productivity relationships. Productivity
gradients may affect biodiversity patterns directly, due to abiotic
suitability (i.e., species' fundamental niches), or indirectly, by
modifying the strength and direction of species interactions (i.e.,
species' realized niches) (Chase \& Leibold 2009; Germain \emph{et al.}
2018; Carscadden \emph{et al.} 2020). Theory suggests that as conditions
improve, communities crowd causing competition for limiting resources
(Harpole \& Tilman 2007; Craine \& Dybzinski 2013), thus reducing
opportunities for niche partitioning and coexistence (Harpole \& Tilman
2007). Yet the intensity of biotic interactions and consequences for
diversity across productivity gradients may not be so straightforward:
competition may vary linearly or nonlinearly or even transition to
facilitative interactions (a key prediction of the stress-gradient
hypothesis) with abiotic stress (Bertness \& Callaway 1994; He \emph{et
al.} 2013; Louthan \emph{et al.} 2021). To disentangle direct effects of
productivity on persistence from indirect effects through biotic
interactions, one could measure \selectlanguage{greek}\emph{λ} \selectlanguage{english}on populations of different
species transplanted across a productivity gradient, removing neighbors
(i.e., isolating the direct component) or leaving biotic interactions
intact. Comparing these \selectlanguage{greek}\emph{λ} \selectlanguage{english}elucidates how biotic interactions
change in magnitude and direction across the productivity gradient.
Although intuitive and straightforward, we emphasize that applying this
kind of manipulative approach has only been proposed to test the
stress-gradient hypothesis in the last half decade (Louthan \emph{et
al.}2015; Jones \& Gilbert 2016), and thus, empirical applications are
still uncommon, especially when scaling from single species to a
community context. Studies taking this approach would mutually benefit
both fields.

The second outstanding question is to what degree does species richness
reflect local conditions vs. conditions at larger scales via linkages
with dispersal. More specifically, a common goal in the stress-gradient
literature is to ask if range limits (i.e., the spatial extent of a
species' distribution) reflect niche limits, as opposed to limited
dispersal (Hargreaves\emph{et al.} 2014). By transplanting individuals
into locations where absent, thereby simulating dispersal, one can ask
if species can maintain populations, and thus if dispersal limitation
decreases diversity. This method can be easily extended to test
dispersal's other effect: the maintenance of ``sink'' populations due to
dispersal excess that, in the absence of dispersal, would fail to
persist (Howe \emph{et al.}1991; Pulliam 2000). Sinks may be common if
there is high heterogeneity in local conditions in space or time
relative to the scale of dispersal (Jorgensen \& Fath 2008; Zelnik
\emph{et al.} 2021). By measuring growth rates of transplanted
individuals along with species natural distributions, we can determine
how dispersal interacts with the biotic and abiotic environment to
result in biodiversity patterns (Leibold \& Chase 2017). Compared to
tests of the stress-gradient hypothesis, dispersal is less often invoked
as a mechanism affecting biodiversity-productivity relationships (but
see P\selectlanguage{ngerman}ärtel \& Zobel 2007) despite being key to theories of biodiversity
maintenance (i.e., metacommunity theory) (Leibold \emph{et al.}2004;
Leibold \& Chase 2017).

In this study, we bridge from population to community ecology, testing
the interplay and strengths of local and regional processes that may
underlie the stress-gradient and biodiversity-productivity
relationships. To do so, we combined occupancy surveys, neighbor
manipulations, and fitness assays on transplanted individuals of four
annual plant species in a highly heterogeneous natural grassland that
spans harsh to productive serpentine habitat. We used these data to
test: (1) if species-level occupancy patterns align with persistence
under natural conditions, (2) the role of environmental filtering versus
biotic interactions in generating stress-gradient and
diversity-productivity relationships, and (3) the influence of dispersal
on diversity patterns. We predicted a poor alignment between occupancy
and persistence due to both dispersal of species beyond their niches and
transient populations caused by high spatiotemporal environmental
variability. Consistent with the stress-gradient hypothesis, we
predicted that competition would be most intense in high productivity
environments, weakening or even transitioning into facilitation in less
productive environments. Finally, paralleling metacommunity theory, we
hypothesized that dispersal would play a key role in structuring
diversity at the community level, while exploring if dispersal varies
across the productivity gradient and if dispersal excess vs. limitation
dominates. By integrating the stress-gradient hypothesis for populations
with diversity-productivity and metacommunity theory for communities, we
quantified both local and regional level processes structuring
biodiversity, thereby testing how well species occupancy mirrors
persistence and the mechanisms that may lead to mismatches.

\section*{Methods}

{\label{methods}}

Study System

We conducted fieldwork at McLaughlin Natural Reserve in Northern
California (38.860643 N, -122.364156 W; Fig. S1). The Reserve lies
within a Mediterranean climate region, characterized by cool wet winters
and hot dry summers. During the 2019/2020 growing season, the average
temperature was 20.1\selectlanguage{english}, in line with a five-year average of 19.3\selectlanguage{english} (i.e.,
2014-2019; range = 17.8\selectlanguage{english}-20.6\selectlanguage{english}; SD = 0.63; Western Regional Climate
Center 2022). Total annual rainfall during 2019/2020 was 35.89cm, lower
than the average of 82.11cm observed during the reference period (range
= 45.14cm-129.79cm; SD = 33.92; Western Regional Climate Center 2022).
McLaughlin Reserve is dominated by serpentine soils, a soil type that is
common in subduction zones. Serpentine soils are characterized by a high
heavy metal content, low soil moisture retention, nutrient limitation,
and high Mg:Ca ratios. Despite these poor conditions, many plants from
serpentine regions have adapted to tolerate serpentine soils (Anacker
2014). However, serpentine soils can vary dramatically in fertility,
chemical composition, and physical properties, resulting in stark
differences in plant productivity even among sites only 100m apart.

Species and Site Selection

We chose four focal annual plant species to use as our
transplants:\emph{Bromus hordeaceus} (non-native grass), \emph{Festuca
microstachys}(native grass), \emph{Micropus californicus} (native herb),
and\emph{Plantago erecta} (native herb). We chose these species because
they differ in life history (two grasses, two herbs), provenance (three
native, one non-native), and are common across the field site. As annual
plants, individuals can be transplanted to new locations as seeds, and
we can measure germination, survival, and reproduction in a growing
season.

We chose six sites for our transplant experiments and to source seeds
from. These sites were chosen because they were in close proximity to
sites used in previous work (Germain \emph{et al.}2017), they varied
dramatically in total plant production (from mostly bare ground (5\%
cover) to dense cover (100\% cover )), and they were relatively evenly
spaced to cover a total spatial extent of 45 km\textsuperscript{2}. In
May of 2019, we sourced seeds from hundreds of individuals in
approximately equal numbers from a total of 18 populations; three
located within each of the six sites. Critically, sourced populations
did not overlap with exact transplant locations to minimize any home
site advantages of seeds collected from and transplanted back into the
same locations. We pooled all collected seeds per species to create a
``regional'' pool of seeds, so that any differences in success among
seeds due to site of origin would be averaged across all of our
transplanted individuals.

\emph{Experimental Design}

At each of our six sites, transplant locations were arranged in a nested
design with three levels (plot, block, and grid), in order to
systematically sample a large and representative variety of
environmental conditions (Fig. S2). Three 5 x 5 m grids were placed
within each site. Each grid contained 25 blocks that consisted of two,
paired 0.09 m\textsuperscript{2} plots. Each paired plot received one of
two treatments: (1) `abiotic only', where the entire plot was cleared of
all above ground vegetation as well the seedbank, or (2) `abiotic +
biotic', where plots were left intact. We cleared plots by clipping
aboveground biomass, then disturbing the soil using trowels to remove an
inch of topsoil and its associated seedbank (Germain \emph{et al.}2017).
We reduced cover by an average of 41\% +- 0.89 SE, thus allowing for
contrast between intact vs relaxed biotic interactions (Fig. S3, S4).

To test how persistence and occupancy varied across a productivity
gradient, we measured `greenness' of photos of every plot taken at peak
biomass (May 2020) as a proxy for productivity at the block level
(n=450). To do so, we used the Fiji package (Schindelin \emph{et
al.}2012) in Image J, choosing the `green band - red band' vegetation
index to measure productivity; this index best predicts aboveground
biomass in low productivity systems, such as serpentine, on a global
scale (Prabhakara \emph{et al.}2015). Although the vegetation index
spanned -22 to 10 , with harsher plots represented by higher numbers,
for a more intuitive interpretation we multiplied our index by -1 so
that more productive plots had higher numbers (Fig. S5). Although
harvesting and weighing aboveground biomass would be a more direct
measure of plot productivity, doing so was not possible as seeds were
collected by local field assistants on emergency funds during the
Covid-19 lockdowns.

\emph{Transplant Experiment and Data Collection}

All four species were transplanted into each plot from our regional pool
of seeds. At the corner of each plot, we hammered a 1 x 2.5 cm (diameter
x length) polypipe tube into the ground with a 0.5 cm lip above the soil
surface (Germain \emph{et al.} 2022). We left 15 cm around each tube to
prevent transplants from interacting directly, as it is a typical
neighborhood size for small annual plants (Mayfield \& Stouffer 2017).
In each tube we planted two seeds of the same species to increase
chances that at least one would germinate (7,200 seeds total). Using
tubes prevents seeds from washing away and allows us to distinguish our
transplanted individuals from individuals that naturally occur in plots
(Germain\emph{et al.} 2022); the tubes are short enough that they are
unlikely to impede root growth or competition belowground. If we
encountered a rock in locations designated to receive a transplant, we
forgoed planting the seed and marked germination and seed production as
`zero' to reflect the unsuitability of this microsite.

At the end of the growing season (May 2020), we returned to quantify
occupancy and persistence. First, to quantify occupancy, we photographed
every block for image analysis. We recorded if our four focal species
occurred naturally (binary), as well as a rough measure of abundance
(i.e., four categories: zero individuals, 1-10 individuals, 11-100
individuals, and \textgreater{}100 individuals per plot). Second, to
quantify persistence, we scored whether transplanted individuals in each
tube germinated (binary), survived to reproduce (binary), and collected
all seed and biomass. We also recorded instances of obvious herbivory
(e.g., lopped off seed head) or if a tube went missing (total of 393
instances, mostly due to birds stealing tubes). We counted every seed
produced by each transplanted individual, as well as noted whether or
not one or both of the two transplanted seeds per tube survived to
produce seed so we could account for it in our analyses. Given that two
seeds were planted into each tube, population growth rates were
calculated per capita (\selectlanguage{greek}\emph{λ} \selectlanguage{english}) and were used to create a binary
variable of whether each population was persistent (\selectlanguage{greek}\emph{λ} \selectlanguage{english}[?]\selectlanguage{english}1) or not
(\selectlanguage{greek}\emph{λ} \selectlanguage{english}\textless{}1). Together, these data allow us to identify how
populations experienced the suitability of the landscape along a
productivity gradient.

\emph{Statistical analyses}

All analyses were conducted in R version 4.1.1 (R Core Team 2021),
generally using the same approach; for brevity, here we first describe
our general approach before describing each analysis. We used
generalized linear mixed effects models with package `glmmTMB' (version
1.1.4) (Brooks \emph{et al.}2017). All models incorporated the same
random effects structure that reflected our nested study design:
(1\textbar{}site/grid/block). `Productivity', which was included as a
predictor in all analyses, was rescaled to center on zero with a
standard deviation of 1 using the `scale' function to ease model
fitting. For any analyses where alternative model structures needed to
be compared, we selected the most appropriate model using an AIC
comparison, where the model selected had the lowest AIC by at least 2
points, and we used package `DHARMa' (version 0.4.6; (Hartig 2022) to
test model assumptions, for example overdispersion. If any issues were
detected, we modified our model until all DHARMa tests were satisfied.
To assess the significance of parameters in our models, we used the
`car' (version 3.0.12) package, starting with type III sums of squares
for models including interactions, defaulting to type II sums of squares
if interactions were non-significant (Fox and Weisberg 2019). For
plotting, fitted relationships between variables based on our fitted
models with 95\% confidence intervals were extracted using the
`ggpredict' function in the `ggeffects' package (version 1.2.3) (L\selectlanguage{ngerman}üdecke
2018).

We first tested patterns at the species level, examining how growth
rates varied across productivity. We applied our general approach above
to perform separate analyses for each species, modeling seed production
as a Poisson-distributed response variable, and productivity, the
presence or absence of neighbors, and their interaction as explanatory
variables. Species could differ in whether or not productivity was a
linear or quadratic predictor, and whether zero inflation was accounted
for as an intercept or allowed to change across the gradient (Table S1).
When zero-inflated models were used, the model fits two components: the
zero component, which is interpreted as a failure to germinate and
survive to adulthood, and the conditional component, which is
interpreted as the reproductive output of adults (Bontrager \& Angert
2019). We repeated these analyses for each species, with occupancy
(i.e., presence/absence) as a binomial-distributed response variable.

We next tested how species-specific responses integrated to predict
persistence and occupancy of species at a community level. In each
`abiotic + biotic' plot, we calculated the proportion of species that
could persist (i.e., \selectlanguage{greek}λ \selectlanguage{english}[?] \selectlanguage{english}1) and the proportion of species that naturally
occurred. These proportions were used as a binomially-distributed
response variable, including a `weight' of number of species (i.e.,
number of `trials'; usually four but fewer in cases where tubes were
lost). Note that here, species richness was observed out of four
potential species, warranting a binomial distribution. For this analysis
we included the following predictors: productivity (competing models
with linear and quadratic relationships), type of data (i.e., three
levels, either persistence with neighbors, persistence without
neighbors, or occupancy), and their interaction. Separating our
proportions by type of data allowed us to identify how biotic
interactions altered mismatches between patterns of occupancy and
persistence.

Lastly, we coupled our persistence and occupancy data to determine how
dispersal limitation, excess, and species-sorting varied across
productivity. When dispersal is limited, species are absent from
locations that could otherwise support their persistence (outcome 1),
whereas when there is excess dispersal relative to the scale of
spatiotemporal variation, leading to sink or pseudo-sink populations,
species are present in locations that do not support persistence
(outcome 2). Dispersal is `sufficient' (Leibold \& Chase 2017) when
species are present where they can persist and absent where they cannot,
also known as `species sorting' (outcome 3). We categorized each species
in each plot as falling in one of these three outcomes; these
categorical data were then used as a response variable in a multinomial
model using the `mblogit' function in the `mclogit package' (version
0.9.6) (Elff 2023). We chose a multinomial model (analogous to a
binomial except allowing more than two outcomes) because the three
outcomes were dependent and required to sum to one. As with our other
analyses, we used productivity, neighbor treatment, and their
interaction as explanatory variables. Predictions for this model were
computed with `predict' in contrast to our other analyses that used
`ggpredict' as the latter was not compatible with multinomial models.

\section*{Results}

{\label{results}}

\emph{Mismatch of Persistence and Occupancy Patterns in Natural
Conditions}

We found support for our prediction that persistence and occupancy were
mismatched across a productivity gradient, both when species were
considered individually and together as a community. Each species tended
to occupy a greater proportion of sites as productivity increased (Fig.
1, bottom row); these increases were strongest for \emph{Bromus} , a
species that was largely absent from sites of low to intermediate
productivity (?1= 1.04 \selectlanguage{ngerman}± 0.30; Table S2), and weakest for\emph{Plantago}
(\selectlanguage{english}?1= 0.26 +- 0.26; Table S2, bottom row of Fig. 1). By contrast, we
observed strong mismatches between persistence (i.e.,\selectlanguage{greek}\emph{λ}
\selectlanguage{english}\(\geq\)1) and occupancy. Under conditions with neighbors, two
species (\emph{Micropus} , \emph{Festuca} ) were significantly more
likely to persist in more productive environments (Table S3), mirroring
occupancy, whereas for the two others (\emph{Plantago} , \emph{Bromus}
), less productive sites were more conducive to persistence (Table S3;
Fig. 1 red lines). Note that \emph{Micropus} was not predicted to
persist in any location (\selectlanguage{greek}\emph{λ} \selectlanguage{english}\textless{}\textless{} 1).
Surprisingly, for all species, occupancy patterns more closely reflect
persistence in the abiotic treatment (Fig. 1, blue) compared to the
biotic treatment (red).

When scaling from species to the community, persistence significantly
decreased with productivity (slope = -0.25 {[}-0.40, -0.096{]}, brackets
denote 95\% CIs), whereas occurrence responded oppositely, increasing
with productivity (slope = 0.57 {[}0.42, 0.72{]}; i.e., significant
interaction between productivity and data type (i.e., persistence data
vs. occupancy data); \selectlanguage{greek}\emph{χ2}\selectlanguage{english} = 84.94, \emph{df} = 2,
\emph{P}\textless{} 0.001; Fig. 2). As a result, in unproductive
environments, fewer species occurred than could persist. In contrast, in
productive environments, most species could occur but relatively few
could persist at their current population size (i.e. \selectlanguage{greek}\emph{λ}
\selectlanguage{english}\textless{}1).

\emph{Support for and nuances underlying the stress-gradient hypothesis
and the role of species interactions}

We found strong support for our hypothesis that biotic interactions
would become increasingly competitive in more productive environments
(Table S4; Fig. 3). Although this pattern was observed for all four
species (i.e., greater difference between blue and red lines in
productive areas in Fig. 1A-D), there were also interesting nuances. For
one species, growth rates increased with productivity when neighbors
were present (\emph{Festuca} : ?1 = 0.167 \selectlanguage{ngerman}± 0.12; Table S2, red data in
Fig. 1D), whereas for two, population growth rates decreased
(\emph{Plantago} : \selectlanguage{english}?1 = -0.10 +- 0.12, \emph{Bromus} : \selectlanguage{english}?1 = -1.00 +- 0.18;
Table S2, red data in Fig. 1B,C). As a result, each species' fundamental
and realized niches differed (see `Neighbor treatments' term for each
species in Table S3). Competition appeared to be absent for all species
at the unproductive end of the gradient, with weak evidence of
facilitation (i.e., \selectlanguage{greek}\emph{λ} \selectlanguage{english}without neighbors \textgreater{}
\selectlanguage{greek}\emph{λ}\selectlanguage{english}with neighbors) only in a few specific cases. \emph{Plantago}
and\emph{Festuca} patterns showed evidence of facilitation for seed
production and early germinate survival (i.e., zero-inflated component
of the model; Fig. S6B, D), while \emph{Bromus} showed weak evidence of
facilitation in the fecundity (i.e., conditional) component of \selectlanguage{greek}\emph{λ}
; \selectlanguage{english}Fig. S6 F).

Taken together, at a community level, productivity had opposing effects
on the number of species that could persist depending on the presence or
absence of neighbors: in the most productive locations (i.e., vegetation
index of 2), persistence without neighbors was 1.58 times greater than
persistence with neighbors (\emph{P} \textless{} 0.001; Fig. 3; Table
S5). Notably, these relationships were linear at the community level
despite a diversity of non-linear relationships observed for individual
species (Table S1; Fig. 2A-D).

\emph{Dispersal underpins mismatches between persistence and occupancy}

By exploring (mis)matches between occupancy and persistence across the
productivity gradient, we found that the role of dispersal is contingent
upon environmental conditions (Fig. 4, Table S6). In unproductive
environments, populations were most likely to be well-matched to
conditions they were found in regardless of whether neighbors were
present or absent--species sorting was observed in 65\% of species
{[}51-81{]} with neighbors, compared to 0.64 {[}0.51, 0.78{]} without
neighbors (Fig. 4; gray). By contrast, in productive environments, sink
populations were common, especially in the presence of neighbors,
suggesting that dispersal tended to be excessive, causing populations in
locations that could not maintain a positive growth rate (Table S6).
Growth rates and proportion of sink populations were not dependent on
intraspecific density dependence (Figs. S7, S8). Generally, dispersal
limitation was uncommon regardless of species interactions. Similar
qualitative trends in species sorting, dispersal limitation, and
dispersal excess occurred with neighbors and without neighbors (Table
S6).

\section*{Discussion}

{\label{discussion}}

Multiple conceptual pillars of community ecology, from spatial and
temporal species accumulation curves to the diversity-productivity
relationship, are built from patterns of species richness (Ugland
\emph{et al.} 2003; van Ruijven \& Berendse 2005; Ulrich 2006). Patterns
of diversity across landscapes are commonly evoked to infer assembly
mechanisms (Scheiner 2003) and are used to inform conservation and
restoration practices (Fleishman \emph{et al.}2006). Here, we find that
for both populations and the aggregate community, species occurrence is
strongly mismatched from species persistence across a productivity
gradient, emphasizing that occupancy patterns are a poor predictor of
where conditions are suitable for maintaining biodiversity. Critically,
by comparing occurrence patterns to persistence of transplanted seeds
under conditions with and without biotic interactions, we disentangled
the impacts of environmental filtering, interactions between neighbors,
and dispersal on community assembly and diversity patterns (Vellend
2010; HilleRisLambers \emph{et al.} 2012). Below, we discuss how our
results bridge from patterns to processes, advancing our understanding
of the mechanisms structuring the diversity-productivity relationship by
integrating niche, range limit, metacommunity, and stress-gradient
theories.

Species' distributions across the productivity gradient largely
supported literature on the diversity-productivity relationship. In our
study, occupancy patterns of the aggregate community show a linear
increase with productivity, rather than the also commonly observed
unimodal, hump-shaped relationship (Mittelbach\emph{et al.} 2001; P\selectlanguage{ngerman}ärtel
\& Zobel 2007; Fraser \emph{et al.} 2015). Given that our experiment is
representative of a smaller area on the harsher side of the global
gradient, we may expect to see the linear slope descend into a
hump-shaped curve if surveyed at a larger spatial scale (Venail \emph{et
al.} 2010; Germain \emph{et al.} 2019). Critically, our observed
diversity-productivity relationship is driven primarily by sink
populations, yielding a mismatch between species' distributions,
realized niches, and fundamental niches (Pulliam 2000; Chase \& Leibold
2009; Carscadden \emph{et al.} 2020).

While environmental filtering structured species' fundamental niches at
the species level (Fig. 1; blue lines), it exhibited a relatively weak
effect on community diversity (Fig. 3; purple line), despite being
evoked as a seminal process structuring populations and communities in
heterogeneous landscapes (Laliberté \emph{et al.}2014; Hallett \emph{et
al.} 2019). Both occupancy and persistence without neighbors was highest
in productive ends of the gradient for three quarters of species,
implying that species distributions commonly matched their fundamental
niches. However, community occupancy patterns showed a weaker link to
persistence without biotic interactions (Fig. 3), with persistence
increasing only slightly with productivity. This suggests other
mechanisms were dominant in driving community diversity, thus countering
previous literature showing environmental filtering as the predominant
mechanism shaping diversity patterns (Laliberté \emph{et al.}2014; Le
Bagousse-Pinguet \emph{et al.} 2017).

Species interactions promoted strong mismatches between persistence and
occupancy for both the species-level and community. At the
species-level, occupancy was consistently highest in productive
environments while persistence with neighbors tended to be maximized in
harsher environments (Fig. 1 B-C, F-G). Unexpectedly, we found that
distributions matched species' fundamental niche more closely than the
realized niche. One explanation is that seeds deposited in a
neighborhood that had a suitable community of neighbors in the maternal
generation may be unlikely to experience a similarly suitable community
of neighbors in the current generation (Germain \emph{et al.}2022).
Neighborhood stochasticity would be especially pronounced in annual
systems with high turnover and with high spatiotemporal variability,
like California grasslands. More generally, our results comparing
species persistence with and without neighbors corroborates range limit
theory: in harsh environments abiotic conditions determine persistence,
whereas in productive species interactions set boundaries on persistence
(Grinnell 1917; Louthan \emph{et al.} 2015; Allbee \emph{et al.} 2023).
Yet, for\emph{Bromus} and \emph{Plantago,} positive interactions among
species promoted persistence in harsh environments, thus potentially
extending species' ranges (Stephan\emph{et al.} 2021). Scaling to the
community, these differences in species interactions across productivity
lend strong support to the stress-gradient hypothesis. Biotic
interactions shift from positive in harsh areas to competitive in more
productive environments, leading to strong differences in persistence
under environmental filtering alone versus when considering environment
by species interaction effects (Fig. 3).

The gaps between patterns of species distributions versus persistence
with neighbors points to the dominant role of dispersal in driving
population and community dynamics. We found collective effects between
dispersal, species interactions, and environment, emphasizing that
processes structuring communities are interactive rather than sequential
(Kraft \emph{et al.}2015; Cadotte \& Tucker 2017). At the species level,
mismatches between occupancy and persistence with neighbors (Fig. 1)
were driven by an excess of dispersal, yielding sink populations,
especially in productive areas. Given this mismatch, our results support
niche theories that allow realized niches to differ in distribution
from, or even exceed, the fundamental niche (Pulliam 2000; Louthan
\emph{et al.} 2015; Carscadden \emph{et al.} 2020). Further, the strong
role of excess dispersal underscores the operational value of distinctly
defining species' realized niche vs distributions (Soberón \& Nakamura
2009). At the community scale, we find that in harsh areas, species tend
to be aligned to their environment (Fig. 4). However, in more productive
environments, sink populations dominate---especially when species
interactions further restrict persistence. These results likely depend
on the scale of environmental heterogeneity; for example, Pinto et. al.
(2010) found that sinks were found in fine scales but not at coarse
scales. Considering seedbanks as a means of dispersal through time could
elucidate further links between dispersal, biotic interactions and
environmental filtering along gradients (Wisnoski \& Shoemaker 2022).
This study reveals the importance of considering a metacommunity
perspective, which emphasizes dispersal as a critical driver of
diversity patterns, when making inferences from observational data. We
identified a need for a more nuanced metacommunity theory (Leibold
\emph{et al.} 2004; Leibold \& Chase 2017; Thompson \emph{et al.} 2020)
including the interplay between environmental conditions and propagule
pressure (Allbee \emph{et al.} 2023).

Overall, our results emphasize the benefits of linking species to
community patterns and contradicts the assumption that persistence
patterns can be approximated via occupancy. While many methods attempt
to statistically link species occurrence patterns to underlying
mechanisms of dispersal, biotic interactions, and environmental
filtering, (Kraft\emph{et al.} 2011; Leibold \emph{et al.} 2022)
inferring patterns from processes is inherently fraught (Tucker \emph{et
al.}2016; Blanchet \emph{et al.} 2020). Rather, by empirically measuring
occupancy and persistence under abiotic and biotic environments where we
manually dispersed seeds, we directly quantified the mechanisms
structuring populations and communities, and in doing so integrate
several theories in ecology. We suggest that future work in annual plant
systems compare multi-year dynamics to disentangle spatial and temporal
assembly mechanisms, especially given the hypothesized role of
environmental fluctuations in maintaining coexistence (Hallett \emph{et
al.}2019; Van Dyke \emph{et al.} 2022). Extending these methods across
larger gradients could inform species distribution modeling under future
climate scenarios (Buckley\emph{et al.} 2010). Similarly, we envision
these methods informing long-term success in restoration practices and
the potential need for active management of competitors or regular seed
addition (Shackelford \emph{et al.} 2021; Aoyama \emph{et al.} 2022).
Our results provide a cautionary tale of inferring mechanisms that
structure populations and communities, or in forecasting future species
distributions or diversity, based solely on current occupancy patterns.

\section*{Acknowledgements}

{\label{acknowledgements}}

This work was funded by the California Native Plant Society, an NSERC
PGS-D awarded to M.S., NSF grants \#EPS-1655726 and \#EPS-2033292
supported E.C., M.S. and L.S, and an NSERC Discovery Grant supported
M.S. and R.G. (2019-04872). Thanks to Benji Mackay and Kately Nikiforuk
for assistance in setting up the experiment, Alec Chiono and Leigh Hiura
for collecting data and saving this project from border restrictions due
to the Covid-19 pandemic, Savanna Skinner for assistance processing the
data, and Dusty Gannon for assistance with statistical methods.

\par\null

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\section*{Figures}

{\label{figures}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1.} Species-level patterns of per capita population
growth rates \textbf{(A-D)} and occupancy \textbf{(E-H)} across a
productivity gradient. Productivity is represented by a green-red
vegetation index, where less productive sites are towards the left. In
panels A-D, dashed lines at \selectlanguage{greek}\emph{λ} \selectlanguage{english}=1 show the threshold for
persistence (i.e., positive population growth); blue and red data are
from the `without neighbors' and `with neighbors' treatments,
respectively, the latter most closely resembling natural conditions. The
isolated zero-inflation (i.e., germination) and conditional (i.e., seed
production) components of population growth are shown Fig. S6. Points
are the raw data jittered for interpretability, lines and 95\%
confidence bands are shown from the best fit models.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2.} Proportion of species along the productivity gradient
found to be occurring (dark brown data) versus persisting (light blue
data) in the presence of neighbors (i.e., under natural conditions).
Productivity is represented by a green-red vegetation index, where less
productive sites are towards the left. Proportions are based on a
maximum number of four species (the number of focal species used in our
experiment). Points are the raw data jittered for interpretability,
lines and 95\% confidence bands are fitted from our models. These data
were fit to a model that also included data on persistence in the
absence of neighbors, presented separately (Fig. 3) to streamline
interpretation; the blue data is common to both figures.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3.} Proportion of species along the productivity gradient
found to persist in the presence (light blue data) vs absence (dark
purple data) of neighbors. Neighbors have an overall facilitative effect
when the blue line is above the purple line and a competitive effect
when the purple line is above the blue line. Productivity is represented
by a green-red vegetation index, where less productive sites are towards
the left. Proportions are based on a maximum number of four species (the
number of focal species used in our experiment). Points are the raw data
jittered for interpretability, lines and 95\% confidence bands are
fitted from our models. These data were fit to a model that also
included data on persistence in the absence of neighbors, presented
separately (Fig. 2) to streamline interpretation; the blue data is
common to both figures.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4.} Proportion of species whose distributions are shaped
by limited (`dispersal limitation', dark red data), sufficient (`species
sorting', gray data), or excess (`sink populations', light blue data)
dispersal across the productivity gradient, as communities are connected
by dispersal to form a larger metacommunity. Data shown separately for
the \textbf{(A)} `with neighbors' and \textbf{(B)} `without neighbors'
treatments, respectively. Dispersal outcomes of species are categorized
as follows: `dispersal limitation' occurs when species can persist but
are absent from a location, `species sorting' is when a species is
present where it can persist or is absent where it cannot persist, and
`sink populations' are when species cannot persist at the current
population size, but are present. Productivity is represented by a
green-red vegetation index, where less productive sites are towards the
left. Proportions are based on a maximum number of four species (the
number of focal species used in our experiment). Points are the raw data
jittered for interpretability, lines and 95\% confidence bands are
fitted from our models.

\selectlanguage{english}
\FloatBarrier
\end{document}

