bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
1
2
3 Resource competition shapes biological rhythms and promotes temporal niche
4 differentiation in a community simulation
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6 Resource competition, biological rhythms, and temporal niches
7
8 Vance Difan Gao1,2*, Sara Morley-Fletcher1,4, Stefania Maccari1,3,4, Martha Hotz Vitaterna2, Fred W. Turek2
9
10 1UMR 8576 Unité de Glycobiologie Structurale et Fonctionnelle, Campus Cité Scientifique, CNRS, University of 11 Lille, Lille, France
12 2 Center for Sleep and Circadian Biology, Northwestern University, Evanston, IL, United States of America
13 3Department of Medico-Surgical Sciences and Biotechnologies, University Sapienza of Rome, Rome, Italy
14 4International Associated Laboratory (LIA) “Perinatal Stress and Neurodegenerative Diseases”: University of Lille, 15 Lille, France; CNRS-UMR 8576, Lille, France; Sapienza University of Rome, Rome, Italy; IRCCS Neuromed, Pozzilli, 16 Italy
17
18
19 * Corresponding author
20 E-mail: [email protected]
21
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22 Abstract
23 Competition for resources often contributes strongly to defining an organism’s ecological niche. Biological
24 rhythms are important adaptations to the temporal dimension of niches, but the role of other organisms in
25 determining such temporal niches have not been much studied, and the role specifically of competition even
26 less so. We investigate how interspecific and intraspecific competition for resources shapes an organism’s
27 activity rhythms. For this, communities of one or two species in an environment with limited resource input
28 were simulated. We demonstrate that when organisms are arrhythmic, one species will always be competitively
29 excluded from the environment, but the existence of activity rhythms allows niche differentiation and indefinite
30 coexistence of the two species. Two species which are initially active at the same phase will differentiate their
31 phase angle of entrainment over time to avoid each other. When only one species is present in an environment,
32 competition within individuals of the species strongly selects for niche expansion through arrhythmicity, but the
33 addition of an interspecific competitor facilitates evolution of increased rhythmic amplitude when combined
34 with additional adaptations for temporal specialization. Finally, if individuals preferentially mate with others
35 who are active at similar times of day, then disruptive selection by intraspecific competition can split one
36 population into two reproductively isolated groups. In summary, these simulations suggest that biological
37 rhythms are an effective method to temporally differentiate ecological niches, and that competition is an
38 important ecological pressure promoting the evolution of rhythms and sleep.
39
40 Author summary
41 Why do we sleep? We are interested in the ecological factors which promote the evolution of biological
42 rhythms like the sleep-wake cycle, focusing especially on competition. When animals compete with each other
43 for resources, they often evolve to avoid each other by specializing to use different resources or separating their
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44 activity in other ways. To test hypotheses about how competition shapes rest-activity rhythms, we performed
45 computer simulations of a community of animals who move, reproduce, and compete for resources. We show
46 that biological rhythms let two species divide time so that one species is active while its competitor is resting,
47 thus avoiding depleting shared resources. When a species has no competitors in the simulation, competition
48 between members of the same species cause population and individual rhythms to decrease, since resource
49 availability is low when everybody is active at the same time. However, having competitors allows strong
50 rhythms to evolve from originally arrhythmic organisms. Competition can even cause a single population to split
51 into two species which are separated in time. In summary, these results suggest that competition is a strong
52 factor promoting rest-activity rhythms.
53
54 Introduction
55 An ecological niche is the particular “space” a species occupies in an ecosystem, comprising a diversity of
56 concepts including the physical environment where it lives, the resources it uses, its interactions with other
57 species, and the adaptations it has evolved to exploit the niche. Both theory and evidence indicate that
58 competition is a major factor which determines species’ niches [1,2]. Competitors for a resource generally will
59 adjust to avoid each other, differentiating their niches by adapting to utilize different types of resources, thus
60 avoiding the depletion of shared resources (exploitative competition) [3] as well as costly acts of aggression and
61 territorial exclusion (interference competition) [4].
62 Time is one dimension which defines a niche. Most species live in environments dominated by a day-night
63 cycle and a seasonal cycle, though other cycles such as tides can also strongly define an ecosystem [5]. A
64 temporal niche is defined by both abiotic elements such as light intensity and temperature [6,7], as well the as
65 by predictable temporal patterns of other organisms [8]. Adaptions for a specific temporal niche include for
66 example specializations in vision, coat color, temperature regulation, and importantly, biological rhythms, i.e.
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67 physiological and behavioral traits which cycle regularly according to an internal biological clock . In this article,
68 we consider activity rhythms through the lens of ecological niche theory, viewing them as a way partition niches
69 among competitors and examining how competition shapes the expression of these biological clocks. Time can
70 be thus viewed as a sort of resource or space which is partitioned by organisms in response to competition [9],
71 both interspecific (between different species) and intraspecific (between members of the same species) [10].
72 While some work has examined predation’s effect on animals’ activity rhythms [11–13], the role of competition
73 has been less examined.
74 A variety of field studies have observed evidence of temporal partitioning between putative competitors.
75 For example, a community of three sympatric species of insectivorous bats were observed to have activity
76 profiles which are displaced from each other, suggesting that they avoid each other [14]. While Argentinian
77 pampas foxes are normally nocturnal, they show a modified half-nocturnal half-diurnal profile in a region where
78 they overlap with crab-eating foxes [15]. Other examples of apparent temporal partitioning have been seen at
79 watering holes [16,17], in desert gerbils [18], carabid beetles [19], and large African carnivores [20]. Stronger
80 evidence comes from semi-natural manipulation experiments. Common spiny mice are nocturnal and golden
81 spiny mice are diurnal in areas where the two species coexist, but when the common spiny mice are
82 experimentally removed, the originally diurnal golden spiny mice shift into nocturnality, suggesting that this
83 species was pushed into diurnality by the competing species [9]. It should be recognized that these examples all
84 occur at the behavioral and ecological time scale, i.e. they are “temporary” displacements from the species’
85 genetically determined preferred activity time. Although certain pairs of taxa are suggestive of evolutionary-
86 level temporal partitioning—nocturnal owls and diurnal hawks, for instance, or the hypothesized nocturnal
87 origin of mammals [21]—the role of competition in causing these evolutionary divergences is near impossible to
88 establish conclusively. Nonetheless, it is probable that temporal shifts at the behavioral/ecological level cause
89 selection for alleles suited for the new time period, eventually translating into long-term changes at the
90 genetic/evolutionary level.
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91 In this work, we explore ways which competition in ecological niche theory can be applied to biological
92 rhythms, using simulation of a community of two species who compete for limited resources in an environment.
93 We first demonstrate that circadian rhythms are a form of niche differentiation which allows two species to
94 stably coexist without competitive exclusion, and that two rhythmic species will quickly differentiate their
95 circadian phases to avoid competition. We show that arrhythmicity is preferred when there is no interspecific
96 competitor present, but the presence of interspecific competition greatly facilitates the development of strong
97 activity rhythms. Finally, we show that if organisms have assortative mating based on circadian timing, then
98 intraspecific competition can drive the division of one population into two mating groups, contributing to
99 speciation.
100
101 Results
102 Briefly, we simulated a community of two species in an environment using Python. Each individual organism
103 has a circadian activity rhythm which is modeled as a cosine wave with two parameters: amplitude ranging from
104 0 to 1, and phase angle ranging from 0° to 360° (Fig 1). Resource input into the environment occurs at a constant
105 rate. If an individual encounters a resource, it consumes that resource and gains energy, which is in turn used for
106 movement and basal metabolism. Death occurs if an individual’s energy drops to zero or if the individual reaches
107 an age limit. Organisms reproduce sexually, and the probability of an individual reproducing is proportional to its
108 energy. During procreation, an offspring’s amplitude and phase are the means of the parents’ traits. When
109 testing the evolution of a trait, the offspring’s trait is the parents’ mean plus or minus a small random variance,
110 which naturally results in natural selection and evolution.
111
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112 Fig 1. Example activity rhythm profiles. Activity profiles are modeled as cosine waves with two properties,
113 amplitude and phase angle. Two example profiles are shown. In blue, the activity rhythm has amplitude = 1 and
114 phase angle = 0°. In orange, amplitude = 0.4 and phase angle = 90°. Regardless of changes in circadian
115 parameters, the number of moves per day is fixed at 20 (equivalent to the area under each curve).
116
117 Rhythmic activity prevents competitive exclusion
118 The competitive exclusion principle asserts that two species cannot occupy the same ecological niche
119 indefinitely; if two species exist in exactly the same niche, then one species will eventually outcompete the
120 other and become the sole occupier of the niche. We modeled this scenario by simulating two species with no
121 circadian rhythms, i.e. with amplitude = 0. The two species are constantly active at a moderate level and thus
122 have no differentiation of temporal niches. In this situation, one species invariably dies out (Fig 2A-B). If both
123 species are rhythmic (amplitude = 1) and are active at the same time of day (same phase angle), there is again
124 no niche differentiation, and one species will eventually die out (Fig 2C-D). However, if both species are rhythmic
125 but are active during opposite times of day, then both species are likely to continue existing (Fig 2E-F). In 2 of
126 the 40 trials of this scenario, one species died out after some time, demonstrating that random fluctuations can
127 still cause a species to disappear. In the remaining 38 trials, both species survived at the end of 2000 days.
128
129 Fig 2. Circadian rhythms prevent competitive exclusion. (A) When two species with no activity rhythms
130 (amplitude = 0) are placed in the environment, one species will always die out. An example of an individual trial
131 is displayed. (B) Summary of 40 trials. Since the two species’ population levels tend to be symmetric, only the
132 species which is excluded is plotted for clarity. The trials were sorted by the day that competitive exclusion is
133 reached, and the median (20th) trial is represented by the dark line, while the 4th, 12th, 28th, and 36th trials are
134 represented by faint lines. (C) When two species have circadian rhythms (amplitude = 1) and are active at the
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135 same time of day, one species will always die out, as before. Example individual trial. (D) Summary of 40 trials.
136 (E) When two species have circadian rhythms are active 180° out of phase, the two species can coexist
137 indefinitely. Example individual trial. (F) Summary of multiple trials. Since no species died out in this scenario,
138 five population profiles were selected at random to be plotted.
139
140 Character displacement of phase-angle
141 Having showed that being active at opposite phase angles is favorable for the coexistence of two species, we
142 ask whether species can evolve over time to reach such a state of temporal separation. When two similar
143 species occupying similar niches are found in the same geographical area, the differences between them tend to
144 become accentuated in order to distinguish their niches, in a phenomenon known as character displacement
145 [22]. We tested whether two circadian-rhythmic species would display character displacement on a temporal
146 axis. In this scenario, all individuals started at approximately at the same phase angle at the beginning of the
147 simulation, and the offspring’s phase angles were allowed to vary and thus evolve, while amplitudes were fixed
148 at 1.
149 The two species’ phase angles of activity did indeed diverge over time in the simulation (Fig 3A). After
150 starting at 0° separation, the phase-angle difference between the two species grew and eventually reached the
151 maximum of 180° and remained so thereafter (Fig 3B). The source of selective pressure is the difference in
152 resource availability between peak and peak-adjacent times (Fig 3C). During times of peak activity, available
153 resources are quickly consumed and resource density is thus very low, while in times adjacent to the peak, less
154 resources are consumed, and resource density is higher. The result of this time-resource gradient is that
155 individuals whose phase angles are at the edges of the population distribution have access to a more resource-
156 dense environment and thus gain more energy (Fig 3D). Since stored energy is proportional to reproduction
157 probability, the individuals at distribution’s edges reproduce more, and the species’ mean phase angle is shifted.
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158
159 Fig 3. Character displacement of circadian phase. (A) Circular histogram displaying the separation of phase
160 angles of activity in two species over time in one trial. The difference in the two species’ phase angles quickly
161 diverges to 180°. (B) Summary of 40 trials. Trials were sorted by days until a phase difference of 150° was
162 reached; the median 20th trial is plotted in a dark line, while the 4th, 12th, 28th, and 36th trials are plotted in faint
163 lines. (C) When the two species are at similar phase angles of entrainment, there is a large difference in total
164 resources in the environment during different times of day. When the two species are separated in phase, there
165 is no longer a predictable cycle in resource availability. (D) Scatterplot of organisms’ stored energy vs their phase
166 angle of entrainment relative to the population mean. The parabolic best fit line is shown in red. Individuals at
167 the edges of the population phase distribution acquire more energy and consequently are more likely to
168 reproduce.
169
170 Intraspecific competition causes temporal niche expansion by arrhythmicity D
171 Previous work has shown that when interspecific competition is absent, the population’s niche width tends
172 to expand, as competition within the species pushes individuals to exploit a greater range of resources [23]. We
173 tested if this pattern would be true in this model. Indeed, when rhythmic amplitude was allowed to vary, the
174 amplitdue steadily decreased to near-zero levels, representing the transition from a temporal specialist to a
175 generalist strategy. To clarify, a broad circadian niche does not necessarily imply the absence of sleep or sleep-
176 like rest; these organisms could follow a cathemeral pattern in which sleep is scattered throughout the day.
177 However, other factors may prevent dampening of rhythms. To adapt to a temporal niche, organisms do not
178 only develop activity rhythms but additional morphological and physiological specializations as well, such as in
179 vision, temperature regulation, and non-locomotor circadian rhythms [9,24]. These adaptations allow an animal
180 to acquire more resources per unit energy expenditure during their specialized “on” phase, but often at the cost
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181 of being less efficient during their “off” phase. A temporally specialized organism would thus incur costs when
182 adopting a generalist activity rhythm. To model these temporal adaptations, we added a specialization term to
183 the simulation. The degree of specialization over the day follows a cosine wave such that at specialization = 0.1,
184 an animal acquires an additional 10% energy from consuming a resource during the peak and 10% less energy
185 during the trough. For simplicity, we assume that the phase angle of the specialization wave matches exactly
186 that of the cosine wave of circadian activity, as opposed to modeling them as separate phenotypes, which would
187 naturally converge to match phase angles anyways so that organisms are most specialized when they are most
188 active.
189 We found that specialization must be quite high to overcome competition’s negative selection for amplitude
190 (Fig 4). At low levels of specialization, the equilibrium amplitude is positively correlated with the degree of
191 specialization. Only when specialization is at least 0.75 does the resulting amplitude approach 1 (Fig 4C). This is
192 rather intense specialization, indicating that resource acquisition is 7 times more efficient during the peak than
193 during the trough. This suggests that, in an environment where resource availability is roughly constant
194 throughout the day, intraspecific competition is a strong factor selecting for arrhythmicity.
195 When a population is freed from competition, the following niche expansion could occur through increasing
196 the niche width within individuals, or through increasing the variance in between individuals who are still
197 relatively specialized . Whereas low rhythmic amplitude represents within-individual niche expansion, we also
198 observed between-individual niche expansion, represented the greater range of phase angles when amplitude is
199 high (Fig 4D). When amplitude is low, there is no selective pressure to promote interindividual variance, so
200 sexual reproduction pulls the population towards the mean.
201
202 Fig 4. Intraspecific competition selects for arrhythmicity. (A) Even with a positive specialization value,
203 amplitude is driven towards low levels when there is only one species. (B) Amplitude settles on an intermediate
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204 value when specialization = 0.4, demonstrating a positive correlation between specialization and resulting
205 amplitude. (C) In the single-species scenario, specialization must be set quite high at 0.75 for amplitude to reach
206 near 1. (D) Standard deviation of phase angle as a function of amplitude. This illustrates an inverse relationship
207 between expanded interindividual niche width (high phase angle variance) and expanded intraindividual niche
208 width (low amplitude).
209
210 Intraspecific competition allows rhythmicity to develop
211 While intraspecific competition acts to prevent rhythmicity, we asked if a competitor species would cause
212 rhythmicity to develop. When specialization = 0, organisms did not show a trend towards either high or low
213 rhythmicity (Fig 5A). Since the two species’ activity rhythms were in approximately opposite phase and similar
214 amplitude, the summed activity of all individuals in the environment was approximately constant throughout
215 the day, which in turn caused resource availability to be approximately constant. This situation is much like the
216 final condition of Fig 3A and Fig 3C. With no time-resource graident, there is no evolutionary pressure for
217 rhythmicity to evolve.
218 While interspecific competition alone does not positively select for amplitude, it also effectively neutralizes
219 intraspecific competition’s negative selection for amplitude. In this state, if the organisms have even a small
220 degree of specialization, it can drive amplitude to increase steadily over time in both species (Fig 5B), with
221 higher specialization values causing amplitude to increase more quickly. Whereas a specialization value of 0.1
222 causes amplitude rise to 1 when there are two species, amplitude barely rises when there is only one species
223 (Fig 4A), and a specialization value as extreme as 0.75 is needed to raise amplitude to the levels seen in the two
224 species scenario (Fig 4C).
225 The amplitudes of the two species tended to be correlated (Fig 5A-B). The correlation of the two species’
226 amplitudes can be explained by the fact that a chance increase in amplitude in one species causes a resource
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227 density difference in time, which encourages the other species to increase their amplitude due to interspecific
228 competition and the first species to decrease their amplitude due to intraspecific competition.
229 The relative strength of interspecific and intraspecific competition influences the equilibrium amplitude of
230 each species. To simulate asymmetric populations, we defined a target population ratio, and the populations
231 were stabilized around this ratio by automatically adjusting their reproduction rate. When species A is set to be
232 two times as numerous as species B, species B develops high rhythmicity while species A’s amplitude hovers
233 around 0.7 (Fig 5C). If species A is set to be nine times as numerous as species B, species A’s amplitude remains
234 only at 0.2, demonstrating that intraspecific rather than interspecific competition is the much stronger force in
235 determining its equilibrium amplitude. This also demonstrates that a dominant species which has even mild
236 rhythms can strongly determine the rhythms of minor competitors which have smaller populations. In total,
237 these results suggest that the presence of competitors is a strong factor promoting the expression of biological
238 rhythms.
239
240 Fig 5. Interspecific competition with specialization allows development of biological rhythms. (A) With two
241 species, amplitude drifts randomly without pressure towards either 0 or 1. (B) When a specialization value is
242 added to the model, amplitudes rise steadily over time. (C) The final equilibrium amplitudes depend on relative
243 population numbers. When the blue species is twice as numerous as the orange, its final amplitude remains
244 lower than the orange’s. (D) When the blue species is nine times as numerous as the orange, blue’s amplitude
245 remains low while orange’s is high.
246
247 Population splitting by differentiation of phase
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248 The single-species scenario illustrated that intraspecific competition causes expansions in both within-
249 individual and between-individual niche widths. Could an increase in between-individual variation cause the
250 population to split into two distinct groups? This would in effect cause speciation, or at least contribute strongly
251 to the ecological divergence and reproductive isolation which are precursors to full speciation. To test this,
252 assortative mating was introduced to the model. Individuals only mate with a partner whose phase differs by
253 less than 9 hours (135°), and the probability of choosing a given partner increases linearly as the phase
254 difference decreases to zero. Amplitudes were fixed at 1 for this test.
255 We found that, with the addition of assortative mating, the population did indeed segregate into two groups
256 (Fig 6A). We defined a cross-group mating value (CGM) to quantify reproductive isolation, where low CGM
257 indicates high reproductive isolation. The CGM tended to stay constant for some time and then drop suddenly
258 (Fig 6B). This suggests that there is a threshold effect, such that once the conditions occur for a secondary
259 population to escape “gene flow” with the main population, full reproductive isolation quickly follows. To
260 separate from the main population, there must be enough individuals at the far edges of the phase distribution
261 to sustain a “breeding population”, such that a tipping point is reached where individuals in the incipient
262 secondary population become more likely to breed within its own population rather than the main population.
263 Once this tipping point is reached, the secondary population quickly splits off from the main group. Given the
264 random nature of mate selection and progeny’s phase variance in our model, the conditions where this happens
265 occurs stochastically, explaining the large variance in speciation time in the simulations.
266
267 Fig 6. Population splitting by phase. A) Circular histograms showing distributions of phase angles of
268 entrainment in one trial. On day 340, The population was a single mating group (cross-group mating = 0.67). On
269 day 580, the population is in the process of splitting into two mating groups (CGM = 0.38). By day 630, there are
270 two populations which are almost completely reproductively isolated (CGM = 0.05). B) Summary of 40 trials.
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271 Trials were sorted by days to reach CGM < 0.1; the 20th trial is plotted in dark blue, while the 4th, 12th, 28th, and
272 36th trials are plotted in light blue.
273
274 Population splitting was not guaranteed for all parameter settings. Conditions necessary to achieve
275 speciation in this model are somewhat constrained, which is unsurprising given the high barriers to sympatric
276 speciation in nature [25]. The time-resource gradient must be quite strong to reach the necessary levels of
277 density-dependent disruptive selection, and thus population splitting will not occur for low resource
278 regeneration rates or low population levels. A smaller mating window of course also promotes reproductive
279 isolation. Higher variance in offsprings’ phases also promotes reproductive isolation by increasing the chance of
280 a breakaway group to escape “gene flow” with the rest of the population. A long lifespan also favors speciation,
281 since individuals at the edges of the distribution then have more time to build up an energy surplus.
282
283 Population splitting vs. individual expansion. Intraindividual niche expansion will tend to oppose speciation,
284 since a decrease of rhythmic amplitude would weaken the time-resource gradient and broaden mating
285 windows. Conversely, speciation into two populations occupying opposite niches will remove selective pressure
286 for broad individual niches since the time-resource gradient would be erased (analogous to the last case in Fig
287 3C). Faced with intraspecific competition, which of these two mutually exclusive paths will a population take?
288 Results suggest that it depends heavily on the relative flexibility of the amplitude or phase traits. We set
289 standard deviations of phase angle and amplitude to various test values, with a higher standard deviation
290 resulting in quicker evolution of that trait. When phase standard deviation was high and amplitude standard
291 deviation was low, populations were more likely to speciate; conversely, when phase standard deviation was
292 low and amplitude standard deviation was high, populations tended to become arrhythmic (Table 1).
293
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294 Table 1. Number of trials achieving speciation depend on the variances of amplitude versus phase angle.
Amplitude standard deviation
0.02 0.03 0.04 0.05
0.04 10/20 0/20 0/20 0/20
Phase standard 0.045 20/20 14/20 9/20 5/20
deviation 0.05 20/20 20/20 17/20 12/20
0.055 20/20 20/20 20/20 17/20
295
296
297 Discussion
298 This is the first modeling study to examine the ecological pressures which favor the evolution of biological
299 rhythms. While other modeling studies have examined the “internal” forces which make rhythms and sleep
300 physiologically efficient [26–28], none have looked at the “external” forces of the environment.
301
302 Timescales of analysis
303 Though we framed our model in terms of organisms evolving genotypically over time, niche partitioning can
304 equally occur at the timescale of individual behavior or ecological community [29], and the conclusions of this
305 study can easily be generalized to sub-evolutionary timescales and mechanisms. Many animals are known to
306 switch their temporal niches depending on various environmental factors [24]; for example, the aforementioned
307 studies on minks, spiny mice [30], and foxes [15] demonstrate temporal partitioning at the sub-evolutionary
308 level. Indeed, every clear observation of competition’s effect on temporal niches has occurred at the
309 behavioral/ecological level, and inferring the role of competition in a species’ evolution is difficult if not
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310 impossible, since those historical interspecies interactions are unobservable. However, if temporal displacement
311 continues for an extended time, it seems likely that organisms would eventually evolve to match their internal
312 clock with their expressed behavior. Research on the health consequences of misalignment between the
313 circadian clock and activity rhythms [7,31,32] suggest clear selective mechanisms by which behavioral
314 displacements can translate into genetic/evolutionary changes.
315 The simulation was framed in terms of circadian rhythms, but the results could equally apply to seasonal
316 rhythms. A major difference between the daily and seasonal timescales is that individuals can adjust their daily
317 behavior to a new time through non-genetic mechanisms, whereas this is probably less common at longer
318 timescales, though it certainly depends heavily on the particular mechanisms governing these rhythms.
319
320 Competitive exclusion and character displacement
321 In our model, we demonstrated that competitive exclusion is unavoidable if two species share an
322 ecological niche. Two species which are temporally separated are much more likely to coexist for extended
323 periods of time. Additionally, we show that two circadian-rhythmic species which initially are active at the same
324 phase evolve to be active at opposite times of day in order to avoid competition for resources. The most likely
325 direct natural analog of this scenario is the introduction of a new species to a region already occupied by
326 another similar species. This could happen, for example, through the breakdown of geographical barriers,
327 chance migration to a new area [33], introduction by humans, or climate change-induced range shifts [34]. The
328 invasive American mink in the United Kingdom offers a good real-life example: originally nocturnal when first
329 introduced, the mink largely switched to diurnality when the native otters and polecats recovered their
330 population levels [35]. The previously mentioned studies in Argentinian foxes [15] and desert spiny mice [9] also
331 demonstrate niche switching.
15 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
332
333 Intraspecific competition and niche expansion
334 Intraspecific competition is hypothesized to increase the niche width in a population, especially in
335 environments where a population is released from competition from other species, which could occur after
336 migration or introduction to a new region, for instance [36,37]. The single-species simulations demonstrate this
337 phenomenon for temporal niches.
338 Niche expansion can happen either by increasing the variance of resource type usage between individuals
339 [38,39] or by increasing the range of resource usage of each individual [40]. Interindividual expansion appears to
340 be the more common pattern in nature in general [41], especially if intraindividual generalization has associated
341 costs [23]. Our single-species simulation displayed both interindividual variation, visible as a broadened phase-
342 angle distribution, and intraindividual generalization, visible as flattened amplitude. The model’s design does not
343 allow for very extreme interindividual expansion, since activity timing was determined strictly by genetics and
344 not by individuals’ behavioral adjustments, and sexual reproduction tended to pull genotypes towards the
345 population mean. Programming a non-genetic behavioral component may be interesting for future studies.
346 A few studies in fish have observed offset patterns of diel feeding activity between individuals, with larger
347 dominant individuals feed at preferred times while subordinates being pushed to other times [13,42]. This
348 suggests that preexisting heterogeneities in the population such as social dominance could predispose niche
349 expansion to occur between rather than within individuals. We are aware of only one study to observe temporal
350 niche expansion in the wild; American minks which were introduced to a remote island with no competitors
351 were observed to have expanded temporal niches compared to their mainland counterparts [43]; it is unknown
352 whether this was due more inter- or intraindividual expansion. Intraspecific competition is likely to also play a
353 role in instances of niche expansion after release from predation [11]. Predator-free space may be seen as a
354 type of resource, which becomes more abundant after removal of the predator. Though never specifically
16 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
355 examined, it is reasonable to suspect that intraspecific competition could then drive the subsequent niche
356 expansion observed after predator release.
357 Arrhythmic/cathemeral activity patterns appear to be somewhat common [44,45]. However, besides the
358 aforementioned observation of invasive minks [43], there have not been any other experiments or observations
359 to directly test competition’s role in causing temporal niche expansion. We suggest that this phenomenon is not
360 uncommon and may explain the behavior and evolution of a number of these arrhythmic animals.
361
362 Competition facilitates emergence of rhythms
363 The presence of an interspecific competitor erases the advantage that arrhythmicity in had in a single-
364 species scenario. A small amount of time-of-day specialization (theoretically, any amount of specialization) can
365 then cause organisms to evolve high amplitudes. We only modeled exploitative competition here, where fitness
366 differences were only driven by differential access to resources. If interference competition were also present,
367 for example if a cost was incurred every time an individual encountered an allospecific, then development of
368 rhythmic amplitude would most likely occur even more quickly.
369 As previously mentioned, the comparison between invasive minks on an island and mainland minks is an
370 instance of apparent competition-mediated niche expansion/contraction [43], but we are not aware of any
371 studies which has observed competition inducing increased amplitude. Again, we believe this phenomenon does
372 exist broadly, but has simply not been observed yet. Another potential real-life analog is if two arrhythmic
373 species existing in a constant environment—cave-dwelling fishes for example [46]—are suddenly exposed to a
374 cycling environment and are thus pushed to temporally differentiate.
375
376 Speciation
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377 When individuals were limited to mating with other individuals who were active at similar times of day,
378 intraspecific competition could cause a single population to separate into two groups which were largely
379 reproductively isolated, in effect causing speciation. This is specifically a case of sympatric speciation, in which
380 new species arise without geographic separation. Speciation required high levels of density-dependent selection
381 (i.e. a strong time-resource gradient) to occur. This is not surprising given that sympatric speciation in general is
382 believed to be quite difficult to achieve in nature, such that its existence at all was questioned before recent
383 decades [25]. A theoretical problem against sympatric speciation is that the phenotype which improves fitness
384 usually has no effect on mate choice, and thus even when disruptive selection exists, there is no mechanism for
385 it to translate to mating preferences. However, speciation by time (allochronic speciation) has an advantage
386 here because it is a “magic” trait [47], i.e. it has fitness effects which are acted on by natural selection, and it is
387 also directly responsible for assortative mating.
388 A recent review [48] finds good evidence for dozens of allochronic speciation events, with most cases
389 occurring at the seasonal rather than the circadian timespan, but although intraspecific competition is known to
390 play a role in promoting speciation in general [49,50], it is unclear how important intraspecific competition was
391 in these specific cases of allochronic speciation. In a study of Madeiran storm petrels, the authors hypothesize
392 that competition for food and nest space may have led to allochronic separation into hot- and cool-season
393 breeding populations [51]. Besides competition, allochronic speciation can occur by other reasons too, such as
394 temporal isolation [52], environmental changes [53], or a founder effect [54]; temporal separation can also be
395 secondary to another adaptation [55] or serve to reinforce reproductive isolation. Intraspecific competition can
396 act alongside these other mechanisms to produce allochronic speciation.
397
398 Sleep
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399 The question of why sleep exists is one of the big questions of biology. Traditionally framed something of a
400 paradox that an animal would abandon motor and sensory activity for several hours per day, it is perhaps not so
401 mysterious after all when considering that temporal niches exist. External pressures, whether they be
402 competition or other environmental forces, push animals to specialize for a time of day. Internal pressures, such
403 as energy conservation [56], the need to perform restorative functions, and the separation or coordination of
404 clashing or synergistic physiological processes [27,28,32], also encourage the evolution of sleep (or at least a rest
405 period). Especially with external and internal pressures combined, sleep/rest appears to be an unsurprising
406 evolutionary consequence. Stated colloquially, “if I can’t be active right now, then I might as well rest. If rest is
407 efficient, then I might as well do it when I can’t be active.”
408 As to why a defined sleep state exists rather than simply circadian-mediated inactivity, we propose that true
409 sleep can be viewed as an adaptation to delay rest. Urgent circumstances sometimes interrupt an animal’s
410 regularly scheduled rest, and thus the defining feature of true sleep, sleep homeostasis (“sleepiness”),
411 encourages animals to later pay back the lost rest. Another feature of true sleep is that it is a relatively distinct
412 mode with a well-defined sleep-wake boundary. In unpredictable environments, such a clear distinction allows
413 animals to maximize rest when the opportunity is available, rather than a slow transition between rest and
414 sleep.
415
416 Methodology and future directions
417 We intentionally created a model without distinct day and night phases, so that it would be more
418 generalizable to a variety of hypothetical conditions. Nevertheless, for most organisms, the changes between
419 day and night represent a major division in the environment [44], and thus alternative models may explicitly
420 include this. Activity patterns other than cosine waves, or testing the variable of daily total activity, could also be
421 interesting.
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422 We decided not to use a genetic model of circadian rhythms, opting instead to model only phenotypes with
423 a constant distribution. We do not believe this is a weakness because it is more or less equivalent to a situation
424 of polygenic inheritance with many genes. However, a genetic model may have some advantages such as
425 allowing a clearer look at population genetics. Additional models have been developed to explain the theoretical
426 benefits of sleep and circadian rhythms from the point of view of internal physiological organization [27,28], and
427 it could be interesting to integrate models of these “internal” benefits of rhythms with the “external” ecological
428 benefits modeled here.
429 Many questions regarding this topic remain open for investigation. Among the many possible axes by which
430 competing species can differentiate, what promotes partitioning of time over partitioning of other resources?
431 How does competition interact with other forces, like predation, to influence rhythms? To what extent does
432 competition shape activity rhythms in nature? In addition to additional field studies, well-designed experiments
433 with lab rodents could even help us understand the circumstances in which activity rhythms are modified by
434 competition.
435
436 Methods
437 Environment and organisms
438 Using Python, we simulated communities of organisms existing in an environment consisting of 60 spaces,
439 where each space may contain a resource, contain an individual organism, contain multiple individuals, or be
440 empty. An individual moves by jumping to another random space, and if it moves to a space which contains a
441 resource, the resource is consumed.
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442 600 resources per day are added randomly to the spaces of the environment at a constant rate. These
443 resources can represent food but can also represent resources in general including water, territory, and the
444 access to those resources.
445 An organism’s amount of movement varies across the day following a circadian activity rhythm, which is
446 modeled as a cosine wave with two parameters: amplitude, ranging from 0 to 1, and phase angle, ranging from
447 0° to 360° (Fig 1). The number of moves performed between times t0 and t1 is:
푡1푀푡표푡푎푙 448 푚 = (1 + a ∗ cos (푡 + 휃))푑푡 ∫ 360° 푡0
449 where m is the number of moves, Mtotal is the total number of moves per day = 20, a is the amplitude, and θ is
450 the phase angle. Moves were calculated in 10 timesteps per day (t1 - t0 = 36°). We believe a sinusoidal activity
451 rhythm is a reasonable approximation, and a more flexible activity pattern would in fact make temporal
452 segregation easier to achieve. Though an animal’s activity profile varies according to its circadian rhythm
453 parameters, the total number of moves is fixed at 20 moves per day; we hold total movement and energy
454 expenditure constant so that the primary variable of interest is is the timing of movement. Each animal has the
455 capacity to store energy; 2 units of energy is expended per day for movement and metabolism, and 0.5 energy is
456 gained when the animal consumes a resource. Animals die if their energy reaches zero, or if they reach 12 days
457 of age. Values for arena size, energy expenditure, resource value, and death age are somewhat arbitrary, and
458 were chosen at reasonable numbers which limited computational load.
459
460 Reproduction
461 Depending on the scenario, simulations are run either with one or two species in the environment.
462 Throughout the day at a constant rate, pairs of animals belonging to the same species are randomly chosen to
463 mate. The probability of an individual being chosen for mating is proportional its energy; animals which have
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464 acquired more energy thus tend to have better fitness. During each mating, one offspring is produced, to whom
465 each parent donates 1/3 of its energy. In some scenarios, the circadian amplitude and phase of all animals
466 remain fixed at the same values, while in other scenarios, there is variation in the circadian parameters, which
467 are acted on by natural selection to cause evolution. In the case of variable parameters, the child’s amplitude is
468 the mean of the parents’ ± 0.04 SD, and the child’s phase angle is the circular mean of the parents’ ± 0.04*360°
469 SD. Matings occur at a frequency such that the population of animals would increase by 10% each day if no
470 animals died. In our two-species simulation scenarios, when not testing competitive exclusion, we stabilized the
471 population levels so that random population fluctuations would not cause one species to disappear by chance.
472 For this, a target population ratio was set (usually 1:1), and the species with a population below target
473 reproduces slightly more, and the species with a higher population reproduces slightly less, proportional to the
474 difference in population.
푃푡표푡푎푙 475 푟 = 푟 ∗ 푘 ∗ 푎푑푗. 푝
476 For each species, radj. is the adjusted population growth rate, which depends on the default growth rate r = 0.1, k
477 the target fraction of the population which is composed of this species (k = 0.5 for a 1:1 ratio), p the population
478 of the this species, and Ptotal the population of all species. The number of progeny in a timestep t0 to t1 is thus:
푡1 ‒ 푡0 479 푁 = 푝 ∗ 푟 ∗ 푝푟표푔푒푛푦 푎푑푗. 360°
480 Calculations were performed in 10 timesteps per day.
481
482 Assortative mating
483 To study speciation, the standard simulation parameters were modified to model assortative mating. We
484 assume that mating must occur in a 9-hour (135°) time window which is fixed relative to the organism’s overall
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485 phase angle of entrainment, and the probability of mating between two individuals is proportional to the
486 amount of overlap of their mating windows, ranging from 0 to 1. In other words, individuals which have a phase
487 difference of nine hours or more do not mate, and the probability of mating increases linearly as the phase
488 difference approaches zero. We define a “cross-group mating” metric to measure reproductive segregation in
489 the population. To calculate this, we first define an overlap matrix of mating windows, i.e. the matrix where
490 each cell Mij is the mating-window overlap between individuals i and j. K-means clustering is used on the overlap
491 matrix to define two clusters of individuals. The cross-group mating index is the mean of the overlap values
492 between individuals from different groups; this is equivalent to the probability that a given mating is between
493 different groups. Cross-group mating of 0 thus indicates complete reproductive isolation of two groups.
494
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615
616 Fig 1. Example activity rhythm profiles. Activity profiles are modeled as cosine waves with properties amplitude
617 and phase angle. Two example profiles are shown. In blue, the activity rhythm has amplitude = 1 and phase
618 angle = 0°. In orange, amplitude = 0.4 and phase angle = 90°. Regardless of changes in circadian parameters, the
619 number of moves per day is fixed at 20 (equivalent to the area under each curve).
27 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
620
621 Fig 2. Circadian rhythms prevent competitive exclusion. (A) When two species with no activity rhythms
622 (amp.=0) are placed in the environment, one species will always die out. An example of an individual trial is
623 displayed. (B) Summary of 40 trials. Since the two species’ population levels tend to be symmetric, only the
624 species which is excluded is plotted for clarity. The trials were sorted by the day that competitive exclusion is
625 reached, and the median (20th) trial is represented by the dark line, while the 4th, 12th, 28th, and 36th trials are
626 represented by faint lines. (C) When two species have circadian rhythms (amp.=1) and are active at the same
627 phase, one species will always die out, as before. An example individual trial is displayed. (D) Summary of 40
628 trials. (E) When two species have circadian rhythms are active 180° out of phase, the two species can coexist
629 indefinitely. An example individual trial is displayed. (F) Summary of multiple trials. Since no species died out in
630 this scenario, five population profiles were selected at random to be plotted.
28 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
631
632 Fig 3. Character displacement of circadian phase. (A) Circular histogram displaying the separation of phase
633 angles of activity in two species over time in one trial. The difference in the two species’ phase angles of
634 entrainment quickly diverges to 180°. (B) Summary of 40 trials. Trials were sorted by days until a phase
635 difference of 150° was reached. The 20th trial is plotted in a dark line, while the 4th, 12th, 28th, and 36th trials are
636 plotted in faint lines. (C) When the two species are at similar phase angles of entrainment, there is a large
637 difference in total resources in the environment during different times of day. When the two species are
638 separated in phase, there is no longer a predictable cycle in resource availability. (D) Scatterplot of organisms’
639 stored energy vs their phase angle of entrainment relative to the population mean. The parabolic best fit line is
640 shown in red. Individuals at the edges of the population phase distribution acquire more energy and
641 consequently are more likely to mate.
29 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
642
643 644 Fig 4. Intraspecific competition selects for arrhythmicity. (A) Even with a positive specialization value,
645 amplitude is driven towards low levels when there is only one species. (B) Amplitude settles on an intermediate
646 value when specialization = 0.4, demonstrating a positive correlation between specialization and resulting
647 amplitude. (C) In the single-species scenario, specialization must be set quite high at 0.75 for amplitude to reach
648 near 1. (D) Standard deviation of phase angle as a function of amplitude. This illustrates an inverse relationship
649 between expanded interindividual niche width (high phase angle variance) and expanded intraindividual niche
650 width (low amplitude).
30 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
651
652 Fig 5. Interspecific competition with specialization allows development of biological rhythms. (A) With two
653 species, amplitude drifts randomly without pressure towards either 0 or 1. (B) When a specialization value is
654 added to the model, amplitudes rise steadily over time. (C) The final equilibrium amplitudes depend on relative
655 population numbers. When the blue species is twice as numerous as the orange, its final amplitude remains
656 lower than the orange’s. (D) When the blue species is nine times as numerous as the orange, blue’s amplitude
657 remains low while orange’s is high.
31 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
658
659 Fig 6. Population splitting by phase. (A) Circular histograms showing distributions of phase angles of
660 entrainment in one trial. On day 340, The population was a single mating group (cross-group mating = 0.67). On
661 day 580, the population is in the process of splitting into two mating groups (CGM = 0.38). By day 630, there are
662 two populations which are almost completely reproductively isolated (CGM = 0.05). (B) Summary of 40 trials.
663 Trials were sorted by days to reach CGM < 0.1; the 20th trial is plotted in dark blue, while the 4th, 12th, 28th, and
664 36th trials are plotted in light blue.
665
32 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
666 Supplementary information captions
667 S1 Dataset. Population sizes over time in competitive exclusion tests. Dataset for Fig 2. Sheets of the Excel file
668 are labeled A-C, and each sheet contains population levels of two species over 1200 days in 40 trials. (A)
669 Organisms have amplitude = 0. Dataset for Fig 2A. (B) Organisms have amplitude = 1, and the two species have
670 the same phase angle. Dataset for Fig 2B. (C) Organisms have amplitude = 1, and the species have a phase angle
671 difference of 180°. Dataset for Fig 2C.
672
673 S2 Dataset. Phase angles during character displacement. Dataset for Fig 3. Mean peak-activity phases for two
674 species over 400 days in 20 trials.
675
676 S3 Dataset. Amplitude of a single species over time. Dataset for Fig 4 A-C. Mean population amplitude for a
677 single species over 8000 days. 20 trials were performed for each of three specialization values: 0.1, 0.4, and
678 0.75.
679
680 S4 Dataset. Relationship between amplitude and phase variance. Dataset for Fig 4D. Amplitudes (representing
681 intraindividual niche expansion) were progressively stepped down from 0.99 to 0. For each amplitude increment
682 of 0.01, 500 samples of the standard deviation of phase angle (representing interindividual niche expansion)
683 were taken.
684
685 S5 Dataset. Amplitude of two species. Dataset for Fig 5 A-B. Sheets of the Excel file are labeled A-B, and each
686 sheet contains the mean population amplitudes of two species over 25000 days in 20 trials. (A) Specialization
33 bioRxiv preprint doi: https://doi.org/10.1101/2020.04.22.055160; this version posted April 22, 2020. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY 4.0 International license.
687 was set to 0, and target population ratio between the two species was set at 1:1. One trial was chosen for Fig
688 5A. (B) Specialization = 0.1, population ratio 1:1. One trial was chosen for Fig 5B.
689
690 S6 Dataset. Amplitude of two species with uneven populations. Dataset for Fig 5 C-D. (A) Specialization was set
691 to 0.1, and target population ratio between the two species was set at 2:1. One trial was chosen for Fig 5C. (B)
692 Specialization = 0.1, population ratio 9:1. One trial was chosen for Fig 5D.
693
694 S7 Dataset. Cross-group mating values during speciation. Dataset for Fig 6. Cross-group mating (CGM) values
695 over 1000 days in 40 trials.
696
697 S8 Dataset. Evolution of amplitude versus speciation. Dataset for Table 1. Amplitude and cross-group mating
698 (CGM) values over 1000 days. Each sheet of the Excel file contains 20 trials in one combination of amplitude
699 standard deviation and phase-angle standard deviation.
700
701 S9 code. Python script for the simulation.
34